Question:
Find two rational numbers of the form $\frac{p}{q}$ between the numbers $0.2121121112 \ldots$ and $0.2020020002 .$
Solution:
The rational numbers between the numbers 0.2121121112... and 0.2020020002... are:
$0.21=\frac{21}{100}$ and $0.205=\frac{205}{1000}=\frac{41}{200}$
Disclaimer: There are an infinite number of rational numbers between two irrational numbers.
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