Re: Which of the following is a terminating decimal, when

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.

Is it only limited to 2^m * 5^n or we can try try to break it in 2^m * 3^n as well??

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.html

Hope it helps..