bulletpoint wrote:
Which of the following has a decimal equivalent that is a terminating decimal?
I. 1/12
II. 1/10^2
III. 1/2^10
A. I only
B. II only
C. I and II
D. I and III
E. II and III
When solving this problem, we should remember that there is a special property about fractions that allows their decimal equivalents to terminate. This property states:
“In its most-reduced form, any fraction with a denominator whose prime factorization contains only 2s, only 5s, or both 2s and 5s, produces decimals that terminate. A denominator with any other prime factors produces decimals that do not terminate.”
Let’s consider each of the Roman numerals and determine which fractions have only 2s, 5s, or both as prime factors.
I. 1/12
Since 1/12 = 1/(3 x 2^2), 1/12 is NOT a terminating decimal.
II. 1/10^2
Since 1/10^2 = 1(2^2 x 5^2), 1/10^2 IS a terminating decimal.
III. 1/2^10
1/2^10 IS a terminating decimal.
Answer: E
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