Repeating Decimal to Fraction

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In this section, we learn how to convert a repeating decimal into a fraction. A repeating decimal is one that repeats the same digit or series of digits forever. We generally identify these by placing a bar over the digit or digits that repeat forever. To perform this operation, we first set our repeating decimal equal to a variable. Next, we multiply both sides of the equation by 10n where n is the number of digits in the repeating string. The next step subtracts the original equation from the transformed equation. We then clear the decimal that remains by multiplying by the appropriate power of ten. Our last step is to solve for x and check the result. We can do this by dividing our numerator by our denominator. We should get the original repeating decimal as our result.
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