2/3 as a Decimal

2/3 as a decimal is 0.666…, with the 6 repeating forever (66.67% rounded).

Result

Answer

\frac{2}{3} = \textcolor{#0b5c56}{0.\overline{6}}

2/3 as a decimal is 0.66666666… – the digit 6 repeats forever.

  • Rounded to 2 places: 0.67
  • Rounded to 4 places: 0.6667
  • Percent: 66.6667%

67 of 100 squares ≈ 2/3

Step-by-step solution

The problem

\frac{2}{3}

  1. Divide 2 by 3 (long division). Write down how many times 3 goes in, carry the remainder, add a 0 and divide again. The remainder 2 came back, so the digits from decimal place 1 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part2 ÷ 3023 × 0 = 0, 2 − 0 = 2
    Decimal place 120 ÷ 3623 × 6 = 18, 20 − 18 = 2

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

    = 2 \div 3 = \textcolor{#0b5c56}{0.\overline{6}}

All the working together

\begin{aligned} &\frac{2}{3} \\[8pt] &= 2 \div 3 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.\overline{6}}\end{aligned}

2/3 in other forms

Decimal0.666… (the 6 repeats forever)
Rounded0.67 (2 places), 0.667 (3 places)
Percent≈ 66.67%
Equivalent fractions4/6, 6/9, 8/12, 10/15
The other way0.6 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 6 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 2/3 as a decimal?

2/3 as a decimal is 0.666… (the 6 repeats forever). Divide 2 by 3 to get it.

What is 2/3 as a percent?

2/3 is ≈ 66.67%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 2/3 a terminating or a repeating decimal?

Repeating – the 6 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 6 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.