Question

3. Express the following in the form , where p and q are integers and q is not equal to 0.

(1) 0. 6(bar)
(2) 0.47(bar) (3)0.001 (bar)

Pls answer it as quickly as u can​

Answer 1

Step-by-step explanation:

(1) Let x = 0.6 recurring

Then, x = 0.666..... ....(i)

implies 10x = 6.666........ .....(ii)

Substracting (i) from (ii),we get

9x = 6 implies x = 6/9

implies x = 2/3 Ans.

(2). Let x = 0.47 recurring

Then, x = 0.4777.... eq(i)

Multiplying by 10 both sides,we get

10x=4.7777…eq(ii)

Multiplying again by 10 both sides,we get

100x=47.7777…eq(iii)

On subtraction eq.(ii) from eq.(iii),we get

(100x-10x)=(47.7777…)-(4.7777)

=> 90x = 43

=> x = 43/90

Hence, 0.4777... = 43/90 Ans.

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