Question

The number of decimal place after which the decimal expansion of the rational number $\frac{23}{2^{2} *5}$ will terminate, is

Answer 1

Question is incomplete .

QUESTION : The number of decimal place after which the decimal expansion of the rational number  23/2²× 5¹   will terminate, is

(a) 1

(b) 2

(c) 3

(d) 4

SOLUTION:

Option (b) is Correct : 2  

Given : 23/2²× 5¹

The decimal expansion of  23/2²× 5¹ terminate after 2 places of decimal.

[m > n , m = 2]  

23/2²× 5¹ = 23 × 5¹ /2²× 5¹ × 5¹

23/2²× 5¹ = 23 × 5¹ /2²×  5²

= 115/(2×5)²

= 115/ 10²

= 115 / 100

= 1.15  

The decimal expansion of 23/2²× 5¹ is 1.15 .

Hence, 23/2²× 5¹ has terminating decimal expansion. The decimal expansion of  23/2²× 5¹ terminate after 2 places of decimal.

★★ If the factors of denominator of the given rational number is of form 2^m 5ⁿ ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.It terminates after k places of decimals where k is the larger of m and n.

HOPE THIS ANSWER  WILL HELP YOU...

Answer 2

hey mate

here's the solution