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Question

# Which of the following fractions will terminate when expressed as a decimal? (Choose all that apply.)

A
1256
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B
27100
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C
10027
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D
231660
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E
7105
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Solution

## The correct options are B 1256 C 231660 D 27100Recall 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. The denominator in A is composed of only 2's, (256=28). The denominator in B is composed of only 2's and 5's, (100=22×52). In fully reduced form, the fraction in D is equal to 720 and the denominator 20 is composed of only 2's and 5's (20=22×5).By contrast, the denominator in C has prime factors other than 2's and 5's (27=33), and in fully reduced form, the fraction in E is equal to 115, and 15 has a prime factor other than 2's and 5's (15=3×5).Therefore, options A, B and D are the correct answers.

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