DJ1986 wrote:

In order to have a terminating decimal, you need a power of ten on the bottom.

I re-wrote original equation as:

3^4/(10^3)*5^3

(3^4)*(10^-3) / 5^3

.081/125

And then you don't even need to finish the long division to see that there will be three zeros.

You don't need a power of ten on the bottom. It has to be a power of 2, 5, or both.

E.g

1/2 = .5, which terminates

1/5 = .2, which terminates

1/20 = .1, which terminates

Anything other than a power of 2, 5, or a a combination of those two powers will not terminate. E.g. 1/3, 1/6, 1/7, 1/9, etc.