Question

without actually performing long diwithout actually calculating the long division state whether the following rational number will have a terminating decimal expansion or a non terminating repeating decimal expansion 15/1600​

Answer 1

Now, taking the following fraction 15/1600, this can be split into:

15/2*2*2*2*2*2*5*5 (1600).

So, if you multiply the denominator by 5*5*5*5, you make the no.of 2's and 5's equal.

So, if you multiply each 2 with 5, You get 6 10's.

The fraction now is

15/10*10*10*10*10*10

So, the fraction terminates in 6 places.

I hope you understood.

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