Question

8. Express each of the following decimal number in the p form 9 i) 0.5 bar ii) 3.8 bar iii) 0.36 bar iv) 3.127bar​

Answer 1

Answer:

(i). 0.5 = 5/10

Simplifying it in the same p/q form,

⇒ 0.5 = 1/2

It cannot be further simplified in p/q form.

1/2 is in the form p/q, where p = 1 and q = 2 are integers and q = 2 ≠ 0.

Hence, the answer is 1/2.

(ii).

This has to be converted in p/q form.

Let

,

That is, x = 3.88888… …(i)

Multiply 10 on both sides,

10 × x = 10 × 3.88888…

⇒ 10x = 38.8888… …(ii)

Subtracting equations (i) from (ii), we get

10x – x = 38.8888… - 3.88888…

⇒ 9x = 35

⇒ x = 35/9

35/9 is in the form of p/q, where p = 35 and q = 9 are integers and q = 9 ≠ 0.

Thus,

.

(iii).

This has to be converted in p/q form.

Let

,

That is, x = 0.363636… …(i)

Multiply 100 on both sides,

100 × x = 100 × 0.363636…

⇒ 100x = 36.363636… …(ii)

Subtracting equations (i) from (ii), we get

100x – x = 36.363636… - 0.363636…

⇒ 99x = 36

⇒ x = 99/36

Simplifying it further,

⇒ x = 11/4

11/4 is in the form of p/q, where p = 11 and q = 4 are integers and q = 4 ≠ 0.

Thus,

.

(iv).

This has to be converted in p/q form.

Let

,

That is, x = 3.127777… …(i)

Multiply 100 by equation (i),

100 × x = 100 × 3.127777…

⇒ 100x = 312.7777… …(ii)

Multiply 1000 by equation (ii),

1000 × x = 1000 × 3.127777…

⇒ 1000x = 3127.7777… …(iii)

Subtract equation (ii) from (iii), we get

1000x – 100x = 3127.7777… - 312.7777…

⇒ 900x = 2815

⇒ x = 2815/900

⇒ x = 563/180

563/180 is in the form of p/q, where p = 563 and q = 180 are integers and q = 180 ≠ 0.

Thus,

.