prashantbacchewar wrote:
Hi Bunuel
As per your explanation if the denominator is not in the form of 2^n 5^m then the fraction will be terminal decimal. If you look at the denominator of other answer choices they are also not in the above form
1. 189 = 3^3 *7^1
2. 196 = 2^2 * 7^2
3. 225 = 3^2 * 5^2
4. 144 = 2^4 * 3^2
So how the last answer choice is correct still not clear based on your explanation?
As per solution:
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.
A.
\frac{10}{189}=\frac{10}{3^3*7} --> denominator has primes other than 2 and 5 in its prime factorization, hence it's repeated
decimal;
B.
\frac{15}{196}=\frac{15}{2^2*7^2} --> denominator has primes other than 2 and 5 in its prime factorization, hence it's repeated
decimal;
C.
\frac{16}{225}=\frac{16}{3^2*5^2} --> denominator has primes other than 2 and 5 in its prime factorization, hence it's repeated
decimal;
D.
\frac{25}{144}=\frac{25}{2^4*3^2} --> denominator has primes other than 2 and 5 in its prime factorization, hence it's repeated
decimal.
E.
\frac{39}{128}=\frac{39}{2^7}, denominator has only prime factor 2 in its prime factorization, hence this fraction
will be terminating decimal.
All other fractions' denominator have primes other than 2 and 5 in its prime factorization, hence they WILL BE repeated decimals:Hope it's clear.
Answer: E.
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33% (01:02) correct
