Count how many digits there are in the repeating part. Write down the same number of 9s. This will be a denominator.
Take the repeating part as the numerator. We now have a fraction. Reduce the fraction by looking for common factors in the numerator and denominator and divide top and bottom by the common factor until it is in its simplest form. You can also use a calculator to divide the top into the bottom to see if it’s a whole number.
EXAMPLE
0.14285714285714... This has the repeating section 142857. That’s 6 digits so we write 999999 as the denominator.
The fraction is 142857/999999 which simplifies to 1/7.
0.69230769230769... This has 692307 as the repeating section and 999999 as the denominator.
The fraction is 692307/999999=76923×9/111111×9=76923/111111=8547×9/(8547×13)=9/13.
