Question

Which fraction has a terminating decimal? - 11/19 - 4/7 - 1/3 - 3/150

Answer 1

Answer: D) 3/150

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Explanation:

With the use of a calculator, we see that,

• 11/19 = 0.57894736842106...., the decimals eventually repeat; but unfortunately my calculator ran out of room to show the repeating portion
• 4/7 = 0.5714285714285714..., the block "571428" repeats forever
• 1/3 = 0.333333.... the 3s go on forever
• 3/150 = 0.02

So 3/150 converts to the terminating decimal 0.02

The word "terminate" means "stop". In the other decimal values, the decimal digits go on forever repeating the patterns mentioned.

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A non-calculator approach will have us simplify 3/150 into 1/50 after dividing both parts by the GCF 3. Then notice how 50 has the prime factorization of 2*5*5. The fact that the denominator 50 can be factored in terms of only 2's and 5's is enough evidence to conclude that the fraction converts to a terminating decimal.

If the denominator factors into some other primes, other than 2s and 5s, then we don't have a terminating decimal. So that's why 11/19, 4/7 and 1/3 convert to non-terminating decimals.