8/3 as a Decimal – 2.666… (with Steps)

Q: What is 8/3 as a decimal?

8/3 as a decimal is 2.666… (the 6 repeats forever). Divide 8 by 3 to get it.

Q: What is 8/3 as a percent?

8/3 is ≈ 266.67%: multiply the decimal by 100 (move the decimal point two places to the right).

8/3 as a Decimal

8/3 as a decimal is 2.666…, the same as 2 2/3 or about 266.67%.

Result

Answer

\frac{8}{3} = \textcolor{#0b5c56}{2.\overline{6}}

8/3 as a decimal is 2.66666666… – the digit 6 repeats forever.

Rounded to 2 places: 2.67
Rounded to 4 places: 2.6667
Percent: 266.6667%

2 wholes + 2 of 3 equal parts

Step-by-step solution

The problem

\frac{8}{3}

Divide 8 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.
Step Divide Digit Remainder Working
Whole part 8 ÷ 3 2 2 3 × 2 = 6, 8 − 6 = 2
Decimal place 1 20 ÷ 3 6 2 3 × 6 = 18, 20 − 18 = 2
Read off the decimal. A bar over digits means they repeat forever.
= 8 \div 3 = \textcolor{#0b5c56}{2.\overline{6}}

Step	Divide	Digit	Remainder	Working
Whole part	8 ÷ 3	2	2	3 × 2 = 6, 8 − 6 = 2
Decimal place 1	20 ÷ 3	6	2	3 × 6 = 18, 20 − 18 = 2

All the working together

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

8/3 in other forms

Decimal	2.666… (the 6 repeats forever)
Rounded	2.67 (2 places), 2.667 (3 places)
Percent	≈ 266.67%
Mixed number	2 2/3
Equivalent fractions	16/6, 24/9, 32/12, 40/15

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

Fraction	Decimal	Percent
1/3	0.333…	≈ 33.33%
2/3	0.666…	≈ 66.67%
4/3	1.333…	≈ 133.33%
5/3	1.666…	≈ 166.67%
7/3	2.333…	≈ 233.33%
8/3	2.666…	≈ 266.67%

Frequently asked questions

What is 8/3 as a decimal?

8/3 as a decimal is 2.666… (the 6 repeats forever). Divide 8 by 3 to get it.

What is 8/3 as a percent?

8/3 is ≈ 266.67%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 8/3 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.