Answers

2015-05-29T20:54:33+05:30
True because
Example: How many rational numbers are there between 1/5 and 4/5?
Solution: You may say there are only two – 2/5, 3/5
But if you rewrite 1/5 as 5/25 and 4/5 as 20/25, then you would have
6/25, 7/25, 8/25, 9/25, 10/25………..10/25.

In all, there are 14 rational numbers and all of them lie between 1/5 and 4/5.
Now if we write 1/5 as 100/500 and 4/5 as 400 500, we would have a new set of rational numbers
occurring between 1/5 and 4/5.
These are 101/500, 102/500, 103/500, 104/500, 105/500,…………..397/500, 398/500, 399/500.
And, you can go on endlessly finding new sets of rational numbers between 1/5 and 4/5/
This method of finding rational numbers can be applied to any two randomly selected rational numbers.
Therefore, it follows that there are countless rational numbers between any two rational numbers.  
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