Without actually performing the long division, tell whether the following statement is true or false.
The rational number $232352$ will have a terminating decimal expansion.

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True

False

answer is A.

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Detailed Solution

Given a statement the rational number

232352

will have a terminating decimal expansion.
Firstly, finding the prime factors of denominator,

= 23 23 × 52 = 23 × 5 23 × 52 × 5 = 23 × 5 23 × 53

Since, denominator is of the form

2 n × 5 n

,
The number

232352

is having terminating decimal expansion.
Hence, the statement is true.
Therefore, option 1 is correct.

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