Question

# There are ______ rational numbers between any two rational numbers

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Solution

## There are infinite rational numbers between any two rational numbers.For example: Let $a=1$ and $b=2$ be any two rational numbers.Then, $1<1.1<1.2<1.3<......1.9<1.10<1.11<1.12<.........1.21<1.22<......1.1111111<1.1111112,.....<2$There are infinite number between $1$ and $2$ whose decimal representation is terminating and also non-terminating and recurring.Hence, There are infinite rational numbers between any two rational numbers.

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