0.6444… as a Fraction

0.6444… (0.64 repeating) as a fraction is 29/45.

How to convert 0.6444… to a fraction

  1. Let x = 0.6444... (the underlined part, 4, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 64.444...
  3. Move the decimal point past the non-repeating digits too: 10x = 6.4444...
  4. Subtract to cancel the repeating tail: 100x − 10x = 64 − 6, so 90x = 58.
  5. Solve: x = 58/90. The greatest common divisor is 2, so x = 29/45.

Check

Divide 29 by 45 on a calculator: 29 ÷ 45 = 0.6444444444… which matches 0.6444….

Similar repeating decimals

DecimalFraction
0.6222…28/45
0.626262…62/99
0.6333…19/30
0.636363…7/11
0.646464…64/99
0.6555…59/90
0.656565…65/99
0.666…2/3

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