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Converting Repeating Decimals to Fractions

To convert a repeating decimal to a fraction, let N be the number, and let n be the number of digits in the repeating block. For example,

has 2 digits in the repeating block, whereas

has only 1.

Setting N equal to its value, multiply both sides of the equation by 10ⁿ. Then subtract N from both sides. You will end up with an equation which you can solve for N as a fractional value.

Start with the equation:

There are two digits in the repeating block, so multiply both sides by 10² = 100.

Now subtract N from both sides. Notice that the repeating part cancels out.

Divide both sides by 99, multiply numerator and denominator by a power of 10 to get rid of the decimal point, and simplify.