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

pepeprepa wrote:Can you explain further your tip because
1/(3^2)= 0.1111111111

1/(3^2) is not equal to 0.1111111111.

1/(3^2) is equal to 0.11111111111111111111............, repeating forever. It is not a terminating decimal; it is what is called a 'recurring' or 'repeating' decimal. You can tell, by looking at the fraction 1/(3^2), that it will be a repeating decimal, because it is a reduced fraction, and there is a prime different from 2 or 5 in the denominator.

I'll try to state the rule as unambiguously as possible. If you need to know whether a fraction represents a terminating decimal:

1) Reduce the fraction completely;
2) Prime factorize the denominator;
3) Look at this prime factorization, and ignore the exponents. If there is a prime besides 2 or 5 in the denominator, the fraction represents a recurring (non-terminating) decimal. If the only primes in the denominator are 2, 5, or both, the fraction represents a terminating decimal.

So 9/125, 3/32, 7/80 and 3/30 are all terminating decimals (when you look at 3/30, you must reduce the fraction first, of course), while 7/121, 5/33, 7/60 and 19/99 all represent recurring decimals.