0.4666… as a Fraction

0.4666… (0.46 repeating) as a fraction is 7/15.

How to convert 0.4666… to a fraction

  1. Let x = 0.4666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 46.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 4.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 46 − 4, so 90x = 42.
  5. Solve: x = 42/90. The greatest common divisor is 6, so x = 7/15.

Check

Divide 7 by 15 on a calculator: 7 ÷ 15 = 0.4666666667… which matches 0.4666….

Similar repeating decimals

DecimalFraction
0.454545…5/11
0.4555…41/90
0.456456456…152/333
0.461461461…461/999
0.464646…46/99
0.474747…47/99
0.4777…43/90
0.484848…16/33

See also: 7/15 as a decimal.

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