Question

insert one rational number between 1/2 and 2​

Answer 1

Answer:

Step-by-step explanation:

As it so happens, there are an infinity of rational numbers between 1/2 and 2! This means that we can pretty much do almost anything that aims between the two numbers and hit paydirt!

So, let’s start by mapping the rational numbers between 1/2 and 2, from the rational numbers between 0 and 1. We can get any arbitrary rational between 0 and 1 really easily. Pick an integer greater than 1. It can be 2, it can be 4, it can be 200004. It doesn’t matter. Call this number ‘q’.

Then, pick any integer greater than 0, but less than that number. We call this number ‘p’.

Doing this, you’ll be able to divide p by q to get an arbitrary rational between 0 and 1.

pq  

Now let’s map this arbitrary number to our target range:

First, we need to adjust the spread to be the same. The distance between 1/2 and 2 is 3/2, so what we need to do is stretch the 0->1 spread out to match our target… we do this by multiplying our number by 3/2

Answer 2

Answer:

2√3 is answer

Step-by-step explanation:

is the rational number between 1/2 and 2