A is smaller than b by 20%, while c is greater than b by 60%. by what percent is a smaller than c?

Now it is time to dive deeper into the utility of the percentage difference as a measurement. It should come as no surprise to you that the utility of percentage difference is at its best when comparing two numbers; but this is not always the case. We should, arguably, refrain from talking about percentage difference when we mean the same value across time. We think this should be the case because in everyday life we tend to think in terms of percentage change, and not percentage difference.

For now, let's see a couple of examples where it is useful to talk about percentage difference. Let's say you want to compare the size of two companies in terms of their employees. In this example, the company C has 93 employees, and company B has 117. To compare the difference in size between these two companies, the percentage difference is a good measure. In this case, using the percentage difference calculator, we can see that there is a difference of 22.86%. One key feature of the percentage difference is that it would still be the same if you switch the number of employees between companies. As we have established before, percentage difference is a comparison without direction.

It is, however, not correct to say that company C is 22.86% smaller than company B, or that B is 22.86% larger than C. In this case, we would be talking about percentage change, which is not the same as percentage difference. Another problem that you can run into when expressing comparison using the percentage difference, is that, if the numbers you are comparing are not similar, the percentage difference might seem misleading. Why?

Imagine that company C merges with company A, which has 20,000 employees. Now the new company, CA, has 20,093 employees and the percentage difference between CA and B is 197.7%. Let's take it up a notch. Now a new company, T, with 180,000 employees, merges with CA to form a company called CAT. We're not quite sure what this company does, but we think it's something feline related. CAT now has 200.093 employees. Now, the percentage difference between B and CAT rises only to 199.8%, despite CAT being 895.8% bigger than CA in terms of percentage increase.

"How is this even possible?" Thats a good question. The reason here is that, despite the absolute difference gets bigger between these two numbers, the change in percentage difference decreases dramatically. The two numbers are so far apart that such a large increase is actually quite small in terms of their current difference. Therefore, if we want to compare numbers that are very different from one another, using the percentage difference becomes misleading. If you want to avoid any of these problems, our recommendation to only compare numbers that are different by no more than one order of magnitude (two if you want to push it). If you want to learn more about orders of magnitude and what this term means, we recommend our scientific notation calculator.

As with anything you do, you should be careful when you are using the percentage difference calculator, and not just use it blindly. In our example, the percentage difference was not a great tool for the comparison of the companiesCAT and B. At the end of the day, there might be more than one way to skin a CAT but not every way was made equally.

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If A is 20 % more than C and B is 60 % more than C, then A is what percentage of B ?

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