0.313131… as a Fraction

0.313131… (0.31 repeating) as a fraction is 31/99.

How to convert 0.313131… to a fraction

  1. Let x = 0.313131... (the underlined part, 31, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 31.313131...
  3. Subtract to cancel the repeating tail: 100x − x = 31 − 0, so 99x = 31.
  4. Solve: x = 31/99. The greatest common divisor is 1, so x = 31/99 (already in lowest terms).

Check

Divide 31 by 99 on a calculator: 31 ÷ 99 = 0.3131313131… which matches 0.313131….

Similar repeating decimals

DecimalFraction
0.2888…13/45
0.292929…29/99
0.303030…10/33
0.307307307…307/999
0.3111…14/45
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.