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

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Chapter 1

NCERT

Class 9

Mathematics

Solutions

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

Question:

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

Answer:

(i) Let x = 0.6

x = 0.6666... ...(i)

Multiplying by 10 both sides

10x = 6.6666... ...(ii)

Subtracting eq. (i) from (ii), we get

9x = 6

x = 6/9 = 2/3

Hence, 0.6 = 2/3

(ii) Let x = 0.47

x = 0.47777... ...(i)

Multiplying eq. (i) by 10

10x = 4.7777... ...(ii)

Multiplying eq. (i) by 100

100x = 47.7777... ...(iii)

Subtracting eq. (ii) from (iii), we get

90x = 43

x = 43/90

Hence, 0.47 = 43/90

(iii) Let x = 0.001

x = 0.001001001... ...(i)

Multiplying eq. (i) by 1000, we get

1000x = 1.001001001... ...(ii)

Subtracting eq. (i) from (ii), we get

999x = 1

x = 1/999

Hence, 0.001 = 1/999

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(All Q's of this Chapter solved)

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