0.135135135… as a Fraction

0.135135135… (0.135 repeating) as a fraction is 5/37.

How to convert 0.135135135… to a fraction

  1. Let x = 0.135135135... (the underlined part, 135, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 135.135135135...
  3. Subtract to cancel the repeating tail: 1000x − x = 135 − 0, so 999x = 135.
  4. Solve: x = 135/999. The greatest common divisor is 27, so x = 5/37.

Check

Divide 5 by 37 on a calculator: 5 ÷ 37 = 0.1351351351… which matches 0.135135135….

Similar repeating decimals

DecimalFraction
0.1222…11/90
0.123123123…41/333
0.131313…13/99
0.1333…2/15
0.141414…14/99
0.142142142…142/999
0.142857142857142857…1/7
0.1444…13/90

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