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Answer:

If the denominator contains any number other tha 2 or 5 ( or powers of 2 or5),then the division  will always yield a recurring decimal.

For example the fraction (2/7) ,  has 7 in the denominator, so the division will give arecurring decimal

0.142857142857142857..........and so on , because 7 is not an integer  power of 2 or 5.

But the fraction (3/25 ) will give terminating decimal 0.12, because the denominator contains only a power of 5( 5^2 =25).

Now the fraction (1/15)  will give a recurring decimal because 15 contains 5 but also contains 3

(5*3 =15)and 3 is not  any integer power of 5 .

In short if the denominator is in the form of 2^n*5^m,where n and m are positive integers,then the division will yield a terminating decimal and in all other cases,it will give a recurring decimal. 

 

 

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