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Q.


Without actually performing the long division, tell whether the following statement is true or false.

The rational number 23 2 3 5 2   will have a terminating decimal expansion.


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a

True

b

False 

answer is A.

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Detailed Solution

Given a statement the rational number 23 2 3 5 2   will have a terminating decimal expansion.
Firstly, finding the prime factors of denominator,
= 23 2 3 × 5 2 = 23×5 2 3 × 5 2 ×5 = 23×5 2 3 × 5 3  
Since, denominator is of the form 2 n × 5 n  ,
The number 23 2 3 5 2    is having terminating decimal expansion.
Hence, the statement is true.
Therefore, option 1 is correct.
 
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