0.7444… as a Fraction

0.7444… (0.74 repeating) as a fraction is 67/90.

How to convert 0.7444… to a fraction

  1. Let x = 0.7444... (the underlined part, 4, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 74.444...
  3. Move the decimal point past the non-repeating digits too: 10x = 7.4444...
  4. Subtract to cancel the repeating tail: 100x − 10x = 74 − 7, so 90x = 67.
  5. Solve: x = 67/90. The greatest common divisor is 1, so x = 67/90 (already in lowest terms).

Check

Divide 67 by 90 on a calculator: 67 ÷ 90 = 0.7444444444… which matches 0.7444….

Similar repeating decimals

DecimalFraction
0.727272…8/11
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0.7555…34/45
0.75666…227/300
0.757575…25/33

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