Question

Write the denominator of the rational number 607÷ 4000 in the form 2m ×5n,where m and n are non negative integers. What are the values of m and n ? Hence, write it's decimal expansion, without actual division

Answer 1

Answer: 0.15175

Step-by-step explanation:

The Numerator is 607 & the denominator is 4000.

4000 = 2 X 2000

= 2 X 2 X 1000

= 2 X 2 X 2 X 500

= 2 X 2 X 2 X 2 X 250

= 2 X 2 X 2 X 2 X 2 X 125

= $2^{5}$ X 5 X 25

=  $2^{5}$ X $5^{3}$

∴ m = 5 & n = 3 , and both are non negative integers.

We have to find 607 / 4000 without actual division

∴ $\frac{607}{4000}$ = $\frac{607}{2^5 X 5^3}$

In order to multiply the denominator's two numbers with each other, we need to bring them to same power.

Since, power of two is 5 and power of 5 is 3, we multiply both numerator and denominator by 25 so that power of 5 also becomes 5 in denominator.

Multiplying numerator and denominator by 25, we get

∴ $\frac{607}{4000}$ = $\frac{607}{2^5 X 5^3}$ X $\frac{25}{25}$

= $\frac{15175}{2^5 X 5^5}$

= $\frac{15175}{10^5}$

= $\frac{15175}{100000}$

= 0.15175

∴ $\frac{607}{4000}$ = = 0.15175

Answer 2

Given :  Rational Number  607/4000

To find : Write denominator in form of  $2^m \times 5^n$

Solution:

Rational number is in the form of   numerator/Denominator

=>in 607 / 4000

Numerator = 607

Denominator = 4000

Denominator 4000

= 2 * 2  * 2 * 2 * 2  * 5 * 5 * 5

= 2⁵ * 5³

Comparing with  $2^m \times 5^n$

m = 5

n = 3

607 / 4000  

=  607 / (2⁵ * 5³)

= 607 ( 2²  * 10 ³)

= 607 * 5² /( 5² * 2² * 10³)

= 607 * 25/ (10⁵)

= 15175  / 100000

= 0.15175

decimal expansion, = 0.15175

m = 5  & n = 3

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