3.8333… as a Fraction

3.8333… (3.83 repeating) as a fraction is 23/6. As a mixed number that is 3 5/6.

How to convert 3.8333… to a fraction

  1. Let x = 3.8333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 383.333...
  3. Move the decimal point past the non-repeating digits too: 10x = 38.3333...
  4. Subtract to cancel the repeating tail: 100x − 10x = 383 − 38, so 90x = 345.
  5. Solve: x = 345/90. The greatest common divisor is 15, so x = 23/6.

Since 23 is larger than 6, it can also be written as the mixed number 3 5/6.

Check

Divide 23 by 6 on a calculator: 23 ÷ 6 = 3.8333333333… which matches 3.8333….

Similar repeating decimals

DecimalFraction
3.444…31/9
3.555…32/9
3.666…11/3
3.777…34/9
3.888…35/9
4.111…37/9
4.222…38/9
4.333…13/3

See also: 23/6 as a mixed number.

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