Question

the decimal expansion of the rational number 47/4000 will terminate after :- ​

Answer 1

We know that if a rational number is of form pq and q can be expressed as 2n5m, then the rational number will terminate after n places, if n>m and the decimal expansion will terminate after m places, if m>n.

Answer 2

Step-by-step explanation:

Let's see

4000 can be written as 2*2*1000

47/4000 = 47/2*2*1000 = 47*5*5/100000

i.e. 47/4000 is x/1 lakh

The decimal will terminate after five decimal places.

In case, the numerator and denominator had common factors, we would have reduced it. And multiply such that we get powers of 10 in denominator.

Than we could determine, when it will terminate.

Which will be the power of number 10.

In this case 5.