0.0666… as a Fraction

0.0666… (0.06 repeating) as a fraction is 1/15.

How to convert 0.0666… to a fraction

  1. Let x = 0.0666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 6.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 0.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 6 − 0, so 90x = 6.
  5. Solve: x = 6/90. The greatest common divisor is 6, so x = 1/15.

Check

Divide 1 by 15 on a calculator: 1 ÷ 15 = 0.0666666667… which matches 0.0666….

Similar repeating decimals

DecimalFraction
0.054054054…2/37
0.0555…1/18
0.060606…2/33
0.070707…7/99
0.074074074…2/27
0.076076076…76/999
0.076923076923076923…1/13
0.0777…7/90

See also: 1/15 as a decimal.

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