Decimal
0.33…
What is 1/3 as a decimal and percent?
Answer
1/3 as a decimal is 0.33…. As a percent, 1/3 is 33.3333%.
Percent
33.3333%
Step-by-step working
1
Divide the numerator by the denominator
To turn any fraction into a decimal, divide the top by the bottom.
1 ÷ 3 = 0.33…
2
Multiply by 100 for the percent
Percent means "out of one hundred". Multiplying a decimal by 100 (or moving the decimal point two places to the right) gives the percent value.
0.33… × 100 = 33.3333%
3
Round if needed
In this case 1/3 produces a recurring decimal, so rounding is required. Two decimal places (≈ 0.33) is enough for most everyday work; four (≈ 0.3333) for precise calculations.
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Decimal
0.33…
Percent
33.3333%
About this fraction
One-third comes up in cooking, three-way splits, and trigonometry (sin 30° involves halves; tangent values use one-third). The recurring 0.333… is a clean way to see why some fractions never finish in decimal form. The denominator has prime factors other than 2 and 5, which is why the decimal repeats forever.
Common conversions
Related fractions and their decimal / percent values for quick comparison.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/3 | 0.(3) | 33.3333% |
| 2/3 | 0.(6) | 66.6667% |
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
Frequently asked questions
What is 1/3 as a decimal?
1/3 as a decimal is 0.33…. The decimal recurs — the digits repeat indefinitely. Divide the numerator by the denominator: 1 ÷ 3 = 0.33…. For most everyday work, round to two or three decimal places.
What is 1/3 as a percent?
1/3 as a percent is 33.3333%. Take the decimal value (0.33…) and move the decimal point two places to the right — the same as multiplying by 100.
Is 1/3 already in lowest form?
Yes. 1/3 is already in lowest form because the greatest common divisor of 1 and 3 is 1.
Does 1/3 terminate or recur as a decimal?
1/3 recurs (does not terminate) as a decimal. The denominator (after simplifying to 1/3) contains prime factors other than 2 and 5, which forces an infinitely repeating block.