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class 9th
Answers
it is too easy...
i. 0.6bar
let x = 0.666.....
:. 10x = 6.666....
10x = 6.666 - 0.666 + x
10x = 6 + x
10x - x = 6
9x = 6
x = 6/9
x = 2/3
same for ii) ,iii)
ii) 0.47 bar, measn 0.477....
iii) 0.001 bar, means 0.001001001....
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Step-by-step explanation:
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i)let x = 0.6 =0.666.....
here only one digit repating so multiple by 10on both sides , we get
10x=10×0.666.....
=》10x=6.6666......... ...... (ii)
on subtracting eq. (i)from eq.(ii), we get
10x-x=(6.666.....)-(0.666....)
=》9x =6 =》x=6/9=2/3
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Hence,0.6=2/3
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ii) let x=0.47=0.4777.....
here, one digit is not repeating , so multiply eq.(i) by 10, we get
100x=47.777......
on subtracting eq(ii)from eq.(iii), we get
(100x-10x)=(47.777.....)-(4.777....)
=》90x =43 =》x=43/90
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hence ,0.47=43/90
(iii) let x=0.001 =0.001001001....
on multiplying eq. (i) by eq. 1000,we get
1000x=1.001001001........
on subtracting eq.(i) from eq.(ii),we get
(1000x-x)=(1.001001001....)-(0.001001001....)
=》999x=1 =》 1/999
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hence 0.001=1/999