Help scaling numbers to 0% and 100%: make 21 as close to zero as possible, and...

[Darklandscape]

Hi, I don't know if what I am trying to do is possible, but here it is.

I want a equation that would make the 1st number as close to 0 as possible and the second number as close to a 100 as possible.

1. 21
2. 177


And one for these numbers
1.82
2. 214

 

[stapel]

Hi, I don't know if what I am trying to do is possible, but here it is.

I want a equation that would make the 1st number as close to 0 as possible and the second number as close to a 100 as possible.

1. 21
2. 177

And one for these numbers
1.82
2. 214

What do you mean by "make the 1st number as close to 0 as possible and the second number as close to a 100 as possible"?

Please reply with the full and exact text of the exercise, along with a clear listing of your thoughts and efforts so far, as this will help us to understand what you're talking about. Thank you!

 

[BigBeachBanana]

Hi, I don't know if what I am trying to do is possible, but here it is.

I want a equation that would make the 1st number as close to 0 as possible and the second number as close to a 100 as possible.

1. 21
2. 177


And one for these numbers
1.82
2. 214

I'm guessing you want to normalize the range [21-177] ->[0,1]

For any value [imath]x_i[/imath] in the range [imath][a,b][/imath], its normalized value is given by the equation:
[math]x_i \, \text{normalized} = \dfrac{x_i-a}{b-a} [/math]
Examples:
[math]\text{normalized } 21 = \dfrac{21-21}{177-21}= 0[/math]
[math]\text{normalized } 177 = \dfrac{177-21}{177-21} = 1[/math]

 

[Dr.Peterson]

Hi, I don't know if what I am trying to do is possible, but here it is.

I want a equation that would make the 1st number as close to 0 as possible and the second number as close to a 100 as possible.

1. 21
2. 177


And one for these numbers
1.82
2. 214

I'll take this answer one step further:

I'm guessing you want to normalize the range [21-177] ->[0,1]

For any value [imath]x_i[/imath] in the range [imath][a,b][/imath], its normalized value is given by the equation:
[math]x_i \, \text{normalized} = \dfrac{x_i-a}{b-a} [/math]
Examples:
[math]\text{normalized } 21 = \dfrac{21-21}{177-21}= 0[/math]
[math]\text{normalized } 177 = \dfrac{177-21}{177-21} = 1[/math]

Since you want the high value to be 100, you'll want to multiply by 100; here's an example showing the scaling of a number in the middle, namely 57: [math]57\rightarrow\dfrac{57-21}{177-21}\cdot100=\dfrac{36}{156}\cdot100\approx23.08[/math]

 

[Dr.Peterson]

Hi, I don't know if what I am trying to do is possible, but here it is.

I want a equation that would make the 1st number as close to 0 as possible and the second number as close to a 100 as possible.

1. 21
2. 177


And one for these numbers
1.82
2. 214

It may also help to show you what we are doing, namely finding the equation of a line joining two given points:

​

This is what we are assuming you want. Please confirm.

The slope of the line is [imath]\dfrac{100-0}{177-21}[/imath]; we multiply that by the horizontal distance from the starting point, [imath]x-21[/imath], to get the value of y: [math]y=\dfrac{100(x-21)}{177-21}=0.641x-13.462[/math]
You can put any other pair of numbers in place of 21 and 177.