rrobiinn wrote:The question is for beyond my intuition. Need help. Please break it down as small parts as possible.
Which of the following fractions will terminate when expressed as a decimal?(Choose all
that apply.)
(A) 1/246
(B) 27/100
(C) 100/27
(D) 231/660
(E) 7/105
Hi!
A terminating decimal is one that ends, i.e. doesn't infinitely repeat.
For example, 1.4, 8, 32.888991 and 27.6 are all terminating decimals.
Some fractions can be turned into terminating decimals, some can't. For example, 1/3 is .33333 (going on forever). 1/5 is .2, which is terminating.
As 1947 aptly notes, the rule for when a decimal will terminate is simple:
if the denominator of the reduced fraction can be expressed as a product of only 2s and 5s, then the decimal will terminate; if the denominator has any other primes in its factorization, then it will not terminate.
So, to answer the question you reduce the fraction in each choice as much as possible and then check the remaining denominators. An aggressive scan should very quickly point you to choice (B), which of course can be written as .27, a terminating decimal.
Now, this isn't a real GMAT question (there's no "choose all that apply"), so I'm guessing that it comes from a math textbook or the GRE (which has multiple answer questions). On the GMAT we'd just stop with B, but if we need to check all the choices:
A) 2+4+6=12, so 246 is a multiple of 3.. NOT terminating.
C) 27 is a multiple of 3.. NOT terminating. (can't reduce this fraction)
D) 231 and 660 are both multiples of 3, so reduce to 77/220.
77 and 220 are both multiples of 11, so reduce to 7/20.
No further reduction possible!
20 = 2*2*5... only 2s and 5s, so 7/20 IS terminating.
E) 7/105 = 1/15. 15 is a multiple of 3... NOT terminating.
Choose (B) and (D)!
