0.91333… as a Fraction

0.91333… (0.913 repeating) as a fraction is 137/150.

How to convert 0.91333… to a fraction

  1. Let x = 0.91333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 913.333...
  3. Move the decimal point past the non-repeating digits too: 100x = 91.3333...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 913 − 91, so 900x = 822.
  5. Solve: x = 822/900. The greatest common divisor is 6, so x = 137/150.

Check

Divide 137 by 150 on a calculator: 137 ÷ 150 = 0.9133333333… which matches 0.91333….

Similar repeating decimals

DecimalFraction
0.898989…89/99
0.909090…10/11
0.9111…41/45
0.91666…11/12
0.919191…91/99
0.9222…83/90
0.923923923…923/999
0.929292…92/99

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