********Welcome to Online IDE!! Happy Coding :)********** NOTE: Precision is limited to 19 digits wide... NOTE: Any decimal with recurring single digit(19 times) will be assumed to be periodic number NOTE: Since computational issues, reduction on decimal component EXCEEDING 9(9 digits) will lose its precision by 1 or more digit depending on the decimal. NOTE: Value of acceptedNumeratorLimit = 9 digits. This can be changed to speed up most reduced form calculations NOTE: Also to AVOID any Session kills or hanging To create sample of decimals and fractions, original numerator will be divided numerator/prime number from: 2 => 5 DENOMINATOR AND NUMERATOR WILL BOTH BE TRUNCATED INLINE WITH INTEGRITY ORIGINAL INPUTS ****************** is a prime number: 2 is a prime number: 3 is not a prime number: 4 is a prime number: 5 *** The Decimal presented: 5.2 The fraction part: 2 this is numerator: 2 this is denominator: 10 This is potential Greatest Common Factor(2) between Numerator(2) Denominator(10) Reduction numerator: (2,1 divisor: 2) Reduction denominator: (10,5 divisor: 2) Reduction in fraction and decimal: 2/10(0.2) => 1/5(0.2) Elapsed time in seconds to reduce fraction: 0.87903818 reduced numerator: 1 reduced denominator: 5 Fraction presented is: 26/5 No whole number before fraction Original whole number from fraction (numerator/denominator):5 remaining numerator: 1 remaining fraction: 1/5 Fraction provided in challenge is improper: 26/5 Mixed number fraction is: 5-1/5 1Mixed number fraction(5) and original decimal(5) have same whole number fraction provided in challenge is fully reduced: 1/5 Original fraction(1/5) provided is exact representation of the initial decimal conversion: 5.2 ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 26/2 Original numerator / PRIME number AS DECIMAL => 13.0 Original numerator / PRIME number AS FRACTION (not reduced) => 26/3 Original numerator / PRIME number AS DECIMAL => 8.666666666666666 Original numerator / PRIME number AS FRACTION (not reduced) => 26/5 Original numerator / PRIME number AS DECIMAL => 5.2 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(5) has prime factor (divisible by prime number of two or five) Original decimal:5.2 is a periodic number *** The Decimal presented: 7.1111111 The fraction part: 1111111 this is numerator: 1111111 this is denominator: 10000000 This is potential Greatest Common Factor(1111111) between Numerator(1111111) Denominator(10000000) Elapsed time in seconds to reduce fraction: 1.202937871 reduced numerator: 1111111 reduced denominator: 10000000 Fraction presented is: 22/1999 No whole number before fraction 1This is the difference(0.10010559724862432) between original(0.1111111) decimal and associated fraction(22/1999) in decimal(0.011005502751375688) 2Original fraction (22/1999) is non- representation of the initial decimal conversion: 0.1111111(1111111/10000000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 22/2 Original numerator / PRIME number AS DECIMAL => 11.0 Original numerator / PRIME number AS FRACTION (not reduced) => 22/3 Original numerator / PRIME number AS DECIMAL => 7.333333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 22/5 Original numerator / PRIME number AS DECIMAL => 4.4 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10000000) has prime factor (divisible by prime number of two or five) Original decimal:7.1111111 is a periodic number *** The Decimal presented: 0.192367 The fraction part: 192367 this is numerator: 192367 this is denominator: 1000000 This is potential Greatest Common Factor(192367) between Numerator(192367) Denominator(1000000) Elapsed time in seconds to reduce fraction: 0.303816441 reduced numerator: 192367 reduced denominator: 1000000 Fraction presented is: 64/9 No whole number before fraction Original whole number from fraction (numerator/denominator):7 remaining numerator: 1 remaining fraction: 1/9 Fraction provided in challenge is improper: 64/9 Mixed number fraction is: 7-1/9 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:7 Original decimal has following whole number:0 *********** 1Original fraction(64/9)has been changed to mixed number fraction(7-1/9) 1This is the difference(0.0812558888888889) between original(0.192367) decimal and associated fraction(1/9) in decimal(0.1111111111111111) 2Original fraction (1/9) is non- representation of the initial decimal conversion: 0.192367(192367/1000000) Original fraction(1/9) is NOT reduced identically to the converted decimal (most reduced form): (192367/1000000) 1Remaining fraction(1/9) is non- representation of the initial decimal conversion: 0.192367 1Remaining fraction (1/9) in decimal is 0.1111111111111111 and NOT:0.192367(original) 2This is the difference(0.0812558888888889) between original(0.192367) decimal and associated mixed number remaining fraction(1/9) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 64/2 Original numerator / PRIME number AS DECIMAL => 32.0 Original numerator / PRIME number AS FRACTION (not reduced) => 64/3 Original numerator / PRIME number AS DECIMAL => 21.333333333333332 Original numerator / PRIME number AS FRACTION (not reduced) => 64/5 Original numerator / PRIME number AS DECIMAL => 12.8 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(1000000) has prime factor (divisible by prime number of two or five) Original decimal:0.192367 is a periodic number *** The Decimal presented: 0.2228 The fraction part: 2228 this is numerator: 2228 this is denominator: 10000 This is potential Greatest Common Factor(2228) between Numerator(2228) Denominator(10000) Reduction numerator: (2228,1114 divisor: 2) Reduction denominator: (10000,5000 divisor: 2) Reduction in fraction and decimal: 2228/10000(0.2228) => 1114/5000(0.2228) Reduction numerator: (1114,557 divisor: 2) Reduction denominator: (5000,2500 divisor: 2) Reduction in fraction and decimal: 1114/5000(0.2228) => 557/2500(0.2228) Elapsed time in seconds to reduce fraction: 4.002E-4 reduced numerator: 557 reduced denominator: 2500 Fraction presented is: 5343/27775 No whole number before fraction 1This is the difference(0.03043276327632763) between original(0.2228) decimal and associated fraction(5343/27775) in decimal(0.19236723672367237) 2Original fraction (5343/27775) is non- representation of the initial decimal conversion: 0.2228(557/2500) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 5343/2 Original numerator / PRIME number AS DECIMAL => 2671.5 Original numerator / PRIME number AS FRACTION (not reduced) => 5343/3 Original numerator / PRIME number AS DECIMAL => 1781.0 Original numerator / PRIME number AS FRACTION (not reduced) => 5343/5 Original numerator / PRIME number AS DECIMAL => 1068.6 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(2500) has prime factor (divisible by prime number of two or five) Original decimal:0.2228 is a periodic number *** The Decimal presented: 0.777777777777778777 The fraction part: 777777777777778777 this is numerator: 777777777777778777 this is denominator: 1000000000000000000 6Numerator truncated from: 18 to 9 digits: 7Denominator truncated from 19 to 10 digits Truncated denominator: 1000000000 Truncated numerator: 777777777 2Single digit recurring:false 2THIS IS THE REGEX TO CHECK FOR POORLY DIVISIBLE NUMERATORS :777777777 THIS IS THE numerator:777777777 3Numerator truncated to: 8 digits (77777777) to mitigate resource limitations of recurrence 9 times (1,3,7,9) 4Denominator truncated to: 9 digits(100000000)inline with numerator This is potential Greatest Common Factor(77777777) between Numerator(77777777) Denominator(100000000) Elapsed time in seconds to reduce fraction: 14.55571082 reduced numerator: 77777777 reduced denominator: 100000000 Fraction presented is: 222/100 No whole number before fraction Original whole number from fraction (numerator/denominator):2 remaining numerator: 22 remaining fraction: 22/100 Fraction provided in challenge is improper: 222/100 Mixed number fraction is: 2-22/100 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:2 Original decimal has following whole number:0 *********** 1Original fraction(222/100)has been changed to mixed number fraction(2-22/100) 1This is the difference(0.5577777777777788) between original(0.777777777777778777) decimal and associated fraction(22/100) in decimal(0.22) 2Original fraction (22/100) is non- representation of the initial decimal conversion: 0.777777777777778777(77777777/100000000) Original fraction(22/100) is NOT reduced identically to the converted decimal (most reduced form): (77777777/100000000) 1Remaining fraction(22/100) is non- representation of the initial decimal conversion: 0.777777777777778777 1Remaining fraction (22/100) in decimal is 0.22 and NOT:0.777777777777778777(original) 2This is the difference(0.5577777777777788) between original(0.777777777777778777) decimal and associated mixed number remaining fraction(22/100) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 222/2 Original numerator / PRIME number AS DECIMAL => 111.0 Original numerator / PRIME number AS FRACTION (not reduced) => 222/3 Original numerator / PRIME number AS DECIMAL => 74.0 Original numerator / PRIME number AS FRACTION (not reduced) => 222/5 Original numerator / PRIME number AS DECIMAL => 44.4 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(100000000) has prime factor (divisible by prime number of two or five) Original decimal:0.777777777777778777 is a periodic number *** The Decimal presented: 3.14857 The fraction part: 14857 this is numerator: 14857 this is denominator: 100000 This is potential Greatest Common Factor(14857) between Numerator(14857) Denominator(100000) Elapsed time in seconds to reduce fraction: 4.88239E-4 reduced numerator: 14857 reduced denominator: 100000 Fraction presented is: 987000200/100000020 No whole number before fraction Original whole number from fraction (numerator/denominator):9 remaining numerator: 87000020 remaining fraction: 87000020/100000020 Fraction provided in challenge is improper: 987000200/100000020 Mixed number fraction is: 9-87000020/100000020 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:9 Original decimal has following whole number:3 *********** 1Original fraction(987000200/100000020)has been changed to mixed number fraction(9-87000020/100000020) 1This is the difference(0.7214300259999948) between original(0.14857) decimal and associated fraction(87000020/100000020) in decimal(0.8700000259999948) 2Original fraction (87000020/100000020) is non- representation of the initial decimal conversion: 0.14857(14857/100000) 1Remaining fraction(87000020/100000020) is non- representation of the initial decimal conversion: 0.14857 1Remaining fraction (87000020/100000020) in decimal is 0.8700000259999948 and NOT:0.14857(original) 2This is the difference(0.7214300259999948) between original(0.14857) decimal and associated mixed number remaining fraction(87000020/100000020) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 987000200/2 Original numerator / PRIME number AS DECIMAL => 4.935001E8 Original numerator / PRIME number AS FRACTION (not reduced) => 987000200/3 Original numerator / PRIME number AS DECIMAL => 3.290000666666667E8 Original numerator / PRIME number AS FRACTION (not reduced) => 987000200/5 Original numerator / PRIME number AS DECIMAL => 1.9740004E8 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(100000) has prime factor (divisible by prime number of two or five) Original decimal:3.14857 is a periodic number *** The Decimal presented: 0.6 The fraction part: 6 this is numerator: 6 this is denominator: 10 This is potential Greatest Common Factor(6) between Numerator(6) Denominator(10) Reduction numerator: (6,3 divisor: 2) Reduction denominator: (10,5 divisor: 2) Reduction in fraction and decimal: 6/10(0.6) => 3/5(0.6) Elapsed time in seconds to reduce fraction: 0.004974285 reduced numerator: 3 reduced denominator: 5 Fraction presented is: 22/7 No whole number before fraction Original whole number from fraction (numerator/denominator):3 remaining numerator: 1 remaining fraction: 1/7 Fraction provided in challenge is improper: 22/7 Mixed number fraction is: 3-1/7 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:3 Original decimal has following whole number:0 *********** 1Original fraction(22/7)has been changed to mixed number fraction(3-1/7) 1This is the difference(0.45714285714285713) between original(0.6) decimal and associated fraction(1/7) in decimal(0.14285714285714285) 2Original fraction (1/7) is non- representation of the initial decimal conversion: 0.6(3/5) Original fraction(1/7) is NOT reduced identically to the converted decimal (most reduced form): (3/5) 1Remaining fraction(1/7) is non- representation of the initial decimal conversion: 0.6 1Remaining fraction (1/7) in decimal is 0.14285714285714285 and NOT:0.6(original) 2This is the difference(0.45714285714285713) between original(0.6) decimal and associated mixed number remaining fraction(1/7) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 22/2 Original numerator / PRIME number AS DECIMAL => 11.0 Original numerator / PRIME number AS FRACTION (not reduced) => 22/3 Original numerator / PRIME number AS DECIMAL => 7.333333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 22/5 Original numerator / PRIME number AS DECIMAL => 4.4 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(5) has prime factor (divisible by prime number of two or five) Original decimal:0.6 is a periodic number *** The Decimal presented: 1.1 The fraction part: 1 this is numerator: 1 this is denominator: 10 This is potential Greatest Common Factor(1) between Numerator(1) Denominator(10) Elapsed time in seconds to reduce fraction: 2.5362E-5 reduced numerator: 1 reduced denominator: 10 Fraction presented is: 2/3 No whole number before fraction 1This is the difference(0.5666666666666667) between original(0.1) decimal and associated fraction(2/3) in decimal(0.6666666666666666) 2Original fraction (2/3) is non- representation of the initial decimal conversion: 0.1(1/10) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 2/2 Original numerator / PRIME number AS DECIMAL => 1.0 Original numerator / PRIME number AS FRACTION (not reduced) => 2/3 Original numerator / PRIME number AS DECIMAL => 0.6666666666666666 Original numerator / PRIME number AS FRACTION (not reduced) => 2/5 Original numerator / PRIME number AS DECIMAL => 0.4 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10) has prime factor (divisible by prime number of two or five) Original decimal:1.1 is a periodic number *** The Decimal presented: 6.1 The fraction part: 1 this is numerator: 1 this is denominator: 10 This is potential Greatest Common Factor(1) between Numerator(1) Denominator(10) Elapsed time in seconds to reduce fraction: 2.276E-5 reduced numerator: 1 reduced denominator: 10 Fraction presented is: 10/9 No whole number before fraction Original whole number from fraction (numerator/denominator):1 remaining numerator: 1 remaining fraction: 1/9 Fraction provided in challenge is improper: 10/9 Mixed number fraction is: 1-1/9 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:1 Original decimal has following whole number:6 *********** 1Original fraction(10/9)has been changed to mixed number fraction(1-1/9) 1This is the difference(0.0111111111111111) between original(0.1) decimal and associated fraction(1/9) in decimal(0.1111111111111111) 2Original fraction (1/9) is non- representation of the initial decimal conversion: 0.1(1/10) 1Remaining fraction(1/9) is non- representation of the initial decimal conversion: 0.1 1Remaining fraction (1/9) in decimal is 0.1111111111111111 and NOT:0.1(original) 2This is the difference(0.0111111111111111) between original(0.1) decimal and associated mixed number remaining fraction(1/9) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 10/2 Original numerator / PRIME number AS DECIMAL => 5.0 Original numerator / PRIME number AS FRACTION (not reduced) => 10/3 Original numerator / PRIME number AS DECIMAL => 3.3333333333333335 Original numerator / PRIME number AS FRACTION (not reduced) => 10/5 Original numerator / PRIME number AS DECIMAL => 2.0 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10) has prime factor (divisible by prime number of two or five) Original decimal:6.1 is a periodic number *** The Decimal presented: 6.1 The fraction part: 1 this is numerator: 1 this is denominator: 10 This is potential Greatest Common Factor(1) between Numerator(1) Denominator(10) Elapsed time in seconds to reduce fraction: 1.9524E-5 reduced numerator: 1 reduced denominator: 10 Fraction presented is: 1-3/9 Whole number before fraction: 1 Fraction after whole number: 3/9 ***2Mismatch in whole numbers**** Mixed number fraction has following whole number:1 Original decimal has following whole number:6 *********** 1This is the difference(0.2333333333333333) between original(0.1) decimal and associated fraction(1-3/9) in decimal(0.3333333333333333) 2Original fraction (1-3/9) is non- representation of the initial decimal conversion: 0.1(1/10) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 3/2 Original numerator / PRIME number AS DECIMAL => 1.5 Original numerator / PRIME number AS FRACTION (not reduced) => 3/3 Original numerator / PRIME number AS DECIMAL => 1.0 Original numerator / PRIME number AS FRACTION (not reduced) => 3/5 Original numerator / PRIME number AS DECIMAL => 0.6 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10) has prime factor (divisible by prime number of two or five) Original decimal:6.1 is a periodic number *** The Decimal presented: 0.10973 The fraction part: 10973 this is numerator: 10973 this is denominator: 100000 This is potential Greatest Common Factor(10973) between Numerator(10973) Denominator(100000) Elapsed time in seconds to reduce fraction: 0.082441117 reduced numerator: 10973 reduced denominator: 100000 Fraction presented is: 5-11/10 Whole number before fraction: 5 Fraction after whole number: 11/10 Original whole number from fraction (numerator/denominator):1 remaining numerator: 1 remaining fraction: 1/10 Fraction provided in challenge is improper: 5-11/10 Mixed number fraction is: 6-1/10 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:6 Original decimal has following whole number:0 *********** 1Original fraction(5-11/10)has been changed to mixed number fraction(6-1/10) 1This is the difference(0.009729999999999989) between original(0.10973) decimal and associated fraction(1/10) in decimal(0.1) 2Original fraction (1/10) is non- representation of the initial decimal conversion: 0.10973(10973/100000) 1Remaining fraction(1/10) is non- representation of the initial decimal conversion: 0.10973 1Remaining fraction (1/10) in decimal is 0.1 and NOT:0.10973(original) 2This is the difference(0.009729999999999989) between original(0.10973) decimal and associated mixed number remaining fraction(1/10) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 11/2 Original numerator / PRIME number AS DECIMAL => 5.5 Original numerator / PRIME number AS FRACTION (not reduced) => 11/3 Original numerator / PRIME number AS DECIMAL => 3.6666666666666665 Original numerator / PRIME number AS FRACTION (not reduced) => 11/5 Original numerator / PRIME number AS DECIMAL => 2.2 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(100000) has prime factor (divisible by prime number of two or five) Original decimal:0.10973 is a periodic number *** The Decimal presented: 0.343 The fraction part: 343 this is numerator: 343 this is denominator: 1000 This is potential Greatest Common Factor(343) between Numerator(343) Denominator(1000) Elapsed time in seconds to reduce fraction: 1.17242E-4 reduced numerator: 343 reduced denominator: 1000 Fraction presented is: 823/7500 No whole number before fraction 1This is the difference(0.23326666666666668) between original(0.343) decimal and associated fraction(823/7500) in decimal(0.10973333333333334) 2Original fraction (823/7500) is non- representation of the initial decimal conversion: 0.343(343/1000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 823/2 Original numerator / PRIME number AS DECIMAL => 411.5 Original numerator / PRIME number AS FRACTION (not reduced) => 823/3 Original numerator / PRIME number AS DECIMAL => 274.3333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 823/5 Original numerator / PRIME number AS DECIMAL => 164.6 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(1000) has prime factor (divisible by prime number of two or five) Original decimal:0.343 is a periodic number *** The Decimal presented: 0.242424 The fraction part: 242424 this is numerator: 242424 this is denominator: 1000000 This is potential Greatest Common Factor(242424) between Numerator(242424) Denominator(1000000) Reduction numerator: (242424,121212 divisor: 2) Reduction denominator: (1000000,500000 divisor: 2) Reduction in fraction and decimal: 242424/1000000(0.242424) => 121212/500000(0.242424) Reduction numerator: (121212,60606 divisor: 2) Reduction denominator: (500000,250000 divisor: 2) Reduction in fraction and decimal: 121212/500000(0.242424) => 60606/250000(0.242424) Reduction numerator: (60606,30303 divisor: 2) Reduction denominator: (250000,125000 divisor: 2) Reduction in fraction and decimal: 60606/250000(0.242424) => 30303/125000(0.242424) Elapsed time in seconds to reduce fraction: 0.522619279 reduced numerator: 30303 reduced denominator: 125000 Fraction presented is: 1/3 No whole number before fraction 1This is the difference(0.09090933333333331) between original(0.242424) decimal and associated fraction(1/3) in decimal(0.3333333333333333) 2Original fraction (1/3) is non- representation of the initial decimal conversion: 0.242424(30303/125000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 1/2 Original numerator / PRIME number AS DECIMAL => 0.5 Original numerator / PRIME number AS FRACTION (not reduced) => 1/3 Original numerator / PRIME number AS DECIMAL => 0.3333333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 1/5 Original numerator / PRIME number AS DECIMAL => 0.2 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(125000) has prime factor (divisible by prime number of two or five) Original decimal:0.242424 is a periodic number *** The Decimal presented: 0.1875325 The fraction part: 1875325 this is numerator: 1875325 this is denominator: 10000000 This is potential Greatest Common Factor(1875325) between Numerator(1875325) Denominator(10000000) Reduction numerator: (1875325,375065 divisor: 5) Reduction denominator: (10000000,2000000 divisor: 5) Reduction in fraction and decimal: 1875325/10000000(0.1875325) => 375065/2000000(0.1875325) Reduction numerator: (375065,75013 divisor: 5) Reduction denominator: (2000000,400000 divisor: 5) Reduction in fraction and decimal: 375065/2000000(0.1875325) => 75013/400000(0.1875325) Elapsed time in seconds to reduce fraction: 1.748738957 reduced numerator: 75013 reduced denominator: 400000 Fraction presented is: 30303/125000 No whole number before fraction 1This is the difference(0.05489150000000001) between original(0.1875325) decimal and associated fraction(30303/125000) in decimal(0.242424) 2Original fraction (30303/125000) is non- representation of the initial decimal conversion: 0.1875325(75013/400000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 30303/2 Original numerator / PRIME number AS DECIMAL => 15151.5 Original numerator / PRIME number AS FRACTION (not reduced) => 30303/3 Original numerator / PRIME number AS DECIMAL => 10101.0 Original numerator / PRIME number AS FRACTION (not reduced) => 30303/5 Original numerator / PRIME number AS DECIMAL => 6060.6 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(400000) has prime factor (divisible by prime number of two or five) Original decimal:0.1875325 is a periodic number *** The Decimal presented: 0.5 The fraction part: 5 this is numerator: 5 this is denominator: 10 This is potential Greatest Common Factor(5) between Numerator(5) Denominator(10) Reduction numerator: (5,1 divisor: 5) Reduction denominator: (10,2 divisor: 5) Reduction in fraction and decimal: 5/10(0.5) => 1/2(0.5) Elapsed time in seconds to reduce fraction: 0.068905001 reduced numerator: 1 reduced denominator: 2 Fraction presented is: 75013/400000 No whole number before fraction 1This is the difference(0.3124675) between original(0.5) decimal and associated fraction(75013/400000) in decimal(0.1875325) 2Original fraction (75013/400000) is non- representation of the initial decimal conversion: 0.5(1/2) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 75013/2 Original numerator / PRIME number AS DECIMAL => 37506.5 Original numerator / PRIME number AS FRACTION (not reduced) => 75013/3 Original numerator / PRIME number AS DECIMAL => 25004.333333333332 Original numerator / PRIME number AS FRACTION (not reduced) => 75013/5 Original numerator / PRIME number AS DECIMAL => 15002.6 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(2) has prime factor (divisible by prime number of two or five) Original decimal:0.5 is a periodic number *** The Decimal presented: 1.25 The fraction part: 25 this is numerator: 25 this is denominator: 100 This is potential Greatest Common Factor(25) between Numerator(25) Denominator(100) Reduction numerator: (25,5 divisor: 5) Reduction denominator: (100,20 divisor: 5) Reduction in fraction and decimal: 25/100(0.25) => 5/20(0.25) Reduction numerator: (5,1 divisor: 5) Reduction denominator: (20,4 divisor: 5) Reduction in fraction and decimal: 5/20(0.25) => 1/4(0.25) Elapsed time in seconds to reduce fraction: 1.69907E-4 reduced numerator: 1 reduced denominator: 4 Fraction presented is: 1/2 No whole number before fraction 1This is the difference(0.25) between original(0.25) decimal and associated fraction(1/2) in decimal(0.5) 2Original fraction (1/2) is non- representation of the initial decimal conversion: 0.25(1/4) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 1/2 Original numerator / PRIME number AS DECIMAL => 0.5 Original numerator / PRIME number AS FRACTION (not reduced) => 1/3 Original numerator / PRIME number AS DECIMAL => 0.3333333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 1/5 Original numerator / PRIME number AS DECIMAL => 0.2 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(4) has prime factor (divisible by prime number of two or five) Original decimal:1.25 is a periodic number *** The Decimal presented: 0.0123 The fraction part: 0123 this is numerator: 123 this is denominator: 10000 This is potential Greatest Common Factor(123) between Numerator(123) Denominator(10000) Elapsed time in seconds to reduce fraction: 1.9818E-5 reduced numerator: 123 reduced denominator: 10000 Fraction presented is: 1-1/4 Whole number before fraction: 1 Fraction after whole number: 1/4 1This is the difference(0.2377) between original(0.0123) decimal and associated fraction(1-1/4) in decimal(0.25) 2Original fraction (1-1/4) is non- representation of the initial decimal conversion: 0.0123(123/10000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 1/2 Original numerator / PRIME number AS DECIMAL => 0.5 Original numerator / PRIME number AS FRACTION (not reduced) => 1/3 Original numerator / PRIME number AS DECIMAL => 0.3333333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 1/5 Original numerator / PRIME number AS DECIMAL => 0.2 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10000) has prime factor (divisible by prime number of two or five) Original decimal:0.0123 is a periodic number *** The Decimal presented: 0.0001 The fraction part: 0001 this is numerator: 1 this is denominator: 10000 This is potential Greatest Common Factor(1) between Numerator(1) Denominator(10000) Elapsed time in seconds to reduce fraction: 2.2104E-5 reduced numerator: 1 reduced denominator: 10000 Fraction presented is: 123/10000 No whole number before fraction 1This is the difference(0.0122) between original(0.0001) decimal and associated fraction(123/10000) in decimal(0.0123) 2Original fraction (123/10000) is non- representation of the initial decimal conversion: 0.0001(1/10000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 123/2 Original numerator / PRIME number AS DECIMAL => 61.5 Original numerator / PRIME number AS FRACTION (not reduced) => 123/3 Original numerator / PRIME number AS DECIMAL => 41.0 Original numerator / PRIME number AS FRACTION (not reduced) => 123/5 Original numerator / PRIME number AS DECIMAL => 24.6 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10000) has prime factor (divisible by prime number of two or five) Original decimal:0.0001 is a periodic number *** The Decimal presented: 0.999 The fraction part: 999 this is numerator: 999 this is denominator: 1000 This is potential Greatest Common Factor(999) between Numerator(999) Denominator(1000) Elapsed time in seconds to reduce fraction: 1.32108E-4 reduced numerator: 999 reduced denominator: 1000 Fraction presented is: 1/10000 No whole number before fraction 1This is the difference(0.9989) between original(0.999) decimal and associated fraction(1/10000) in decimal(1.0E-4) 2Original fraction (1/10000) is non- representation of the initial decimal conversion: 0.999(999/1000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 1/2 Original numerator / PRIME number AS DECIMAL => 0.5 Original numerator / PRIME number AS FRACTION (not reduced) => 1/3 Original numerator / PRIME number AS DECIMAL => 0.3333333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 1/5 Original numerator / PRIME number AS DECIMAL => 0.2 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(1000) has prime factor (divisible by prime number of two or five) Original decimal:0.999 is a periodic number *** The Decimal presented: 0.15 The fraction part: 15 this is numerator: 15 this is denominator: 100 This is potential Greatest Common Factor(15) between Numerator(15) Denominator(100) Reduction numerator: (15,3 divisor: 5) Reduction denominator: (100,20 divisor: 5) Reduction in fraction and decimal: 15/100(0.15) => 3/20(0.15) Elapsed time in seconds to reduce fraction: 0.059610496 reduced numerator: 3 reduced denominator: 20 Fraction presented is: 999/1000 No whole number before fraction 1This is the difference(0.849) between original(0.15) decimal and associated fraction(999/1000) in decimal(0.999) 2Original fraction (999/1000) is non- representation of the initial decimal conversion: 0.15(3/20) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 999/2 Original numerator / PRIME number AS DECIMAL => 499.5 Original numerator / PRIME number AS FRACTION (not reduced) => 999/3 Original numerator / PRIME number AS DECIMAL => 333.0 Original numerator / PRIME number AS FRACTION (not reduced) => 999/5 Original numerator / PRIME number AS DECIMAL => 199.8 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(20) has prime factor (divisible by prime number of two or five) Original decimal:0.15 is a periodic number *** The Decimal presented: 0.86 The fraction part: 86 this is numerator: 86 this is denominator: 100 This is potential Greatest Common Factor(86) between Numerator(86) Denominator(100) Reduction numerator: (86,43 divisor: 2) Reduction denominator: (100,50 divisor: 2) Reduction in fraction and decimal: 86/100(0.86) => 43/50(0.86) Elapsed time in seconds to reduce fraction: 1.05129E-4 reduced numerator: 43 reduced denominator: 50 Fraction presented is: 15/100 No whole number before fraction 1This is the difference(0.71) between original(0.86) decimal and associated fraction(15/100) in decimal(0.15) 2Original fraction (15/100) is non- representation of the initial decimal conversion: 0.86(43/50) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 15/2 Original numerator / PRIME number AS DECIMAL => 7.5 Original numerator / PRIME number AS FRACTION (not reduced) => 15/3 Original numerator / PRIME number AS DECIMAL => 5.0 Original numerator / PRIME number AS FRACTION (not reduced) => 15/5 Original numerator / PRIME number AS DECIMAL => 3.0 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(50) has prime factor (divisible by prime number of two or five) Original decimal:0.86 is a periodic number *** The Decimal presented: 10.4 The fraction part: 4 this is numerator: 4 this is denominator: 10 This is potential Greatest Common Factor(4) between Numerator(4) Denominator(10) Reduction numerator: (4,2 divisor: 2) Reduction denominator: (10,5 divisor: 2) Reduction in fraction and decimal: 4/10(0.4) => 2/5(0.4) Elapsed time in seconds to reduce fraction: 8.1666E-5 reduced numerator: 2 reduced denominator: 5 Fraction presented is: 86/100 No whole number before fraction 1This is the difference(0.45999999999999996) between original(0.4) decimal and associated fraction(86/100) in decimal(0.86) 2Original fraction (86/100) is non- representation of the initial decimal conversion: 0.4(2/5) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 86/2 Original numerator / PRIME number AS DECIMAL => 43.0 Original numerator / PRIME number AS FRACTION (not reduced) => 86/3 Original numerator / PRIME number AS DECIMAL => 28.666666666666668 Original numerator / PRIME number AS FRACTION (not reduced) => 86/5 Original numerator / PRIME number AS DECIMAL => 17.2 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(5) has prime factor (divisible by prime number of two or five) Original decimal:10.4 is a periodic number *** The Decimal presented: 23.5 The fraction part: 5 this is numerator: 5 this is denominator: 10 This is potential Greatest Common Factor(5) between Numerator(5) Denominator(10) Reduction numerator: (5,1 divisor: 5) Reduction denominator: (10,2 divisor: 5) Reduction in fraction and decimal: 5/10(0.5) => 1/2(0.5) Elapsed time in seconds to reduce fraction: 8.0041E-5 reduced numerator: 1 reduced denominator: 2 Fraction presented is: 10-2/5 Whole number before fraction: 10 Fraction after whole number: 2/5 ***2Mismatch in whole numbers**** Mixed number fraction has following whole number:10 Original decimal has following whole number:23 *********** 1This is the difference(0.09999999999999998) between original(0.5) decimal and associated fraction(10-2/5) in decimal(0.4) 2Original fraction (10-2/5) is non- representation of the initial decimal conversion: 0.5(1/2) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 2/2 Original numerator / PRIME number AS DECIMAL => 1.0 Original numerator / PRIME number AS FRACTION (not reduced) => 2/3 Original numerator / PRIME number AS DECIMAL => 0.6666666666666666 Original numerator / PRIME number AS FRACTION (not reduced) => 2/5 Original numerator / PRIME number AS DECIMAL => 0.4 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(2) has prime factor (divisible by prime number of two or five) Original decimal:23.5 is a periodic number *** The Decimal presented: 0.75 The fraction part: 75 this is numerator: 75 this is denominator: 100 This is potential Greatest Common Factor(75) between Numerator(75) Denominator(100) Reduction numerator: (75,15 divisor: 5) Reduction denominator: (100,20 divisor: 5) Reduction in fraction and decimal: 75/100(0.75) => 15/20(0.75) Reduction numerator: (15,3 divisor: 5) Reduction denominator: (20,4 divisor: 5) Reduction in fraction and decimal: 15/20(0.75) => 3/4(0.75) Elapsed time in seconds to reduce fraction: 1.69385E-4 reduced numerator: 3 reduced denominator: 4 Fraction presented is: 23-1/2 Whole number before fraction: 23 Fraction after whole number: 1/2 1This is the difference(0.25) between original(0.75) decimal and associated fraction(23-1/2) in decimal(0.5) 2Original fraction (23-1/2) is non- representation of the initial decimal conversion: 0.75(3/4) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 1/2 Original numerator / PRIME number AS DECIMAL => 0.5 Original numerator / PRIME number AS FRACTION (not reduced) => 1/3 Original numerator / PRIME number AS DECIMAL => 0.3333333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 1/5 Original numerator / PRIME number AS DECIMAL => 0.2 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(4) has prime factor (divisible by prime number of two or five) Original decimal:0.75 is a periodic number *** The Decimal presented: 0.1111111111111111111 The fraction part: 1111111111111111111 this is numerator: 1111111111111111111 this is denominator: 10000000000000000000 Denominator(1000000000000000000) considered too large for computation Denominator reduced to 10 digits wide: (1000000000) due to recurrence numerator Truncated denominator: 1000000000 Numerator (1111111111111111111) considered too large for computation Numerator truncated to 9 digits wide: (111111111) due to recurrence numerator Truncated numerator: 111111111 BACK TO HERE 2THIS IS THE REGEX TO CHECK FOR POORLY DIVISIBLE NUMERATORS :111111111 THIS IS THE numerator:111111111 2Single digit recurring:true 1Numerator truncated to: 8 digits (11111111) to mitigate resource limitations of recurrence 9 times (1,3,7,9) 2Denominator truncated to: 9 digits(100000000) inline with numerator Truncated numerator: 11111111 Truncated numerator: 100000000 This is potential Greatest Common Factor(11111111) between Numerator(11111111) Denominator(100000000) 11Numerator truncated to: 7 digits to mitigate idle hanging of numerator: (1111111) 12Denominator truncated to: 8 digits(10000000) inline with numerator Truncated numerator: 1111111 Truncated denominator: 10000000 Elapsed time in seconds to reduce fraction: 1.995957231 reduced numerator: 1111111 reduced denominator: 10000000 Fraction presented is: 3/4 No whole number before fraction 1This is the difference(0.6388888888888888) between original(0.1111111111111111111) decimal and associated fraction(3/4) in decimal(0.75) 2Original fraction (3/4) is non- representation of the initial decimal conversion: 0.1111111111111111111(1111111/10000000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 3/2 Original numerator / PRIME number AS DECIMAL => 1.5 Original numerator / PRIME number AS FRACTION (not reduced) => 3/3 Original numerator / PRIME number AS DECIMAL => 1.0 Original numerator / PRIME number AS FRACTION (not reduced) => 3/5 Original numerator / PRIME number AS DECIMAL => 0.6 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10000000) has prime factor (divisible by prime number of two or five) Original decimal:0.1111111111111111111 is a periodic number *** The Decimal presented: 0.1111111111111111111 The fraction part: 1111111111111111111 this is numerator: 1111111111111111111 this is denominator: 10000000000000000000 Denominator(1000000000000000000) considered too large for computation Denominator reduced to 10 digits wide: (1000000000) due to recurrence numerator Truncated denominator: 1000000000 Numerator (1111111111111111111) considered too large for computation Numerator truncated to 9 digits wide: (111111111) due to recurrence numerator Truncated numerator: 111111111 BACK TO HERE 2THIS IS THE REGEX TO CHECK FOR POORLY DIVISIBLE NUMERATORS :111111111 THIS IS THE numerator:111111111 2Single digit recurring:true 1Numerator truncated to: 8 digits (11111111) to mitigate resource limitations of recurrence 9 times (1,3,7,9) 2Denominator truncated to: 9 digits(100000000) inline with numerator Truncated numerator: 11111111 Truncated numerator: 100000000 This is potential Greatest Common Factor(11111111) between Numerator(11111111) Denominator(100000000) 11Numerator truncated to: 7 digits to mitigate idle hanging of numerator: (1111111) 12Denominator truncated to: 8 digits(10000000) inline with numerator Truncated numerator: 1111111 Truncated denominator: 10000000 Elapsed time in seconds to reduce fraction: 1.912321787 reduced numerator: 1111111 reduced denominator: 10000000 Fraction presented is: 3/27 No whole number before fraction 1This is the difference(0.0) between original(0.1111111111111111111) decimal and associated fraction(3/27) in decimal(0.1111111111111111) 2Original fraction (3/27) is exact representation of the initial decimal conversion: 0.1111111111111111111(1111111/10000000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 3/2 Original numerator / PRIME number AS DECIMAL => 1.5 Original numerator / PRIME number AS FRACTION (not reduced) => 3/3 Original numerator / PRIME number AS DECIMAL => 1.0 Original numerator / PRIME number AS FRACTION (not reduced) => 3/5 Original numerator / PRIME number AS DECIMAL => 0.6 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10000000) has prime factor (divisible by prime number of two or five) Original decimal:0.1111111111111111111 is a periodic number *** The Decimal presented: 0.33533 The fraction part: 33533 this is numerator: 33533 this is denominator: 100000 This is potential Greatest Common Factor(33533) between Numerator(33533) Denominator(100000) Elapsed time in seconds to reduce fraction: 9.44989E-4 reduced numerator: 33533 reduced denominator: 100000 Fraction presented is: 1/9 No whole number before fraction 1This is the difference(0.2242188888888889) between original(0.33533) decimal and associated fraction(1/9) in decimal(0.1111111111111111) 2Original fraction (1/9) is non- representation of the initial decimal conversion: 0.33533(33533/100000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 1/2 Original numerator / PRIME number AS DECIMAL => 0.5 Original numerator / PRIME number AS FRACTION (not reduced) => 1/3 Original numerator / PRIME number AS DECIMAL => 0.3333333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 1/5 Original numerator / PRIME number AS DECIMAL => 0.2 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(100000) has prime factor (divisible by prime number of two or five) Original decimal:0.33533 is a periodic number *** The Decimal presented: 5.1111111111111111111 The fraction part: 1111111111111111111 this is numerator: 1111111111111111111 this is denominator: 10000000000000000000 Denominator(1000000000000000000) considered too large for computation Denominator reduced to 10 digits wide: (1000000000) due to recurrence numerator Truncated denominator: 1000000000 Numerator (1111111111111111111) considered too large for computation Numerator truncated to 9 digits wide: (111111111) due to recurrence numerator Truncated numerator: 111111111 BACK TO HERE 2THIS IS THE REGEX TO CHECK FOR POORLY DIVISIBLE NUMERATORS :111111111 THIS IS THE numerator:111111111 2Single digit recurring:true 1Numerator truncated to: 8 digits (11111111) to mitigate resource limitations of recurrence 9 times (1,3,7,9) 2Denominator truncated to: 9 digits(100000000) inline with numerator Truncated numerator: 11111111 Truncated numerator: 100000000 This is potential Greatest Common Factor(11111111) between Numerator(11111111) Denominator(100000000) 11Numerator truncated to: 7 digits to mitigate idle hanging of numerator: (1111111) 12Denominator truncated to: 8 digits(10000000) inline with numerator Truncated numerator: 1111111 Truncated denominator: 10000000 Elapsed time in seconds to reduce fraction: 1.607480814 reduced numerator: 1111111 reduced denominator: 10000000 Fraction presented is: 33533/100000 No whole number before fraction 1This is the difference(0.2242188888888889) between original(0.1111111111111111111) decimal and associated fraction(33533/100000) in decimal(0.33533) 2Original fraction (33533/100000) is non- representation of the initial decimal conversion: 0.1111111111111111111(1111111/10000000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 33533/2 Original numerator / PRIME number AS DECIMAL => 16766.5 Original numerator / PRIME number AS FRACTION (not reduced) => 33533/3 Original numerator / PRIME number AS DECIMAL => 11177.666666666666 Original numerator / PRIME number AS FRACTION (not reduced) => 33533/5 Original numerator / PRIME number AS DECIMAL => 6706.6 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10000000) has prime factor (divisible by prime number of two or five) Original decimal:5.1111111111111111111 is a periodic number *** The Decimal presented: 5.1111111111111111111 The fraction part: 1111111111111111111 this is numerator: 1111111111111111111 this is denominator: 10000000000000000000 Denominator(1000000000000000000) considered too large for computation Denominator reduced to 10 digits wide: (1000000000) due to recurrence numerator Truncated denominator: 1000000000 Numerator (1111111111111111111) considered too large for computation Numerator truncated to 9 digits wide: (111111111) due to recurrence numerator Truncated numerator: 111111111 BACK TO HERE 2THIS IS THE REGEX TO CHECK FOR POORLY DIVISIBLE NUMERATORS :111111111 THIS IS THE numerator:111111111 2Single digit recurring:true 1Numerator truncated to: 8 digits (11111111) to mitigate resource limitations of recurrence 9 times (1,3,7,9) 2Denominator truncated to: 9 digits(100000000) inline with numerator Truncated numerator: 11111111 Truncated numerator: 100000000 This is potential Greatest Common Factor(11111111) between Numerator(11111111) Denominator(100000000) 11Numerator truncated to: 7 digits to mitigate idle hanging of numerator: (1111111) 12Denominator truncated to: 8 digits(10000000) inline with numerator Truncated numerator: 1111111 Truncated denominator: 10000000 Elapsed time in seconds to reduce fraction: 1.897284791 reduced numerator: 1111111 reduced denominator: 10000000 Fraction presented is: 4-64/9 Whole number before fraction: 4 Fraction after whole number: 64/9 Original whole number from fraction (numerator/denominator):7 remaining numerator: 1 remaining fraction: 1/9 Fraction provided in challenge is improper: 4-64/9 Mixed number fraction is: 11-1/9 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:11 Original decimal has following whole number:5 *********** 1Original fraction(4-64/9)has been changed to mixed number fraction(11-1/9) 1This is the difference(0.0) between original(0.1111111111111111111) decimal and associated fraction(1/9) in decimal(0.1111111111111111) 2Original fraction (1/9) is exact representation of the initial decimal conversion: 0.1111111111111111111(1111111/10000000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 64/2 Original numerator / PRIME number AS DECIMAL => 32.0 Original numerator / PRIME number AS FRACTION (not reduced) => 64/3 Original numerator / PRIME number AS DECIMAL => 21.333333333333332 Original numerator / PRIME number AS FRACTION (not reduced) => 64/5 Original numerator / PRIME number AS DECIMAL => 12.8 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10000000) has prime factor (divisible by prime number of two or five) Original decimal:5.1111111111111111111 is a periodic number *** The Decimal presented: 0.555 The fraction part: 555 this is numerator: 555 this is denominator: 1000 This is potential Greatest Common Factor(555) between Numerator(555) Denominator(1000) Reduction numerator: (555,111 divisor: 5) Reduction denominator: (1000,200 divisor: 5) Reduction in fraction and decimal: 555/1000(0.555) => 111/200(0.555) Elapsed time in seconds to reduce fraction: 2.00263E-4 reduced numerator: 111 reduced denominator: 200 Fraction presented is: 64/9 No whole number before fraction Original whole number from fraction (numerator/denominator):7 remaining numerator: 1 remaining fraction: 1/9 Fraction provided in challenge is improper: 64/9 Mixed number fraction is: 7-1/9 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:7 Original decimal has following whole number:0 *********** 1Original fraction(64/9)has been changed to mixed number fraction(7-1/9) 1This is the difference(0.44388888888888894) between original(0.555) decimal and associated fraction(1/9) in decimal(0.1111111111111111) 2Original fraction (1/9) is non- representation of the initial decimal conversion: 0.555(111/200) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 64/2 Original numerator / PRIME number AS DECIMAL => 32.0 Original numerator / PRIME number AS FRACTION (not reduced) => 64/3 Original numerator / PRIME number AS DECIMAL => 21.333333333333332 Original numerator / PRIME number AS FRACTION (not reduced) => 64/5 Original numerator / PRIME number AS DECIMAL => 12.8 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(200) has prime factor (divisible by prime number of two or five) Original decimal:0.555 is a periodic number *** The Decimal presented: 10.0 The fraction part: 0 this is numerator: 0 this is denominator: 10 This is potential Greatest Common Factor(0) between Numerator(0) Denominator(10) Elapsed time in seconds to reduce fraction: 1.9181E-5 reduced numerator: 0 reduced denominator: 10 Fraction presented is: 64/9 No whole number before fraction Original whole number from fraction (numerator/denominator):7 remaining numerator: 1 remaining fraction: 1/9 Fraction provided in challenge is improper: 64/9 Mixed number fraction is: 7-1/9 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:7 Original decimal has following whole number:10 *********** 1Original fraction(64/9)has been changed to mixed number fraction(7-1/9) 1This is the difference(0.1111111111111111) between original(0.0) decimal and associated fraction(1/9) in decimal(0.1111111111111111) 2Original fraction (1/9) is non- representation of the initial decimal conversion: 0.0(0/10) 1Remaining fraction(1/9) is non- representation of the initial decimal conversion: 0.0 1Remaining fraction (1/9) in decimal is 0.1111111111111111 and NOT:0.0(original) 2This is the difference(0.1111111111111111) between original(0.0) decimal and associated mixed number remaining fraction(1/9) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 64/2 Original numerator / PRIME number AS DECIMAL => 32.0 Original numerator / PRIME number AS FRACTION (not reduced) => 64/3 Original numerator / PRIME number AS DECIMAL => 21.333333333333332 Original numerator / PRIME number AS FRACTION (not reduced) => 64/5 Original numerator / PRIME number AS DECIMAL => 12.8 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10) has prime factor (divisible by prime number of two or five) Original decimal:10.0 is a periodic number *** The Decimal presented: 0.011005502751375 The fraction part: 011005502751375 this is numerator: 11005502751375 this is denominator: 1000000000000000 6Numerator truncated from: 14 to 9 digits: 7Denominator truncated from 16 to 11 digits Truncated denominator: 10000000000 Truncated numerator: 110055027 2Single digit recurring:false 2THIS IS THE REGEX TO CHECK FOR POORLY DIVISIBLE NUMERATORS :111111111 THIS IS THE numerator:110055027 This is potential Greatest Common Factor(110055027) between Numerator(110055027) Denominator(10000000000) Elapsed time in seconds to reduce fraction: 26.179539804 reduced numerator: 110055027 reduced denominator: 10000000000 Fraction presented is: 20/2 No whole number before fraction Original whole number from fraction (numerator/denominator):10 remaining numerator: 0 remaining fraction: 0/2 Fraction provided in challenge is improper: 20/2 Mixed number fraction is: 10-0/2 ***Mismatch in whole numbers**** Mixed number fraction has following whole number:10 Original decimal has following whole number:0 *********** 1Original fraction(20/2)has been changed to mixed number fraction(10-0/2) 1This is the difference(9.988994497248624) between original(0.011005502751375) decimal and associated fraction(0/2) in decimal(10.0) 2Original fraction (0/2) is non- representation of the initial decimal conversion: 0.011005502751375(110055027/10000000000) Original fraction(0/2) is NOT reduced identically to the converted decimal (most reduced form): (110055027/10000000000) 1Remaining fraction(0/2) is non- representation of the initial decimal conversion: 0.011005502751375 1Remaining fraction (0/2) in decimal is 10.0 and NOT:0.011005502751375(original) 2This is the difference(0.011005502751375) between original(0.011005502751375) decimal and associated mixed number remaining fraction(0/2) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 20/2 Original numerator / PRIME number AS DECIMAL => 10.0 Original numerator / PRIME number AS FRACTION (not reduced) => 20/3 Original numerator / PRIME number AS DECIMAL => 6.666666666666667 Original numerator / PRIME number AS FRACTION (not reduced) => 20/5 Original numerator / PRIME number AS DECIMAL => 4.0 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10000000000) has prime factor (divisible by prime number of two or five) Original decimal:0.011005502751375 is a periodic number *** The Decimal presented: 7.1111111111111111111 The fraction part: 1111111111111111111 this is numerator: 1111111111111111111 this is denominator: 10000000000000000000 Denominator(1000000000000000000) considered too large for computation Denominator reduced to 10 digits wide: (1000000000) due to recurrence numerator Truncated denominator: 1000000000 Numerator (1111111111111111111) considered too large for computation Numerator truncated to 9 digits wide: (111111111) due to recurrence numerator Truncated numerator: 111111111 BACK TO HERE 2THIS IS THE REGEX TO CHECK FOR POORLY DIVISIBLE NUMERATORS :111111111 THIS IS THE numerator:111111111 2Single digit recurring:true 1Numerator truncated to: 8 digits (11111111) to mitigate resource limitations of recurrence 9 times (1,3,7,9) 2Denominator truncated to: 9 digits(100000000) inline with numerator Truncated numerator: 11111111 Truncated numerator: 100000000 This is potential Greatest Common Factor(11111111) between Numerator(11111111) Denominator(100000000) 11Numerator truncated to: 7 digits to mitigate idle hanging of numerator: (1111111) 12Denominator truncated to: 8 digits(10000000) inline with numerator Truncated numerator: 1111111 Truncated denominator: 10000000 Elapsed time in seconds to reduce fraction: 12.401305246 reduced numerator: 1111111 reduced denominator: 10000000 Fraction presented is: 22/1999 No whole number before fraction 1This is the difference(0.10010560835973542) between original(0.1111111111111111111) decimal and associated fraction(22/1999) in decimal(0.011005502751375688) 2Original fraction (22/1999) is non- representation of the initial decimal conversion: 0.1111111111111111111(1111111/10000000) ************************************************ This will just be final part of the code... Since several prime numbers have been generated, I will use the existing numerator And store the results in a String array: Numerator/prime number AS fraction and Numerator/prime number AS decimal and store results. IT IS TO GET A FEEL OF DIFFERENT PATTERNS AS EXPLORED IN DOCUMENTATION! This will provide a sample should I wish to populate initial array also! It will also show examples in which repetends have occurred two or more times in the decimal precision (19 digits wide) THIS IS ONLY circumstances available to enhance my code to utilize mapping to fractional equivalent.... ************************************************** Original numerator / PRIME number AS FRACTION (not reduced) => 22/2 Original numerator / PRIME number AS DECIMAL => 11.0 Original numerator / PRIME number AS FRACTION (not reduced) => 22/3 Original numerator / PRIME number AS DECIMAL => 7.333333333333333 Original numerator / PRIME number AS FRACTION (not reduced) => 22/5 Original numerator / PRIME number AS DECIMAL => 4.4 *************************************************** CHECK TO SEE IF ORIGINAL FRACTION IS TERMINATING: Terminating fraction since reduced denominator(10000000) has prime factor (divisible by prime number of two or five) Original decimal:7.1111111111111111111 is a periodic number ** Process exited - Return Code: 0 **