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1/3 as a Decimal
Last updated: May 31, 2026
Written by Blake Boege
A fraction to decimal conversion maps a ratio of whole numbers to a terminating or repeating decimal representation.
Find out how to convert 1/3 as a decimal. Learn about repeating decimals, view the step-by-step conversion, and try our live interactive fraction-to-decimal widget.
Quick Answer
1/3 as a decimal equals 0.333… (repeating, written with bar as 0.3̄). Calculated by dividing 1 by 3.
1/3 = 0.333…
e.g. 3
Cannot be 0. · e.g. 4
Adjust numerator and denominator to dynamically recalculate the value.
Decimal value
0.3333333333
1/3 as a decimal
Divide the numerator by the denominator.
How it works
To find the decimal representation of the fraction 1/3, divide the numerator by the denominator:
Division Formula
1 ÷ 3 = 0.333…
Decimal Type
This is a repeating decimal, where the digit repeats infinitely. It can be written as 0.3̄ using a combining overline bar, or rounded to 0.333 for most practical applications.
Step-by-Step Division for 1/3
To perform this conversion manually, use long division. Treat the fraction line as a division symbol. Write 1 as 1.000 and divide by 3:
1. 1 divided by 3 is 0 with a remainder of 1.
2. Add a decimal point and bring down a 0, making it 10.
3. Keep performing long division until the division resolves or enters a repeating loop.
4. Result = 0.333…
Terminating vs. Repeating Decimals
Fractions whose denominators only have prime factors of 2 or 5 will always result in a terminating decimal (like 1/2, 1/4, or 1/8). Denominators with other prime factors (like 3 or 6) result in repeating decimal sequences.
Common Fraction Equivalents Reference Table
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.3% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
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Frequently asked questions
1/3 as a decimal is 0.333… which is a repeating decimal. It can also be written with a repeating bar as 0.3̄ or rounded to 0.333.
It is a repeating decimal because the digit 3 repeats infinitely in the decimal representation.
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