Terminating Decimal Calculator
Check if a fraction produces a terminating or repeating decimal
Understanding Terminating Decimals
A terminating decimal is a decimal that ends after a finite number of digits. Whether a fraction produces a terminating or repeating decimal depends on the prime factors of its denominator.
The Terminating Decimal Rule
A fraction in simplest form will produce a terminating decimal if and only if the denominator's only prime factors are 2 and/or 5.
This is because 10 = 2 × 5, and our decimal system is base 10.
Examples
Terminating: 3/8
8 = 2³, only contains factor 2 → 0.375 (terminates)
Terminating: 7/20
20 = 2² × 5, only contains factors 2 and 5 → 0.35 (terminates)
Repeating: 1/3
3 = 3, contains factor 3 → 0.333... (repeats)
Repeating: 5/6
6 = 2 × 3, contains factor 3 → 0.8333... (repeats)
Common Terminating Fractions
Common Repeating Fractions
Frequently Asked Questions
What is a terminating decimal?
A terminating decimal is a decimal that ends after a finite number of digits, like 0.5, 0.25, or 0.375. It doesn't go on forever.
How can you tell if a fraction will terminate?
Simplify the fraction first, then check the denominator's prime factors. If they're only 2 and/or 5, it terminates. If there are any other prime factors, it repeats.
Why do only factors of 2 and 5 result in terminating decimals?
Because our decimal system is base 10, and 10 = 2 × 5. Denominators with only these factors can be expressed as exact powers of 10, which terminate.
Can a fraction be both terminating and repeating?
No, a fraction (in simplest form) is either terminating or repeating, never both. The prime factorization of the denominator determines which type it is.
What if the fraction isn't in simplest form?
Always simplify the fraction first before checking. For example, 6/12 simplifies to 1/2, which terminates (0.5), even though 12 has factor 3.
Are all whole numbers terminating decimals?
Yes, whole numbers are terminating decimals. For example, 5 = 5.0. They can be thought of as having denominator 1, which has no prime factors.