What is a terminating decimal?

Answer 1

A terminating decimal number is a decimal number with a finite number of digits after the decimal point. For example: 95.3652

It is an exact multiple of a (positive or negative) power of 10. For example: 95.3652 can be written as an exact fraction of 953652 / 10000, or 953652 * 10-4.

Rational numbers where the simplified denominator is not a factor of a power of 10 (i.e. where the denominator has factors that aren't divisible by 2 or 5, and are not common to the numerator) are not terminating decimals.

For example:

- 1/3 (0.333333.....) does not terminate - the sequence of '3's repeats endlessly. Notice that the denominator is a multiple of 3 (and the numerator isn't), so it does not divide any power of 10.

- 103/70 (1.4714285714285...) does not terminate. The sequence of numbers '714285' repeats endlessly. The denominator does have 2 and 5 as factors, but also 7 (which is not a factor of the numerator), so it does not divide a power of 10.

Irrational Numbers (such as π=3.14159265.....), are also not terminating decimals. There is an infinite number of numbers after the decimal point, but unlike fractions, there is no infinitely recurring sequence.