# Express the following in the form p/q, where p and q are integers and q ≠ 0. - Mathematics

Express the following in the form p/q, where p and q are integers and q ≠ 0.

(i) 0.bar6

(ii) 0.4bar7

(iii) 0.bar001

#### Solution

(i) 0.bar6

Let x = 0.666 ....................(1)

∴10x = 6.666 ......................(2)

(2) - (1)

⇒9x = 6

x = 6/9 = 2/3

(ii) 0.4bar7

"Let "x = 0.4bar7 = 4.7777 ....................(1)

Multiplying both sides by 10 (since one digit is repeating),

we get 10x = 4.7777 ..........................(2)

(2) - (1)

⇒ 10x - x = 4.3

⇒ 9x = 4.3

⇒ x = (4.3/9) = 43/90

"Thus, " 0.4bar7=43/90

Here p = 43, q = 90(≠0)

(iii) 0.bar001

"Let "x = 0.bar001 = 0.001001001 .........................(1)

Multiplying both sides by 1000(since three digits are repeating),

we get 1000x = 1.001001 ..........................(2)

(2) - (1)

⇒ 100x - x = 1

⇒ 999x = 1

⇒ x = 1/999

"Thus, "0.bar001 = 1/999

Here P = 1, q=999(≠0)

Concept: Real Numbers and Their Decimal Expansions
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#### APPEARS IN

NCERT Class 9 Maths
Chapter 1 Number Systems
Exercise 1.3 | Q 3 | Page 14