Q. 34.0( 365 Votes )

Express the follo

Answer :

(i)  = 0.666…

Let x = 0.666666…


Multiplying both sides by 10


10 x = 6.666= 6 + 0.666


10 x = 6 + x   


9 x = 6



(ii)


Let x = 0.4777777
Now multiplying both sides by 10,
10 x = 4.77777777........    eq(1)
Now multiplying eq(1) by 100 we get
100 x = 47.777777........    eq(2)
Now eq(2) - eq(1)
100 x - 10 x = 47 - 4
90 x = 43
x = 43/90 

(iii)


Let x = 0.001001…eq(1)


Multiplying both sides by 1000


1000x = 1.001001… = 1 + 0.001001...    eq(2)
we can see that,

1000x = 1 + x

999x = 1

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