Scaling something back to 1

Question

I'm currently working in an modeling program and scaled something down to 85%. I would like to use another scale to transform it to back to its original size, however is proving more difficult than I thought. Simply reversing the scale does not work:

1 * .85 = .85

.85 * 1.15 = 0.9775

What's the actual scale I'd want to use to bring my model back to 1, and what's the formula I'd want to use so I can repeat it in the future?

I had a feeling it was something incredibly easy like that. Thanks guys! — Gigazelle, Aug 18 '13 at 17:41
hey @AndréNicolas, is there's a way to make it more precise. for example, when the scale goes below 50% like 35%, its values comes with more error ?? — Atul Chaudhary, Feb 22 '22 at 07:29

score 2 · Accepted Answer · answered Aug 18 '13 at 17:39

If you have a number, call it $a$, and you scale it by $\lambda$, you will get a new number, $$b=\lambda a.$$

In order to return $b$ to its original value $a$ you just need to divide $b$ by $\lambda$ since $$\frac{b}{\lambda} = \frac{\lambda a}{\lambda}=\frac{\lambda}{\lambda}{a}=1\cdot a = a.$$

Another way to see this is to note that dividing by $\lambda$ is the same as multiplying by $1/\lambda$. So your scaling factor to return $b$ back to the original value of $a$ is $1/\lambda$.

Scaling something back to 1

1 Answers1