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 A111148 D29145
Recall 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 inC 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.