Terminating Decimals Calculator

What Is a Terminating Decimal?

A terminating decimal is a decimal expansion that ends after a finite number of digits. A rational number has a terminating decimal if and only if, in lowest terms, its denominator has no prime factors other than 2 and 5. For example, $\frac{7}{8} = 0.875$ terminates, while $\frac{1}{3} = 0.333\ldots$ repeats forever.

For more fraction tools, see our Fraction to Decimal Calculator and Decimal to Fraction Calculator.

How to Tell If a Decimal Terminates

Simplify the fraction $\frac{p}{q}$, then factor $q$:

$$q = 2^a \cdot 5^b \cdot (\text{other primes})$$

If no other primes appear, the decimal terminates. Otherwise it repeats with a cycle.

Worked Example

For $\frac{12}{15}$, simplify to $\frac{4}{5}$. Since $5 = 5^1$, the decimal terminates: $\frac{4}{5} = 0.8$.