Vamshi8411 wrote:
Which of the following is a terminating decimal, when expressed in decimals?
A. 17/223
B. 13/231
C. 41/3
D. 41/256
E. 35/324
Can we do this just by taking the unit digit in numerator and denominator?
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*5^2. Fraction
\frac{3}{30} is also a terminating decimal, as
\frac{3}{30}=\frac{1}{10} and denominator
10=2*5.
BACK TO THE QUESTION:
\frac{41}{256}=\frac{41}{2^8}, denominator has only prime factor 2 in its prime factorization, hence this fraction will be terminating decimal.
All other fractions (after reducing, if possible) have primes other than 2 and 5 in its prime factorization, hence they will be repeated decimals.
Answer: D.
For more check Number Theory chapter of Math Book:
math-number-theory-88376.htmlHope it helps..
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41% (01:42) correct
