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 (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.)
Questions testing this concept:
700-question-94641.html?hilit=terminating%20decimalis-r-s2-is-a-terminating-decimal-91360.html?hilit=terminating%20decimalpl-explain-89566.html?hilit=terminating%20decimalwhich-of-the-following-fractions-88937.html?hilit=terminating%20decimalBACK TO THE ORIGINAL QUESTION:Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 12, 0.13, and 4.068 are three terminating decimals. If j and k are positive integers and the ratio j/k is expressed as a decimal, is j/k a terminating decimal?(1)
k = 3 --> now, if
j=3p (j is a multiple of 3) then
\frac{j}{k}=\frac{3p}{3}=p=integer=terminating \ decimal but if
j is not a multiple of 3 then reduced fraction
\frac{j}{k}=\frac{j}{3} won't be a terminating decimal, as denominator has primes other than 2 and/or 5. Not sufficient.
(2)
j is an odd multiple of 3 -->
j=3(2k+1), clearly insufficient as no info about the denominator
k.
(1)+(2)
\frac{j}{k}=\frac{3(2k+1)}{3}=2k+1=integer=terminating \ decimal. Sufficient.
Answer: C.
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