# Terminating Decimals Calculator

URL: https://speedycalculator.com/calculators/math/terminating-decimals/
Last updated: 2026-10-30

> The terminating decimals calculator tells you whether a fraction gives a terminating or a repeating decimal, explains why from the prime factors of the denominator, and shows the exact decimal with its repeating block.

## Inputs

- Numerator
- Denominator

## Results

- Terminating or repeating?
- Decimal expansion
- Why
- Fraction in lowest terms

## Formula

```
n/d in lowest terms terminates ⇔ d = 2ᵃ × 5ᵇ
```

## Explanation

Some fractions end (3/8 = 0.375), others repeat forever (1/7 = 0.142857142857…). The difference depends only on the denominator: in base 10 a fraction terminates exactly when the denominator has no prime factors other than 2 and 5.

### How to use the Terminating Decimals Calculator

- **Numerator**
- **Denominator**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

The fraction is reduced, the denominator is factorised and the decimal expansion is computed by exact long division, with the repeating part shown in brackets.

## Worked example

Inputs — Numerator: 3; Denominator: 12.

Results — **Terminating or repeating? = Terminating decimal**; Decimal expansion = 0.25; Why = In lowest terms the denominator is 4, whose only prime factors are 2 and 5, so the decimal ends.; Fraction in lowest terms = 1/4.

## Key terms

- **Terminating decimal**: A decimal with finitely many digits.
- **Repeating decimal**: A decimal with a block that repeats forever.

## FAQ

**Does 1/3 terminate?**
No – 0.333… repeats because 3 is not 2 or 5.

**Does 7/20 terminate?**
Yes – 20 = 2² × 5, giving 0.35.

**How long can the repeating block be?**
At most d − 1 digits for denominator d.

**Is a repeating decimal rational?**
Yes, always.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Repeating decimal](https://mathworld.wolfram.com/RepeatingDecimal.html)