0.9333… as a Fraction

0.9333… (0.93 repeating) as a fraction is 14/15.

How to convert 0.9333… to a fraction

  1. Let x = 0.9333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 93.333...
  3. Move the decimal point past the non-repeating digits too: 10x = 9.3333...
  4. Subtract to cancel the repeating tail: 100x − 10x = 93 − 9, so 90x = 84.
  5. Solve: x = 84/90. The greatest common divisor is 6, so x = 14/15.

Check

Divide 14 by 15 on a calculator: 14 ÷ 15 = 0.9333333333… which matches 0.9333….

Similar repeating decimals

DecimalFraction
0.91666…11/12
0.919191…91/99
0.9222…83/90
0.923923923…923/999
0.929292…92/99
0.939393…31/33
0.9444…17/18
0.949494…94/99

See also: 14/15 as a decimal.

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