5/3 as a Decimal

5/3 as a decimal is 1.666…, the same as 1 2/3 or about 166.67%.

Result

Answer

\frac{5}{3} = \textcolor{#0b5c56}{1.\overline{6}}

5/3 as a decimal is 1.66666666… – the digit 6 repeats forever.

  • Rounded to 2 places: 1.67
  • Rounded to 4 places: 1.6667
  • Percent: 166.6667%

1 whole + 2 of 3 equal parts

Step-by-step solution

The problem

\frac{5}{3}

  1. Divide 5 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 part5 ÷ 3123 × 1 = 3, 5 − 3 = 2
    Decimal place 120 ÷ 3623 × 6 = 18, 20 − 18 = 2

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

    = 5 \div 3 = \textcolor{#0b5c56}{1.\overline{6}}

All the working together

\begin{aligned} &\frac{5}{3} \\[8pt] &= 5 \div 3 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{1.\overline{6}}\end{aligned}

5/3 in other forms

Decimal1.666… (the 6 repeats forever)
Rounded1.67 (2 places), 1.667 (3 places)
Percent≈ 166.67%
Mixed number1 2/3
Equivalent fractions10/6, 15/9, 20/12, 25/15

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

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 5/3 as a decimal?

5/3 as a decimal is 1.666… (the 6 repeats forever). Divide 5 by 3 to get it.

What is 5/3 as a percent?

5/3 is ≈ 166.67%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 5/3 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.