Q2 of 51 Page 32

Express each of the following decimals in the rational form .

let x = 

x = 0.99999….. -→(i)


Here the periodicity of the decimal is one


So, we multiply both sides of (i) by 10 and we get


10x = 9.999…-→(ii)


Subtract (i) from (ii)


10x = 9.999….


x = 0.999…

10x - x = 9.999... - 0.999...

9x = 9.0

x = 1

Hence = 1

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6

Find ten rational numbers betweenand .

 1

Express each of the following decimal in theform.

(i) 0.57


(ii) 0.176


(iii) 1.00001


(iv) 25.125

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Express each of the following decimals in the rational form .

 3

Find (x + y) ÷ (x − y) if