0.41666… as a Fraction

0.41666… (0.416 repeating) as a fraction is 5/12.

How to convert 0.41666… to a fraction

  1. Let x = 0.41666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 416.666...
  3. Move the decimal point past the non-repeating digits too: 100x = 41.6666...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 416 − 41, so 900x = 375.
  5. Solve: x = 375/900. The greatest common divisor is 75, so x = 5/12.

Check

Divide 5 by 12 on a calculator: 5 ÷ 12 = 0.4166666667… which matches 0.41666….

Similar repeating decimals

DecimalFraction
0.404040…40/99
0.4111…37/90
0.41333…31/75
0.414141…41/99
0.4222…19/45
0.424242…14/33
0.428428428…428/999
0.4333…13/30

See also: 5/12 as a decimal.

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