7/15 as a Decimal

7/15 as a decimal is 0.4666…, with the 6 repeating forever (46.67% rounded).

Result

Answer

\frac{7}{15} = \textcolor{#0b5c56}{0.4\overline{6}}

7/15 as a decimal is 0.466666666… – the digit 6 repeats forever.

  • Rounded to 2 places: 0.47
  • Rounded to 4 places: 0.4667
  • Percent: 46.6667%

47 of 100 squares ≈ 7/15

Step-by-step solution

The problem

\frac{7}{15}

  1. Divide 7 by 15 (long division). Write down how many times 15 goes in, carry the remainder, add a 0 and divide again. The remainder 10 came back, so the digits from decimal place 2 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part7 ÷ 150715 × 0 = 0, 7 − 0 = 7
    Decimal place 170 ÷ 1541015 × 4 = 60, 70 − 60 = 10
    Decimal place 2100 ÷ 1561015 × 6 = 90, 100 − 90 = 10

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

    = 7 \div 15 = \textcolor{#0b5c56}{0.4\overline{6}}

All the working together

\begin{aligned} &\frac{7}{15} \\[8pt] &= 7 \div 15 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.4\overline{6}}\end{aligned}

7/15 in other forms

Decimal0.4666… (the 6 repeats forever)
Rounded0.47 (2 places), 0.467 (3 places)
Percent≈ 46.67%
Equivalent fractions14/30, 21/45, 28/60, 35/75

Why it repeats

In lowest terms the denominator is 15 = 3 × 5. 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 15 as decimals

FractionDecimalPercent
1/150.0666…≈ 6.67%
2/150.1333…≈ 13.33%
3/150.220%
4/150.2666…≈ 26.67%
5/150.333…≈ 33.33%
6/150.440%
7/150.4666…≈ 46.67%
8/150.5333…≈ 53.33%
9/150.660%
10/150.666…≈ 66.67%
11/150.7333…≈ 73.33%
12/150.880%
13/150.8666…≈ 86.67%
14/150.9333…≈ 93.33%

Frequently asked questions

What is 7/15 as a decimal?

7/15 as a decimal is 0.4666… (the 6 repeats forever). Divide 7 by 15 to get it.

What is 7/15 as a percent?

7/15 is ≈ 46.67%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 7/15 a terminating or a repeating decimal?

Repeating – the 6 repeats forever. In lowest terms the denominator is 15 = 3 × 5. 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.