0.3222… as a Fraction

0.3222… (0.32 repeating) as a fraction is 29/90.

How to convert 0.3222… to a fraction

  1. Let x = 0.3222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 32.222...
  3. Move the decimal point past the non-repeating digits too: 10x = 3.2222...
  4. Subtract to cancel the repeating tail: 100x − 10x = 32 − 3, so 90x = 29.
  5. Solve: x = 29/90. The greatest common divisor is 1, so x = 29/90 (already in lowest terms).

Check

Divide 29 by 90 on a calculator: 29 ÷ 90 = 0.3222222222… which matches 0.3222….

Similar repeating decimals

DecimalFraction
0.303030…10/33
0.307307307…307/999
0.3111…14/45
0.313131…31/99
0.323232…32/99
0.333…1/3
0.343434…34/99
0.3444…31/90

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