1/3 as a Decimal

1/3 as a decimal is 0.333…, with the 3 repeating forever (33.33% rounded).

Result

Answer

\frac{1}{3} = \textcolor{#0b5c56}{0.\overline{3}}

1/3 as a decimal is 0.33333333… – the digit 3 repeats forever.

  • Rounded to 2 places: 0.33
  • Rounded to 4 places: 0.3333
  • Percent: 33.3333%

33 of 100 squares ≈ 1/3

Step-by-step solution

The problem

\frac{1}{3}

  1. Divide 1 by 3 (long division). Write down how many times 3 goes in, carry the remainder, add a 0 and divide again. The remainder 1 came back, so the digits from decimal place 1 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part1 ÷ 3013 × 0 = 0, 1 − 0 = 1
    Decimal place 110 ÷ 3313 × 3 = 9, 10 − 9 = 1

  2. Read off the decimal. A bar over digits means they repeat forever.

    = 1 \div 3 = \textcolor{#0b5c56}{0.\overline{3}}

All the working together

\begin{aligned} &\frac{1}{3} \\[8pt] &= 1 \div 3 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.\overline{3}}\end{aligned}

1/3 in other forms

Decimal0.333… (the 3 repeats forever)
Rounded0.33 (2 places), 0.333 (3 places)
Percent≈ 33.33%
Equivalent fractions2/6, 3/9, 4/12, 5/15
The other way0.3 repeating as a fraction

Why it repeats

In lowest terms the denominator is 3 = 3. It has the prime factor 3, which does not divide any power of 10, so the long division never ends: the 3 repeats forever.

Fractions over 3 as decimals

FractionDecimalPercent
1/30.333…≈ 33.33%
2/30.666…≈ 66.67%
4/31.333…≈ 133.33%
5/31.666…≈ 166.67%
7/32.333…≈ 233.33%
8/32.666…≈ 266.67%

Frequently asked questions

What is 1/3 as a decimal?

1/3 as a decimal is 0.333… (the 3 repeats forever). Divide 1 by 3 to get it.

What is 1/3 as a percent?

1/3 is ≈ 33.33%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 1/3 a terminating or a repeating decimal?

Repeating – the 3 repeats forever. In lowest terms the denominator is 3 = 3. It has the prime factor 3, which does not divide any power of 10, so the long division never ends: the 3 repeats forever.

More fractions as decimals

Any other fraction: use the Fraction to Decimal Calculator, or see every fraction to sixteenths on the printable fraction chart.