How would you convert a repeating decimal to a rational number?

Answer 1

Suppose there are c digits after the decimal place where the digits are non-repeating, and then you get a repeating pattern of a string of d digits.

Then the numerator is the old original string including one lot of the repeated digits minus the original string with none of the repeating digits. The denominator is 10^c*(10^d - 1), which is a string of d 9s followed by c 0s.

For example

123.26159159… There are 2 digits, "26", after the decimal point before the repeats kick in so c = 2, and the repeating string "159" is 3 digits long so d = 3.

So the numerator is 12326159 – 12326 = 12313833

and the denominator is 99900

Therefore the fraction is 12313833/99900.