Repeating Decimals to Fractions

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A repeating decimal is a decimal that has a pattern of digits that repeat forever. To convert a repeating decimal to a fraction, you can use a simple process.

Here's how:

Write down the repeating decimal as a fraction. Put the repeating part of the decimal over a power of 10 that will make the repeating part become a whole number. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor. For example, let's convert the repeating decimal 0.666... to a fraction.

Write down the repeating decimal as a fraction: 0.666... = 6.666.../10 Put the repeating part over a power of 10: 6.666.../10 = (666...)/1000 Simplify the fraction: (666...)/1000 = (666)/1000 = 333/500 Now we have the fraction 333/500, which represents the repeating decimal 0.666...

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