13/30 as a Decimal

13/30 as a decimal is 0.4333…, with the 3 repeating forever (43.33% rounded).

Result

Answer

\frac{13}{30} = \textcolor{#0b5c56}{0.4\overline{3}}

13/30 as a decimal is 0.433333333… – the digit 3 repeats forever.

  • Rounded to 2 places: 0.43
  • Rounded to 4 places: 0.4333
  • Percent: 43.3333%

43 of 100 squares ≈ 13/30

Step-by-step solution

The problem

\frac{13}{30}

  1. Divide 13 by 30 (long division). Write down how many times 30 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 part13 ÷ 3001330 × 0 = 0, 13 − 0 = 13
    Decimal place 1130 ÷ 3041030 × 4 = 120, 130 − 120 = 10
    Decimal place 2100 ÷ 3031030 × 3 = 90, 100 − 90 = 10

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

    = 13 \div 30 = \textcolor{#0b5c56}{0.4\overline{3}}

All the working together

\begin{aligned} &\frac{13}{30} \\[8pt] &= 13 \div 30 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.4\overline{3}}\end{aligned}

13/30 in other forms

Decimal0.4333… (the 3 repeats forever)
Rounded0.43 (2 places), 0.433 (3 places)
Percent≈ 43.33%
Equivalent fractions26/60, 39/90, 52/120, 65/150

Why it repeats

In lowest terms the denominator is 30 = 2 × 3 × 5. 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 30 as decimals

FractionDecimalPercent
1/300.0333…≈ 3.33%
7/300.2333…≈ 23.33%
11/300.3666…≈ 36.67%
13/300.4333…≈ 43.33%
17/300.5666…≈ 56.67%
19/300.6333…≈ 63.33%
23/300.7666…≈ 76.67%
29/300.9666…≈ 96.67%

Frequently asked questions

What is 13/30 as a decimal?

13/30 as a decimal is 0.4333… (the 3 repeats forever). Divide 13 by 30 to get it.

What is 13/30 as a percent?

13/30 is ≈ 43.33%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 13/30 a terminating or a repeating decimal?

Repeating – the 3 repeats forever. In lowest terms the denominator is 30 = 2 × 3 × 5. 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.