0.1333… as a Fraction

0.1333… (0.13 repeating) as a fraction is 2/15.

How to convert 0.1333… to a fraction

  1. Let x = 0.1333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 13.333...
  3. Move the decimal point past the non-repeating digits too: 10x = 1.3333...
  4. Subtract to cancel the repeating tail: 100x − 10x = 13 − 1, so 90x = 12.
  5. Solve: x = 12/90. The greatest common divisor is 6, so x = 2/15.

Check

Divide 2 by 15 on a calculator: 2 ÷ 15 = 0.1333333333… which matches 0.1333….

Similar repeating decimals

DecimalFraction
0.1222…11/90
0.123123123…41/333
0.131313…13/99
0.135135135…5/37
0.141414…14/99
0.142142142…142/999
0.142857142857142857…1/7
0.1444…13/90

See also: 2/15 as a decimal.

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