How can you change a repeating decimal into a fraction?

Answer 1

Until you become expert at this I suggest you do this in two stages (using c and d separately). Suppose there are c digits after the decimal place where the digits are non-repeating, and then you get a repeating pattern of strings 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 – 123216 = 12313833 and the denominator is 99900 Therefore the fraction is 12313833/99900.