Please Help: I don't understand and I need as much help I can get

In a reduced form.....If we can express the denominator solely as a power of 2 or a power of 5 - or both - the fraction will terminate....else..it repeats.....

1/ 40  terminates  = 1 / [ 2^3 * 5]

1/ 24 does not =  1 / [ 2^3 * 3 ]

2/125 terminates  = 2 / 5^3

2/ 99 does not  =  2 / [ 3^2 * 11]  

7/ 300  does not =  7 / [ 2^2 * 5^2 * 3 ] 

7 / 200  terminates  =  7 / [ 2^3 * 5^2]

Here's the provision for the reduced form

3 / 300     appears to not terminate....however

3 / 300  =   1 / 100  =    1 /  [  2^2 * 5^2 ]    so this actually does terminate  !!!

And that's all there is to it  !!!!

Thanks Chris,  

I had not thought about that before.

To put it another way..

If the decimal is to terminate then

The prime factors of the denominator must ONLY  be the prime factors of 10 

 (which are  2 and 5 )

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I assume this can be extended to other bases.

So

1/5 base 8 is a recurring decimal because the prime factors of 5 are not the prime factors 8

That works.

I just did the division

and got 

\(\frac{1}{5_8}=0.14\bar6\bar3\)   (base8)    

How about that!     

Thanks Chris