Question

3. Express the following in the form, where p and q are integers and q + 0.
(D) 0.6
(ii) 0.47
(ii) 0.001​

Answer 1

Answer:

(i) 0.6 = 0.666…

Let x = 0.666……. (1)

Here only one digit is repeating so multiply by 10 on both sides

10 × x = 10× 0.666….

10x = 6.666…. (2)

On subtracting equation 1 from equation 2

10x- x = 6.666…. - 0.666….

9x = 6

x = 9/ 6 = ⅔

Here , 0.6 = ⅔

(ii)

Let x= 0.47 = 0.4777…. (1)

Here, 1 digit is not repeating so multiply eq. 1 by 10

10 × x = 10 × 0.47777

10 x = 4.7777…… (2)

Now only 1 digit is repeating so multiply eq 2 by 10 we get

10 × 10x = 10 × 4.777….

100 x = 47.777….. (3)

On subtracting equation 2 from equation 3 we get

100 x-10 x= 47.777…. - 4.777….

90 x=43

X=43/90

Here, 0.47 = 43/90

(iii) 0.001 = 0.001001001…

Let x = 0.001001001…. (1)

Here, 3 digit is repeating so multiply by 1000

1000 × x = 1000 × . 001001001….

1000x = 1.001001001…. (2)

On subtracting equation 1 from equation 2

1000x -x = 1.001001001…. - 0.001001001...

999x = 1

x = 1/999

Hence ,0.001 = 1/999

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Hope this will help you...