0.384384384… as a Fraction

0.384384384… (0.384 repeating) as a fraction is 128/333.

How to convert 0.384384384… to a fraction

  1. Let x = 0.384384384... (the underlined part, 384, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 384.384384384...
  3. Subtract to cancel the repeating tail: 1000x − x = 384 − 0, so 999x = 384.
  4. Solve: x = 384/999. The greatest common divisor is 3, so x = 128/333.

Check

Divide 128 by 333 on a calculator: 128 ÷ 333 = 0.3843843844… which matches 0.384384384….

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