Question

express 0.001 bar in the form of p/q, where p and q are integers and q is not equal to 0.

Answer 1

x= 0.001bar eq. 1

100x = 1.001 eq. 2

eq. 2 - eq. 1

1000x - x

999x=1.001- 0.001

999x = 1

x= 1/999

Answer 2

The required p/q form is 1/999.

Given:

0.001 bar

To find:

The p/q form

Solution:

The required form can be obtained by multiplying the given number by 1000.

Let the given number be X.

X=0.001 bar (1)

Now, by multiplying it by 1000, we get

1000X=1.001 bar (2)

On subtracting (1) from (2),

1000X-X=1.001 bar-0.001 bar

999X=1

X=1/999

So, p/q=1/999.

Therefore, the required p/q form is 1/999.