Question

the decimal expansion of the rational number 43/2^4 5 ^3 will terminate after how many places of decimal

Answer 1

43/2^4 5 ^3= 43 ×5/2^4 5 ^3 ×5
43 ×5/2^4 5 ^4
43 ×5/(2×5)^4
43 ×5/(10)^4
215/10000
0.0215
4 places of decimal

Answer 2

If the denominator of a rational number is of the form 2n5m, then it will terminate after n places if n>m or m places if m>n.

The given rational number is

43/24*53

Here, n = 4 > 3 = m

So, the given rational number will terminate after 4 places.