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# How do you convert fractions to recuring decimals?

Converting fractions to any kind of decimal is done in exactly the same way: divide the numerator by the denominator.

The reverse of converting a recurring decimal to a fraction is done:

Look at the digits that recur in the decimal. Count how many there are and then put the recurring digits as the numerator of a fraction with that number of 9s as the denominator.

eg to convert 0.33333.... to a fraction, see that the recurring decimal is the digit 3, thus the fraction would be 3/9 = 1/3.

eg to convert 0.09090909... to a fraction, see that the recurring decimal is 09 (or 9) and there are 2 digits (the leading 0 is important in counting the number of digits), thus the fraction is 09/99 or 9/99 = 1/11.

eg: to convert: 0.142857142857.... to a fraction, see that the digits 142857 recur and there are 6 of them, thus it is 142857/999999 which reduces down (simplifies) to 1/7.

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