0.8444… as a Fraction

0.8444… (0.84 repeating) as a fraction is 38/45.

How to convert 0.8444… to a fraction

  1. Let x = 0.8444... (the underlined part, 4, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 84.444...
  3. Move the decimal point past the non-repeating digits too: 10x = 8.4444...
  4. Subtract to cancel the repeating tail: 100x − 10x = 84 − 8, so 90x = 76.
  5. Solve: x = 76/90. The greatest common divisor is 2, so x = 38/45.

Check

Divide 38 by 45 on a calculator: 38 ÷ 45 = 0.8444444444… which matches 0.8444….

Similar repeating decimals

DecimalFraction
0.8333…5/6
0.83333…5/6
0.83666…251/300
0.838383…83/99
0.846846846…94/111
0.848484…28/33
0.8555…77/90
0.857857857…857/999

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