23/30 as a Decimal

23/30 as a decimal is 0.7666…, with the 6 repeating forever (76.67% rounded).

Result

Answer

\frac{23}{30} = \textcolor{#0b5c56}{0.7\overline{6}}

23/30 as a decimal is 0.766666666… – the digit 6 repeats forever.

  • Rounded to 2 places: 0.77
  • Rounded to 4 places: 0.7667
  • Percent: 76.6667%

77 of 100 squares ≈ 23/30

Step-by-step solution

The problem

\frac{23}{30}

  1. Divide 23 by 30 (long division). Write down how many times 30 goes in, carry the remainder, add a 0 and divide again. The remainder 20 came back, so the digits from decimal place 2 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part23 ÷ 3002330 × 0 = 0, 23 − 0 = 23
    Decimal place 1230 ÷ 3072030 × 7 = 210, 230 − 210 = 20
    Decimal place 2200 ÷ 3062030 × 6 = 180, 200 − 180 = 20

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

    = 23 \div 30 = \textcolor{#0b5c56}{0.7\overline{6}}

All the working together

\begin{aligned} &\frac{23}{30} \\[8pt] &= 23 \div 30 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.7\overline{6}}\end{aligned}

23/30 in other forms

Decimal0.7666… (the 6 repeats forever)
Rounded0.77 (2 places), 0.767 (3 places)
Percent≈ 76.67%
Equivalent fractions46/60, 69/90, 92/120, 115/150

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 6 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 23/30 as a decimal?

23/30 as a decimal is 0.7666… (the 6 repeats forever). Divide 23 by 30 to get it.

What is 23/30 as a percent?

23/30 is ≈ 76.67%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 23/30 a terminating or a repeating decimal?

Repeating – the 6 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 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.