0.414141… as a Fraction

0.414141… (0.41 repeating) as a fraction is 41/99.

How to convert 0.414141… to a fraction

  1. Let x = 0.414141... (the underlined part, 41, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 41.414141...
  3. Subtract to cancel the repeating tail: 100x − x = 41 − 0, so 99x = 41.
  4. Solve: x = 41/99. The greatest common divisor is 1, so x = 41/99 (already in lowest terms).

Check

Divide 41 by 99 on a calculator: 41 ÷ 99 = 0.4141414141… which matches 0.414141….

Similar repeating decimals

DecimalFraction
0.404040…40/99
0.4111…37/90
0.41333…31/75
0.41666…5/12
0.4222…19/45
0.424242…14/33
0.428428428…428/999
0.4333…13/30

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