2.5333… as a Fraction

2.5333… (2.53 repeating) as a fraction is 38/15. As a mixed number that is 2 8/15.

How to convert 2.5333… to a fraction

  1. Let x = 2.5333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 253.333...
  3. Move the decimal point past the non-repeating digits too: 10x = 25.3333...
  4. Subtract to cancel the repeating tail: 100x − 10x = 253 − 25, so 90x = 228.
  5. Solve: x = 228/90. The greatest common divisor is 6, so x = 38/15.

Since 38 is larger than 15, it can also be written as the mixed number 2 8/15.

Check

Divide 38 by 15 on a calculator: 38 ÷ 15 = 2.5333333333… which matches 2.5333….

Similar repeating decimals

DecimalFraction
2.1666…13/6
2.222…20/9
2.333…7/3
2.444…22/9
2.555…23/9
2.666…8/3
2.777…25/9
2.888…26/9

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