Fraction to Decimal Converter
Convert any fraction — proper, improper or mixed — into its decimal equivalent. Choose how many decimal places to display, and see whether the decimal terminates or repeats. Every conversion shows the division step so you can verify the result.
Enter a fraction
Enter a fraction and press Convert.
How fraction-to-decimal conversion works
A fraction is simply a division: a/b means a ÷ b.
Converting to a decimal is therefore one division operation. The interesting
part is what happens after the division — the decimal either terminates
(stops) or repeats forever.
Terminating decimals
A fraction in lowest terms produces a terminating decimal only if its denominator has no prime factors other than 2 and 5. For example:
1/4 = 0.25— denominator 4 = 2²3/8 = 0.375— denominator 8 = 2³7/20 = 0.35— denominator 20 = 2² × 5
Repeating decimals
If the denominator in lowest terms contains any prime factor other than 2 or 5, the decimal will repeat:
1/3 = 0.333…1/6 = 0.1666…1/7 = 0.142857142857…
The repeating block can be any length up to b − 1 digits, where
b is the denominator. 1/7 has a six-digit repeat;
1/97 has a 96-digit repeat.
Common fraction-to-decimal conversions
| Fraction | Decimal | Type |
|---|---|---|
| 1/2 | 0.5 | Terminating |
| 1/3 | 0.333… | Repeating |
| 1/4 | 0.25 | Terminating |
| 1/5 | 0.2 | Terminating |
| 1/6 | 0.1666… | Repeating |
| 1/8 | 0.125 | Terminating |
| 1/9 | 0.111… | Repeating |
| 1/10 | 0.1 | Terminating |
| 2/3 | 0.666… | Repeating |
| 3/4 | 0.75 | Terminating |
| 5/6 | 0.8333… | Repeating |
| 7/8 | 0.875 | Terminating |
Worked examples
Example 1 — Simple terminating fraction
Convert 3/4 to a decimal.
3 ÷ 4 = 0.75. The division stops because the remainder is zero.
3/4 = 0.75
Example 2 — Repeating fraction
Convert 1/3 to a decimal.
1 ÷ 3 = 0.333…. The remainder 1 repeats indefinitely, so the
digit 3 recurs forever.
1/3 = 0.333… (repeating)
Example 3 — Mixed number
Convert 2 ½ to a decimal.
Convert to improper fraction: 5/2. Divide: 5 ÷ 2 = 2.5.
2 ½ = 2.5
Example 4 — Long repeating pattern
Convert 1/7 to a decimal.
1 ÷ 7 = 0.142857142857…. The block 142857 repeats.
1/7 = 0.142857142857… (repeating)
Common mistakes
-
Reading a repeating decimal as terminating.
1/3 = 0.333…and 0.333 are not the same number. The decimals shown are truncated for display, but the underlying value is a repeating fraction. -
Assuming "long" decimals terminate.
Some fractions have very short repeating patterns (like
1/9 = 0.111…), while others have long ones (1/97has a 96-digit pattern). The length of the display does not indicate whether a decimal terminates. -
Confusing the numerator and denominator.
3/4means "3 divided by 4" (0.75), not "4 divided by 3" (1.333…). The top number always divides the bottom. -
Forgetting to handle the whole part of a mixed number.
2 ½is2.5, not0.5and not2.05. The whole part is added to the fractional part after conversion.
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Frequently asked questions
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. For a mixed number, first convert to an improper fraction, then divide.
Reduce the fraction to lowest terms, then factor the denominator. If its only prime factors are 2 and 5, the decimal terminates. If any other prime factor appears, the decimal repeats.
The converter analyses the prime factors of the denominator in lowest terms. If they include any prime other than 2 or 5, the decimal is flagged as repeating and the exact display is truncated at the selected precision.
Yes. Enter the minus sign in the numerator (for example, −3/4). The whole number can also be negative for mixed numbers.
Repeating decimals cannot be displayed in full. The converter rounds to the precision you selected. Increasing the precision shows more digits of the repeating pattern but never the entire sequence.