0.3111… as a Fraction

0.3111… (0.31 repeating) as a fraction is 14/45.

How to convert 0.3111… to a fraction

  1. Let x = 0.3111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 31.111...
  3. Move the decimal point past the non-repeating digits too: 10x = 3.1111...
  4. Subtract to cancel the repeating tail: 100x − 10x = 31 − 3, so 90x = 28.
  5. Solve: x = 28/90. The greatest common divisor is 2, so x = 14/45.

Check

Divide 14 by 45 on a calculator: 14 ÷ 45 = 0.3111111111… which matches 0.3111….

Similar repeating decimals

DecimalFraction
0.2888…13/45
0.292929…29/99
0.303030…10/33
0.307307307…307/999
0.313131…31/99
0.3222…29/90
0.323232…32/99
0.333…1/3

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