Question

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

Drag and drop the fractions into the boxes to correctly complete the table.



Terminating Decimal               Repeating Decimal



25/60            17/60             31/44         54/72

Answer 1

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

Answer 2

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:

`(25)/(60) = (5)/(12) =0.4166666666...` 6 is repeating forever, so this is a repeating decimal.


`(17)/(60) =0.283333333....` 3 is repeating forever, so this is a repeating decimal.


`(31)/(44) =07045454545....` 45 is repeating forever, so this is a repeating decimal.


`(54)/(72) = (3)/(4) =0.75` No digit is repeating forever, so this is a terminating decimal.

We can conclude that:
Repeating decimals:
`(25)/(60)`,
`(17)/(60)`, and
`(31)/(44)`
Terminating decimals:
`(54)/(72)`