Question

How to write repeating decimals as fractions

Answer 1

Answer:

You take the repeating group of digits and divide it by the same number of digits but formed only by 9s.

Step-by-step explanation:

Let's say you have 0.111111111111...., your repeating pattern is 1, that consists of one digit (1).  You take that digit and you divide it by 9:

1/9 is the fraction equivalent to 0.111111111111111...

Let's say you have 0.12121212121212...., the repeating pattern is 12, that consists of 2 digits (12).  You take those 2 digits and divide them by 99:

12/99 is the fraction equivalent to 0.12121212121212...

which can be reduced to 4/33

If you have 0.363363363363..., your repeating pattern is 363, which is 3 digits, so you divide 363by 999:

363/999 is the fraction equivalent to  0.363363363363...

which can be simplified to 121/333