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Question

# Which of the following is terminating decimal?2390,111148,29145,16

A
111148
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B
2390
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C
29145
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D
16
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Solution

## The correct options are A 111148 D 29145Recall that in order for the decimal expansion of a fraction to terminate, the fraction's denominator, in fully reduced form, must have a prime factorization that consists of only 2's and/or 5's. In fully reduced form, the denominator in A is 4 ,composed of only 2's, (4=22). In fully reduced form, the denominator in C is 5, composed of only 5's, (5=51). Hence, they have terminating decimals 0.75 and 0.2, respectively.By contrast, the denominator in B has prime factors other than 2's and 5's (90=5×2××32),and the fraction in D has the denominator 6, composed of prime factors other than 2's and 5's (6=2×3).Therefore, options A and C are the correct answers.

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