SOLUTION: What number is in between -2 and -0.75

Question 1205268: What number is in between -2 and -0.75

Found 3 solutions by MathLover1, math_tutor2020, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

if a number is in between:

and are rational numbers, so there are infinitely many rational numbers between these two numbers
I am going to choose random number between and which is (one example)

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

There are infinitely many numbers between -2 and -0.75, but one number we could pick on is the midpoint.

Add up the values and then divide in half

Add: -2+(-0.75) = -2-0.75 = -2.75
Divide in half: -2.75/2 = -1.375
The value -1.375 is between -2 and -0.75
This is known as the arithmetic mean.

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Or we could apply the geometric mean
Multiply the values and then apply the square root.

Multiply: -2*(-0.75) = 1.5
sqrt(1.5) = 1.2247 approximately
Make the result negative so it's in between the two negative values
-1.2247 approximately is between -2 and -0.75

Edit: @ikleyn, fair enough, the geometric mean approach seemed a bit flimsy. However, we could treat it like finding the geometric mean of 2 and 0.75 and then make the result negative.

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Another thing we could do is find the distance between the given values
distance = |a-b| = |-2-(-0.75)| = |-2+0.75| = |-1.25| = 1.25
Then cut this distance into N pieces, let's say N = 10
1.25/N = 1.25/10 = 0.125

Let k be some integer on the interval 0 < k < N
In this case 0 < k < 10

Then let's add some multiple of 0.125 to the left endpoint -2, to land somewhere between -2 and -0.75
We're evaluating -2+0.125k for k = 1 through k = 9
If k = 1, then -2 + 0.125k = -2 + 0.125*1 = -1.875
If k = 2, then -2 + 0.125k = -2 + 0.125*2 = -1.75
If k = 3, then -2 + 0.125k = -2 + 0.125*3 = -1.625
If k = 4, then -2 + 0.125k = -2 + 0.125*4 = -1.5
If k = 5, then -2 + 0.125k = -2 + 0.125*5 = -1.375
If k = 6, then -2 + 0.125k = -2 + 0.125*6 = -1.25
If k = 7, then -2 + 0.125k = -2 + 0.125*7 = -1.125
If k = 8, then -2 + 0.125k = -2 + 0.125*8 = -1
If k = 9, then -2 + 0.125k = -2 + 0.125*9 = -0.875
Each of the results {-1.875, -1.75, -1.625, -1.5, -1.375, -1.25, -1.125, -1, -0.875} are between -2 and -0.75

Notes: If k = 0, then -2+0.125k = -2 is the left endpoint, while k = 10 means -2+0.125k = -0.75 is the right endpoint.

There's nothing special about N = 10. We could have easily made N = 20 or whatever positive whole number you want.

And yet another approach is to select the number -1 since it's between -2 and -0.75, and then tack on some random string of decimal digits.
Eg: -1.2345 or -1.6789

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

One small correction to the post by @math_tutor2020.

Traditionally, geometric mean is defined for positive numbers, ONLY.

See this source (Wikipedia article)
https://en.wikipedia.org/wiki/Geometric_mean

So, ignore the consideration in his post, that relates to geometric mean of the numbers -2 and -0.75.

The rest in that post is Ok.

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