TriColor wrote:
Please, explain your answer. Thank you,
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Q15:
Which of the following fractions has a decimal equivalent that is a terminating decimal?
A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128
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:As \(128=2^7\), then \(\frac{39}{128}\) will be terminating decimal.
Answer: E.
Hope it helps.
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