Question

Express the following in the form p÷ q where p and q are integer and q not equal to zero 1. 0.6 bar 2. 0.47 bar 3. 0.001 bar​

Answer 1

Answer:

1. 0.6 bar

ans.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

2. 0.47 bar

ans.The value of 0.47 bar will be in the form of fraction is 43/90

To find:

p/q = ???

Solution:

Given : We have to express 0.47 (bar on 7) in the form of p/q.

Let us assume that  

x = 0.47777  

Multiplying both the sides by 10, we get

10x = 4.7777 ---------(1)

Multiplying both the sides by 100, we get

100x = 47.777 ---------(2)

Subtract equation (2) and (1),

100x = 47.777

10x =   4.777

90x = 43.000

x = 43/90

Thus, the value of 0.47 bar will be in the form of fraction is 43/90

3.0.001 bar

ans.Let x=0.001 bar=0.001001001....... and

1000x = 1.001001001.............

subtract x from 1000x

1000x = 1.001001001.........

-      x = 0.001001001.........

 999x = 1.000000000..........

 999x = 1

     x  =   1/999

HOPE THIS HELPS YOU

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