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Fraction to Decimal Converter

Convert any fraction to its decimal equivalent with detailed explanation.

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Fraction to Decimal Converter

Convert any fraction to its decimal equivalent with detailed explanation.

Key values: 3/4 · = 0.75

Convert 1/3 to a Decimal

A fraction that produces a repeating decimal — useful to recognise in data.

Key values: 1/3 · = 0.333...

Documentation

Converting Fractions to Decimals

To convert $\frac{a}{b}$ to a decimal, divide the numerator by the denominator: $a \div b$ . The result either terminates (ends) or eventually repeats in a cycle.

The Long Division Method

Convert $\frac{3}{8}$ by dividing 3 by 8:

$3 \div 8 = 0$ remainder $3$ . Write $0.$ and bring down a zero: $30$ .
$30 \div 8 = 3$ remainder $6$ . Write $3$ , bring down: $60$ .
$60 \div 8 = 7$ remainder $4$ . Write $7$ , bring down: $40$ .
$40 \div 8 = 5$ remainder $0$ . Write $5$ . Done — no remainder.

\frac{3}{8} = 0.375

When Decimals Repeat

If the remainder never reaches 0, the decimal repeats. Since there are only $b - 1$ possible nonzero remainders when dividing by $b$ , the cycle must begin within $b$ steps.

The repeating block is written with an overline:

\frac{1}{7} = 0.\overline{142857}

Cycle Length Patterns

Fraction	Decimal	Cycle length
$\frac{1}{3}$	$0.\overline{3}$	1
$\frac{1}{6}$	$0.1\overline{6}$	1 (after 1 non-repeating digit)
$\frac{1}{7}$	$0.\overline{142857}$	6
$\frac{1}{11}$	$0.\overline{09}$	2
$\frac{1}{13}$	$0.\overline{076923}$	6
$\frac{1}{37}$	$0.\overline{027}$	3

The cycle length of $\frac{1}{p}$ for a prime $p$ always divides $p - 1$ . For $p = 7$ , the cycle length is 6, which equals $7 - 1$ — the maximum possible. Primes where the cycle length equals $p - 1$ are called full reptend primes.

Common Fraction-Decimal Equivalences

Fraction	Decimal	Percent
$\frac{1}{2}$	0.5	50%
$\frac{1}{3}$	$0.\overline{3}$	33.3%
$\frac{1}{4}$	0.25	25%
$\frac{1}{5}$	0.2	20%
$\frac{1}{8}$	0.125	12.5%
$\frac{2}{3}$	$0.\overline{6}$	66.7%
$\frac{3}{4}$	0.75	75%

Memorizing these common equivalences helps with mental math — knowing that $\frac{1}{8} = 0.125$ lets you quickly compute that $\frac{3}{8} = 3 \times 0.125 = 0.375$ .

Mixed Numbers to Decimals

For a mixed number like $3\frac{5}{8}$ , convert only the fractional part and add the whole number:

3\frac{5}{8} = 3 + \frac{5}{8} = 3 + 0.625 = 3.625

Alternatively, convert to an improper fraction first: $3\frac{5}{8} = \frac{29}{8} = 29 \div 8 = 3.625$ .

Frequently Asked Questions

How do I convert a fraction to a decimal?

Divide the numerator by the denominator using long division: $\frac{a}{b} = a \div b$ . For example, $\frac{3}{8} = 3 \div 8 = 0.375$ . The result either terminates (finite digits) or repeats in a cycle.

How can I tell if a fraction will produce a terminating or repeating decimal?

A fraction in lowest terms terminates if and only if the denominator has no prime factors other than 2 and 5. So $\frac{1}{8}$ ( $8 = 2^3$ ) terminates as 0.125, but $\frac{1}{3}$ repeats as $0.333\ldots$ because 3 is not 2 or 5.

What does the overline notation mean in a repeating decimal?

The overline marks the repeating block. For example, $\frac{1}{7} = 0.\overline{142857}$ , meaning those six digits repeat forever.

How do I convert a mixed number like 3 5/8 to a decimal?

Convert only the fractional part and add the whole number: $\frac{5}{8} = 0.625$ , so $3\frac{5}{8} = 3.625$ . Alternatively, convert to an improper fraction first: $3\frac{5}{8} = \frac{29}{8} = 29 \div 8 = 3.625$ .

What is a full reptend prime?

A full reptend prime is a prime $p$ where the decimal expansion of $\frac{1}{p}$ has the maximum possible cycle length of $p - 1$ . For example, 7 is a full reptend prime because $\frac{1}{7} = 0.\overline{142857}$ has a cycle length of $6 = 7 - 1$ .