0.2666… as a Fraction

0.2666… (0.26 repeating) as a fraction is 4/15.

How to convert 0.2666… to a fraction

  1. Let x = 0.2666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 26.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 2.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 26 − 2, so 90x = 24.
  5. Solve: x = 24/90. The greatest common divisor is 6, so x = 4/15.

Check

Divide 4 by 15 on a calculator: 4 ÷ 15 = 0.2666666667… which matches 0.2666….

Similar repeating decimals

DecimalFraction
0.252525…25/99
0.2555…23/90
0.262626…26/99
0.272727…3/11
0.2777…5/18
0.282828…28/99
0.285285285…95/333
0.2888…13/45

See also: 4/15 as a decimal.

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