1/3 as a Decimal
The fraction 1/3 converted to a decimal, with a step-by-step solution.
How to Convert 1/3 to a Decimal (Long Division)
- 1
Set up the division of the numerator by the denominator.
1 ÷ 3
- 2
3 does not go into 1, so the whole-number part is 0. Write "0." and continue with a remainder of 1.
0 . …
- 3
Bring down a 0 to make 10. 3 goes into 10 3 times (3 × 3 = 9), remainder 1. (This is where the repeating block begins.) The remainder 1 has appeared before, so the digits from here on repeat forever.
10 ÷ 3 = 3, r 1
Is 1/3 a Terminating or Repeating Decimal?
1/3 is a repeating decimal. Written in full it is 0.(3) — the digit 3 repeats forever. The parentheses mark the repeating block.
1/3 Rounded to Each Place
| Rounded to | Value |
|---|---|
| Nearest tenth | 0.3 |
| Nearest hundredth | 0.33 |
| Nearest thousandth | 0.333 |
1/3 as a Mixed Number
1/3 is a proper fraction (the numerator is smaller than the denominator), so it is less than 1 and has no whole-number part — its value is just 0.333333.
Try Another Fraction
Step-by-Step Solution
- 1
Divide the numerator by the denominator.
1 ÷ 3 = 0.333333
- 2
Multiply by 100 to get the percentage.
0.333333 × 100 = 33.333333%
Frequently Asked Questions
What is 1/3 as a decimal?
1/3 as a decimal is 0.333333. You get it by dividing the numerator 1 by the denominator 3.
Is 1/3 a terminating or repeating decimal?
1/3 is a repeating decimal. Written out it is 0.(3), where the digit 3 repeats forever.
What is 1/3 rounded to the nearest thousandth?
Rounded to the nearest thousandth, 1/3 ≈ 0.333. To the nearest hundredth it is 0.33, and to the nearest tenth it is 0.3.
Is 1/3 a rational number?
Yes. 1/3 is a ratio of two integers (1 over 3), so it is a rational number — even though its decimal form repeats.