phumbert wrote:chidcguy wrote:Answer is B
If we can express the denominator in the form of 2^x X 5^y the decimal will terminate.
4 is 2 ^ 2 X 5 ^ 0
Would anyone be willing to elaborate on this a little for me? I think I get the explanation, but on a broader scope, Im not sure that Im grasping the concept, and what I would do if the answer set were different. Thanks for anyone that can help!
I'll try. Think first of how you would write a terminating decimal as a fraction. If you saw, for example:
0.203
you'd write that as 203/1000. That is, any terminating decimal can be written with a power of 10 in the denominator. Here, we've used 10^3; prime factorize 10^3 and you have (2^3)*(5^3). That is, any terminating decimal can be written with only 2s and 5s in the prime factorization of the denominator. Some of the 2s and 5s might cancel; using a different example:
0.204 = 204/1000 = 51/250 = 51/[(2^1)*(5^3)]
but the point is, if you only see 2s and/or 5s in the denominator of a completely reduced fraction, the fraction definitely represents a terminating decimal, because you could multiply the numerator and denominator by 2s or 5s to get a power of 10 in the denominator. For example, if you had 11/125, which is 11/5^3, you could multiply by 2^3 to get 1000 in the denominator:
11/125 = 11/(5^3) = [11*(2^3)]/[(2^3)(5^3)] = 88/1000 = 0.088
