Question

the decimal expansion of rational no. 43÷2⁴5³ will terminate after how many places of decimal?

Answer 1

=> 43/ 2⁴×5³

=> 43 /( 2*5)³*2

=> 43/1000 * 1/2

=> 0.043/2

=> 0.0215

Therefore ,The decimal expansion of ,43/2⁴*3³ is 4 .

Answer 2

Answer:

The given rational number will terminate after 4 places.

Step-by-step explanation:

Given : The decimal expansion of rational number $\frac{43}{2^45^3}$

To find : Number will terminate after how many places of decimal?

Solution :

If the denominator of a rational number is of the form $2^n5^m$ , then it will terminate after n places if n>m or m places if m>n.

In the given rational number $\frac{43}{2^45^3}$

n=4 and m=3 (on comparison)

We see that, n=4>3=m

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

As $\frac{43}{2^45^3}$

$=\frac{43}{(16)(125)}$

$=\frac{43}{2000}$

$=0.0215$

Therefore, The given rational number will terminate after 4 places.