0.08666… as a Fraction

0.08666… (0.086 repeating) as a fraction is 13/150.

How to convert 0.08666… to a fraction

  1. Let x = 0.08666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 86.666...
  3. Move the decimal point past the non-repeating digits too: 100x = 8.6666...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 86 − 8, so 900x = 78.
  5. Solve: x = 78/900. The greatest common divisor is 6, so x = 13/150.

Check

Divide 13 by 150 on a calculator: 13 ÷ 150 = 0.0866666667… which matches 0.08666….

Similar repeating decimals

DecimalFraction
0.076076076…76/999
0.076923076923076923…1/13
0.0777…7/90
0.080808…8/99
0.081081081…3/37
0.08333…1/12
0.0888…4/45
0.090909…1/11

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