Q. 24.3( 36 Votes )

Express each of the following decimals in the form :

(i) (ii) (iii) (iv) (v) (vi) (vii)

Answer :

(i) Let x =

Now, x = 0.4̅ = 0.444 (1)


Multiplying both sides of equation (1) by 10, we get,


10x = 4.444… (2)


Subtracting equation (1) by (2)


10x – x = 4.444… - 0.444…


9x = 4


x =


Hence, =


(ii) Let x =


Now, x = 0.3737…. (1)


Multiplying equation (1) by 10


10x = 3.737…. (2)


Multiplying equation (2) by 10


100x = 37.3737…. (3)


100x – x = 37


99x = 37


x =


Hence, =


(iii) Now x =


= 0.5454… (i)


Multiplying both sides of equation (i) by 100, we get


100x = 54.5454…. (ii)


Subtracting (i) by (ii), we get


100x – x = 54.5454…. – 0.5454….


99x = 54


x =


(iv) Now x =


= 0.621621…. (i)


Multiplying both sides by 1000, we get


1000x = 621.621621…. (ii)


Subtracting (i) by (ii), we get


1000x – x = 621.621621…. – 0.621621….


999x = 621


x = =


(v) Now x =


= 125.3333…. (i)


Multiplying both sides of equation (i) by 10, we get


10x = 1253.3333…. (ii)


Subtracting (i) by (ii), we get


10x – x = 1253.3333…. – 125.3333….


9x = 1128


x = 1128 / 9 = 376/3


(vi) Now x =


= 4.7777…. (i)


Multiplying both sides of equation (i) by 10, we get


10x = 47.7777…. (ii)


10x – x = 47.7777…. – 4.7777….


9x = 43


x =


(vii) Now, x =


= 0.47777….


Multiplying both sides by 10, we get


10x = 4.7777…. (i)


Multiplying both sides of equation (i) by 10, we get


100x = 47.7777…. (ii)


Subtracting (i) from (ii), we get


100x – 10x = 47.7777…. – 4.7777….


90x = 43


x =


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