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

Question

Find one irrational number between 0.2101 and 0.2222 &#x2026;.= .

Philoid · Accepted Answer

Let a = 0.2101

And, b = 0.2222….

We observe that the second decimal place a has digit 1 and b has digit 2, therefore, a < b. In the third decimal place a has digit 0. So, if we consider irrational number

x = 0.211011001100011…

We find that,

a < x < b

Hence, x is required irrational number.