Insert an irrational number between the following.
(i) 1/3 and ½
(ii) -2/5 and ½
(iii) 0 and 0.1
Solution:
(i) One irrational number between 1/3 and ½
½ = 0.5
So there are infinite irrational numbers between 1/3 and ½.
One irrational number among them can be 0.4040040004…
(ii) One irrational number between -2/5 and ½
½ = 0.5
So there are infinite irrational numbers between -2/5 and ½.
One irrational number among them can be 0.1010010001…
(iii) One irrational number between 0 and 0.1
There are infinite irrational numbers between 0 and 1.
One irrational number among them can be 0.06006000600006…
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