0.727272… as a Fraction

0.727272… (0.72 repeating) as a fraction is 8/11.

How to convert 0.727272… to a fraction

  1. Let x = 0.727272... (the underlined part, 72, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 72.727272...
  3. Subtract to cancel the repeating tail: 100x − x = 72 − 0, so 99x = 72.
  4. Solve: x = 72/99. The greatest common divisor is 9, so x = 8/11.

Check

Divide 8 by 11 on a calculator: 8 ÷ 11 = 0.7272727273… which matches 0.727272….

Similar repeating decimals

DecimalFraction
0.707070…70/99
0.7111…32/45
0.714714714…238/333
0.717171…71/99
0.7222…13/18
0.7333…11/15
0.737373…73/99
0.7444…67/90

See also: 8/11 as a decimal.

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