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Tell whether the following statement is true or false:

The rational number $278$ have terminating decimal expansion.

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True

False

answer is A.

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Detailed Solution

We need to check whether the rational number

278

have terminating decimal expansion. Assume

x = 278

.
Compare with

x = p q

,
Therefore, p = 27 and q = 8.
If the factors of the denominator of the given rational number is of form

2 m 5 n,

where n and m are non-negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.
Writing denominator in the form of

2 m 5 n

,
Factors of the denominator are,

= 23 ​ ​ × ​ ​ 50

It is of the form

2 m 5 n

.
Hence,

278

has a terminating decimal expansion.
Given statement is true.
Hence, option 1 is correct.

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