0.4333… as a Fraction

0.4333… (0.43 repeating) as a fraction is 13/30.

How to convert 0.4333… to a fraction

  1. Let x = 0.4333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 43.333...
  3. Move the decimal point past the non-repeating digits too: 10x = 4.3333...
  4. Subtract to cancel the repeating tail: 100x − 10x = 43 − 4, so 90x = 39.
  5. Solve: x = 39/90. The greatest common divisor is 3, so x = 13/30.

Check

Divide 13 by 30 on a calculator: 13 ÷ 30 = 0.4333333333… which matches 0.4333….

Similar repeating decimals

DecimalFraction
0.41333…31/75
0.414141…41/99
0.41666…5/12
0.4222…19/45
0.424242…14/33
0.428428428…428/999
0.434343…43/99
0.444…4/9

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