Q8 of 51 Page 1

Give two rational numbers lying between 0.515115111511115…. and 0.5353353335….

Let a = 0.515115111511115….

b = 0.5353353335….


We observe that the second decimal place a has digit 1 and b has digit 3, therefore, a < b. So if we consider rational numbers


x = 0.52


y = 0.52052052


Then,


a < x < y < b


Hence, x and y are required rational numbers.


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6

Give an example of each, of two irrational numbers whose:

(i) Difference is a rational number.


(ii) Difference is an irrational number.


(iii) Sum is a rational number.


(iv) Sum is an irrational number.


(v) Product is a rational number.


(vi) Product is an irrational number.


(vii) Quotient is a rational number.


(viii) Quotient is an irrational number.

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Give two rational numbers lying between 0.232332333233332…. and 0.212112111211112.

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Find one irrational number between 0.2101 and 0.2222 ….= .

 10

Find a rational number and also irrational number lying between the numbers 0.3030030003…..and 0.3010010001….