Question
Find one irrational number between $0.2101$ and $0.2222\ ...=0.\bar{2}$
✓
Answer
Let, a = 0.2101 and,
b = 0.2222...
We observe that in 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 numbers
x = 0.211011001100011...
We find that a < x < b
Hence x is required irrational number.
b = 0.2222...
We observe that in 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 numbers
x = 0.211011001100011...
We find that a < x < b
Hence x is required irrational number.
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