0.2777… as a Fraction

0.2777… (0.27 repeating) as a fraction is 5/18.

How to convert 0.2777… to a fraction

  1. Let x = 0.2777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 27.777...
  3. Move the decimal point past the non-repeating digits too: 10x = 2.7777...
  4. Subtract to cancel the repeating tail: 100x − 10x = 27 − 2, so 90x = 25.
  5. Solve: x = 25/90. The greatest common divisor is 5, so x = 5/18.

Check

Divide 5 by 18 on a calculator: 5 ÷ 18 = 0.2777777778… which matches 0.2777….

Similar repeating decimals

DecimalFraction
0.2555…23/90
0.262626…26/99
0.2666…4/15
0.272727…3/11
0.282828…28/99
0.285285285…95/333
0.2888…13/45
0.292929…29/99

See also: 5/18 as a decimal.

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