This decimal is rational: 0.12515622210319585788252097839671.....How do I convert it to proper fraction a/b. In other words, what are "a" and "b"? Thanks for help.
One very simple but "foolproof" method of converting rational decimals to proper fractions is the "continued fraction" method, which goes as follows:
Take the reciprocal of the fraction: 0.12515622210319585788252097839671, and you should get:
7.9900142653352353780313837375178. Subtract the integer part, or 7, and take the reciprocal of the fraction and you should get:
1.0100864553314121037463976945245. Subtract the integer part, or 1, and take the reciprocal of the fraction and you should get:
99.142857142857142857142857142857. Subtract the integer part, or 99, and take the reciprocal of the fraction and you should get:
7. Once it converges to a whole number, then do this:
Multiply: 7 x 99.142857142857142857142857142857 =694. Then multiply this: 694 x 1.0100864553314121037463976945245 = 701. Since this is the second last multiplication, then this must the NUMERATOR.
Finally, multiply this NUMERATOR x the first number that we listed and you should get:
701 x 7.9900142653352353780313837375178=5,601 - This is the DENOMINATOR. So, the proper fraction of this rational decimal is:
701 / 5,601.
Note: This decimal fraction does not repeat its digits for 933 decimal places. Or, Its "period" is 933 digits long.
