sanjib wrote:Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?
(1) 90 < r < 100
(2) s = 4
terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?
(1) 90 < r < 100
(2) s = 4

I need the explanation please that why the answer is straight B

A fraction will always be a terminating decimal if in its reduced form it has a denominator with only 2 or 5 as its prime factors.

This is because to convert a fraction say p/q to a terminating decimal, we need to convert it to an equivalent fraction with an integer in the numerator and a non-negative power of 10 in the denominator. Here, note that 10 = 2 * 5.

To illustrate with an example, let p/q = 3/8.
Now, let us check a power of 10 that 8 divides.
The smallest is 1000. Also, 1000/8 = 125.
So 3/8 = (125*3)/1000 = 375/1000 = 0.375
Or 3/8 is a terminating decimal.
Note that 8 = 2^3.
So 8 has 2 as its prime factor.

In the above question, (2) tells us that denominator of the fraction is 4.
Now 4 = 2^2.
Also 4 divides 100 = 10^2.
So r/4 = (r*25)/100 = terminating decimal.
Or (2) alone is sufficient.