THEORY:
Reduced fraction
\frac{a}{b} (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal
if and only b (the denominator) is of the form
2^n5^m, where
m and
n are non-negative integers. For example:
\frac{7}{250} is a terminating decimal
0.028, as
250 (denominator) equals to
2*5^3. Fraction
\frac{3}{30} is also a terminating decimal, as
\frac{3}{30}=\frac{1}{10} and denominator
10=2*5.
Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.For example
\frac{x}{2^n5^m}, (where x, n and m are integers) will always be terminating decimal.
(We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction
\frac{6}{15} has 3 as prime in denominator and we need to know if it can be reduced.)
BACK TO THE QUESTION:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?(1) 90 < r < 100. Nothing about the denominator. Not sufficient.
(2) s = 4. According to the above, any fraction r/4=r/2^2 when expressed as a decimal will be a terminating decimal. Sufficient.
Answer: B.
Questions testing this concept:
700-question-94641.htmlis-r-s2-is-a-terminating-decimal-91360.htmlpl-explain-89566.htmlwhich-of-the-following-fractions-88937.htmlHope it helps.
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