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
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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
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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
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