0.75333… as a Fraction

0.75333… (0.753 repeating) as a fraction is 113/150.

How to convert 0.75333… to a fraction

  1. Let x = 0.75333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 753.333...
  3. Move the decimal point past the non-repeating digits too: 100x = 75.3333...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 753 − 75, so 900x = 678.
  5. Solve: x = 678/900. The greatest common divisor is 6, so x = 113/150.

Check

Divide 113 by 150 on a calculator: 113 ÷ 150 = 0.7533333333… which matches 0.75333….

Similar repeating decimals

DecimalFraction
0.737373…73/99
0.7444…67/90
0.747474…74/99
0.7555…34/45
0.75666…227/300
0.757575…25/33
0.7666…23/30
0.767676…76/99

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