Question
Find two irrational numbers between $0.5$ and $0.55.$
✓
Answer
Let $a =0.5=0.50$ and $b =0.55$
We observe that in the second decimal place a has digit $0$ and $b$ has digit $5$ ,therefore $a<0$ so, if
we consider irrational numbers $x=0.51051005100051 \ldots y=0.530535305353530 \ldots$
We find that $a<x<y < b$
Hence $x$ and $y$ are required irrational numbers.
We observe that in the second decimal place a has digit $0$ and $b$ has digit $5$ ,therefore $a<0$ so, if
we consider irrational numbers $x=0.51051005100051 \ldots y=0.530535305353530 \ldots$
We find that $a<x<y < b$
Hence $x$ and $y$ are required irrational numbers.
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