Definition
Terminating decimal
A terminating decimal is a decimal that stops after a finite number of decimal places.
What it means
When you divide to write a fraction as a decimal, the digits of a terminating decimal eventually stop. You can imagine the decimal reaching a finish line: after its last needed digit, every later place is zero. Denominators built only from factors 2 and 5 can be changed into a power of 10, which is why their decimal divisions finish.
Remember it
A terminating decimal reaches a finish line: after the last needed digit, only zeros follow.
Example
For 7/40, the denominator is 40 = 2 × 2 × 2 × 5, so it uses only factors 2 and 5. Dividing gives 7/40 = 0.175, and the decimal stops after three places.
Watch for
The decimal for 1/3 is 0.333…; the 3s continue forever, so it is recurring, not terminating.
Common mix-up
Terminating does not mean trailing zeros are forbidden. The numbers 0.5, 0.50, and 0.500 are the same terminating decimal value.
Exact meaning
A terminating decimal is a decimal representation that ends after finitely many decimal places; zeros may follow without changing the value. A fraction in simplest form has a terminating decimal exactly when its denominator has no prime factors other than 2 and 5.