Write repeating decimals as fractions
Let x be the decimal. Multiply by a power of 10 to line up the repeating part, then subtract.
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The decimal 0.828282… has the digits 82 repeating forever. Write it as a fraction in lowest terms.
Answer: 82/99
The decimal 0.444444… has the digits 4 repeating forever. Write it as a fraction in lowest terms.
Answer: 4/9
The decimal 0.171717… has the digits 17 repeating forever. Write it as a fraction in lowest terms.
Answer: 17/99
Tip: Let x be the decimal. Multiply by a power of 10 to line up the repeating part, then subtract.
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