0.428428428… as a Fraction

0.428428428… (0.428 repeating) as a fraction is 428/999.

How to convert 0.428428428… to a fraction

  1. Let x = 0.428428428... (the underlined part, 428, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 428.428428428...
  3. Subtract to cancel the repeating tail: 1000x − x = 428 − 0, so 999x = 428.
  4. Solve: x = 428/999. The greatest common divisor is 1, so x = 428/999 (already in lowest terms).

Check

Divide 428 by 999 on a calculator: 428 ÷ 999 = 0.4284284284… which matches 0.428428428….

Similar repeating decimals

DecimalFraction
0.41333…31/75
0.414141…41/99
0.41666…5/12
0.4222…19/45
0.424242…14/33
0.4333…13/30
0.434343…43/99
0.444…4/9

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