Question

Find two irrational numbers between 0.5 and 0.55.

Answer 1

Answer:

The two irrational numbers between 0.5 and 0.55 are of non-terminating and non-repeating decimal numbers. For example, 0.512122122212222 ..... and 0.539399399939999....! Irrational numbers are those no.

Answer 2

Let a = 0.50…. and b = 0.55….

 

We observe that the second place of their decimal representations are distinct . Number a has digit 0 and b has digit 5. So, a < b.  

 Consider the numbers c = 0.51051005100051…. and d = 0.523052300523000523….

Clearly, c (0.51051005100051….) and d (0.523052300523000523….) both are irrational numbers such that a < c < d < b

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