0.131313… as a Fraction

0.131313… (0.13 repeating) as a fraction is 13/99.

How to convert 0.131313… to a fraction

  1. Let x = 0.131313... (the underlined part, 13, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 13.131313...
  3. Subtract to cancel the repeating tail: 100x − x = 13 − 0, so 99x = 13.
  4. Solve: x = 13/99. The greatest common divisor is 1, so x = 13/99 (already in lowest terms).

Check

Divide 13 by 99 on a calculator: 13 ÷ 99 = 0.1313131313… which matches 0.131313….

Similar repeating decimals

DecimalFraction
0.121212…4/33
0.1222…11/90
0.123123123…41/333
0.1333…2/15
0.135135135…5/37
0.141414…14/99
0.142142142…142/999
0.142857142857142857…1/7

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