How this calculation works
Cancellation can change the result. The fraction 3/6 reduces to 1/2 and terminates even though 6 contains a factor of 3.
THE FORMULA
Reduce a/b. A decimal terminates when the remaining denominator has only 2 and 5 as prime factors.A worked example
3/40 terminates because 40 = 2³ × 5.
Good to know
The test applies to decimal notation.
Reference: OpenStax Prealgebra (opens in a new tab) ↗
Read the result
Decide whether a fraction has a finite base-ten expansion by inspecting its reduced denominator.
The primary result is labeled “Decimal type”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The test applies to decimal notation.
For a related exercise, try the fraction calculator.
A few questions, answered
How can I check the default inputs by hand?
3/40 terminates because 40 = 2³ × 5.
Which rule does this calculator apply?
Reduce a/b. A decimal terminates when the remaining denominator has only 2 and 5 as prime factors.