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
Answers
repeating decimals: 56/72,21/22
terminating decimals : 11/121,60/120
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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