insert five rational number Between –1/2and 2/3
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There are a lot more than five of them. In fact there are infinitely many rational numbers between any two numbers (rational or irrational.
To illustrate, let’s find a method that will allow us to come up with 100 rational numbers in between 1/2 and 2/3.
- Step 1: make those two numbers comparable.
I won’t go on about common denominators, but that what we’re doing really.
1/2 = 3/6 and 2/3=4/6
So the difference between them is 1/6
- That difference is definitely less than, 1/10 (to make things easy for ourselves.
- So 1/2+1/1000, 1/2+2/1000, … 1/2+100/1000 are all rational numbers between 1/2 and 2/3
- Here’s one of them specified more completely
1/2+2/1000=500/1000+2/1000=502/1000
That isn’t expressed in its simplest terms (251/500) but is is certainly rational and certainly is between 1/2 and 2/3 as required.
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