Question

Express 0.33 bar as a rational number ( pq form)

Answer 1

let x=0.33__bar(we can also write it as 0.3 or 0.3333to infinity)

as one digit is being repeated so multiply it by 10 on both sides

10x=3.3

(upto this we got two equations i.e, x=0.3 and 10x=3.3)

now subtracting both equations we get

10x-x=3.3-0.3

9x=3

x=3/9

x=1/3

(for your convenience I want to say that 0.33bar -0.3bar is 0 it's not 0.03 cause it's a bar digit it's non ending process as it gets subtracted at the infinte. so we need to imagine the infinte point where 3-3 =0 the 000....0)

hope it helps

Answer 2

Given:

A number= 0.33 bar

To find:

The number in its rational form

Solution:

0.33 bar as a rational number is 1/3.

We can find the form by following the given steps-

We know that a rational number is of the form p/q, where q is not equal to 0.

The number=0.33 bar

The non-terminating part of the number is after the decimal.

Let the number be X

X=0.33 bar (1)

To make it rational, we will multiply it by 10. This is done to eliminate the repeating part of the decimal.

On multiplying by 10 on both sides, we get

10X=3.33 bar (2)

Now we have two equations of X.

On subtracting the two, we get

10X-X=3.33 bar-0.33 bar

9X=3

X=3/9

X=1/3

As a rational number in p/q form, p=1 and q=3.

Therefore, 0.33 bar as a rational number is 1/3.