0.7222… as a Fraction

0.7222… (0.72 repeating) as a fraction is 13/18.

How to convert 0.7222… to a fraction

  1. Let x = 0.7222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 72.222...
  3. Move the decimal point past the non-repeating digits too: 10x = 7.2222...
  4. Subtract to cancel the repeating tail: 100x − 10x = 72 − 7, so 90x = 65.
  5. Solve: x = 65/90. The greatest common divisor is 5, so x = 13/18.

Check

Divide 13 by 18 on a calculator: 13 ÷ 18 = 0.7222222222… which matches 0.7222….

Similar repeating decimals

DecimalFraction
0.707070…70/99
0.7111…32/45
0.714714714…238/333
0.717171…71/99
0.727272…8/11
0.7333…11/15
0.737373…73/99
0.7444…67/90

See also: 13/18 as a decimal.

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