Find the two rational numbers between 2/3 and 3/2
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I did think of another way of generating lists of rational numbers between those two limits. Any finite decimal can be written as a fraction, eg 65.873 = 65873/100000. Now 23 is less than 0.7, and 32 is of course 1.5.
So, how about this list of rational numbers, that are between those limits:
7/10, 8/10, 9/10, 10/10, 11/10, 12/10, 13/10, 14/10.
And going down one level further:
71/100, 72/100, 73/100, …, 78/100, 79/100, 81/100, …, 138/100, 139/100
The next level down starts with 701/1000 and ends with 1399/1000.
Hopefully you can see how we can generate an infinite number of rationals in this way!
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I think this is helpful to you
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