Question

if 241/4000=241/2^mx5^n, find the value of m and n as non-negative integers. hence write its decimal expansion without actual division

Answer 1

Answer:

The value of m is 5 and n is 3

Step-by-step explanation:

Given the fraction

$\frac{241}{4000}$

we have to convert above in the form

$\frac{241}{4000}=\frac{241}{2^m\times 5^n}$

To find the value of m and n

The prime factorization of 4000 is

$4000=2\times 2\times 2\times 2\times 2\times 5\times 5\times 5=2^5\times 5^3$

which is in the form $2^m\times 5^n$

implies m=5 and n=3

The decimal expansion is

$\frac{241}{4000}=\frac{241}{4\times 1000}=\frac{60.25}{1000}=0.06025$

Answer 2

241/4000=241*2m*5n

Prime factorize 4000

4000=2*2*5*5*5*2*2*2=2^5*5³

2^m=2^5

5n=5³

i.e m=5,n=3