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Rational numbers are fractions. There are infinitely many fractions between 1 and 100. You cannot list them all.

But numbers like 1/2 and 1/3 are rational and so are ones like 7 which is 7/1.

If you give me any two rational numbers, say 6/8 and 7/8, I can find a rational number in the middle. Let's just right 6/8 as 12/16 and 7/8 as 14/16 then 13/16 is in the middle of those two. I can do that again with 13/16 and 14/6 by writing them as
26/32 and 28/32 and 27/32 in the middle.
I am sure you can see how I can keep doing this forever. This illustrates how between any two rational numbers there is always another. In fact, I just pick the number in the middle of the two, but there are many others between any two rational numbers. We say the rational numbers are a dense subset of the real numbers.
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16y ago

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