Question

Item 5
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 56/72 /21/22 /11/121 60/120

Answer 1

repeating decimals: 56/72,21/22

terminating decimals : 11/121,60/120

Answer 2

Given : Few Fractions 56/72 , 21/22 , 11/121 , 60/120

To find : Classify fraction as a terminating decimal or a repeating decimal.

Solution:

A simple fraction is terminating decimal

if denominator has only prime factors 2 & 5

A simple fraction is non terminating / repeating  decimal

if denominator has any prime factor other than 2 & 5

56/72

= 7/9

= 7/(3 * 3)

3 is a factor other than 2 & 5

Hence 56/72 non terminating  / repeating decimal

21/22

= (3 * 7)/(2 * 11)

11 is a factor other than 2 & 5

Hence 21/22 non terminating  / repeating decimal

11/121

= 1/11

11 is a factor other than 2 & 5

Hence 11/121 non terminating  / repeating decimal

60/120

= 1/2

2 is only factor in denominator

=> 60/120 is a terminating decimal

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