0.83666… as a Fraction

0.83666… (0.836 repeating) as a fraction is 251/300.

How to convert 0.83666… to a fraction

  1. Let x = 0.83666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 836.666...
  3. Move the decimal point past the non-repeating digits too: 100x = 83.6666...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 836 − 83, so 900x = 753.
  5. Solve: x = 753/900. The greatest common divisor is 3, so x = 251/300.

Check

Divide 251 by 300 on a calculator: 251 ÷ 300 = 0.8366666667… which matches 0.83666….

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0.846846846…94/111
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Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.