Question

Classify the decimal expansion of each fraction as a terminating decimal or a repeating decimal.

Answer 1

A repeating decimal is a decimal that has a digit, or a group of digits, that repeat forever. A terminating decimal, on the other hand, is a decimal that ends. To find which decimals are repeating and which ones are terminal, we are going to simplify our fractions, and express them in decimal form:
$\frac{25}{60} = \frac{5}{12} =0.4166666666...$ 6 is repeating forever, so this is a repeating decimal.

$\frac{17}{60} =0.283333333....$ 3 is repeating forever, so this is a repeating decimal.

$\frac{31}{44} =07045454545....$ 45 is repeating forever, so this is a repeating decimal.

$\frac{54}{72} = \frac{3}{4} =0.75$ No digit is repeating forever, so this is a terminating decimal.

We can conclude that:
Repeating decimals: $\frac{25}{60}$, $\frac{17}{60}$, and $\frac{31}{44}$
Terminating decimals: $\frac{54}{72}$

Answer 2

Repeating decimals:25/60 17/60 31/44
Terminating decimals: 54/72