0.7111… as a Fraction

0.7111… (0.71 repeating) as a fraction is 32/45.

How to convert 0.7111… to a fraction

  1. Let x = 0.7111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 71.111...
  3. Move the decimal point past the non-repeating digits too: 10x = 7.1111...
  4. Subtract to cancel the repeating tail: 100x − 10x = 71 − 7, so 90x = 64.
  5. Solve: x = 64/90. The greatest common divisor is 2, so x = 32/45.

Check

Divide 32 by 45 on a calculator: 32 ÷ 45 = 0.7111111111… which matches 0.7111….

Similar repeating decimals

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0.692692692…692/999
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0.7222…13/18
0.727272…8/11
0.7333…11/15

Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.