11/24 as a Decimal – 0.458333… (with Steps)

Q: What is 11/24 as a decimal?

11/24 as a decimal is 0.458333… (the 3 repeats forever). Divide 11 by 24 to get it.

Q: What is 11/24 as a percent?

11/24 is ≈ 45.83%: multiply the decimal by 100 (move the decimal point two places to the right).

11/24 as a Decimal

11/24 as a decimal is 0.458333…, with the 3 repeating forever (45.83% rounded).

Result

Answer

\frac{11}{24} = \textcolor{#0b5c56}{0.458\overline{3}}

11/24 as a decimal is 0.45833333333… – the digit 3 repeats forever.

Rounded to 2 places: 0.46
Rounded to 4 places: 0.4583
Percent: 45.8333%

46 of 100 squares ≈ 11/24

Step-by-step solution

The problem

\frac{11}{24}

Divide 11 by 24 (long division). Write down how many times 24 goes in, carry the remainder, add a 0 and divide again. The remainder 8 came back, so the digits from decimal place 4 on repeat forever.

Step	Divide	Digit	Remainder	Working
Whole part	11 ÷ 24	0	11	24 × 0 = 0, 11 − 0 = 11
Decimal place 1	110 ÷ 24	4	14	24 × 4 = 96, 110 − 96 = 14
Decimal place 2	140 ÷ 24	5	20	24 × 5 = 120, 140 − 120 = 20
Decimal place 3	200 ÷ 24	8	8	24 × 8 = 192, 200 − 192 = 8
Decimal place 4	80 ÷ 24	3	8	24 × 3 = 72, 80 − 72 = 8

Read off the decimal. A bar over digits means they repeat forever.
= 11 \div 24 = \textcolor{#0b5c56}{0.458\overline{3}}

All the working together

\begin{aligned} &\frac{11}{24} \\[8pt]  &= 11 \div 24 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt]  &= \textcolor{#0b5c56}{0.458\overline{3}}\end{aligned}

11/24 in other forms

Decimal	0.458333… (the 3 repeats forever)
Rounded	0.46 (2 places), 0.458 (3 places)
Percent	≈ 45.83%
Equivalent fractions	22/48, 33/72, 44/96, 55/120

Why it repeats

In lowest terms the denominator is 24 = 2³ × 3. 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 24 as decimals

Fraction	Decimal	Percent
1/24	0.041666…	≈ 4.17%
5/24	0.208333…	≈ 20.83%
7/24	0.291666…	≈ 29.17%
11/24	0.458333…	≈ 45.83%
13/24	0.541666…	≈ 54.17%
17/24	0.708333…	≈ 70.83%
19/24	0.791666…	≈ 79.17%
23/24	0.958333…	≈ 95.83%

Frequently asked questions

What is 11/24 as a decimal?

11/24 as a decimal is 0.458333… (the 3 repeats forever). Divide 11 by 24 to get it.

What is 11/24 as a percent?

11/24 is ≈ 45.83%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 11/24 a terminating or a repeating decimal?

Repeating – the 3 repeats forever. In lowest terms the denominator is 24 = 2³ × 3. 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.