Percentage value higher than 100%

Question

I have two values A= 3.8620E+00 B = 1.4396E+00

According to this post, to calculate how much A is higher than B in percentage we do this:

((A-B)/B)*100 = ((3.8620E+00 - 1.4396E+00)/1.4396E+00)*100 = 168.2690%

Does this mean the value A is 168.2690% higher than B?

Does this calculation is correct?

When the percentage is higher than 100%, what does that exactly mean?

Answer 1

Your method is absolutely correct. There is nothing intrinsically wrong with using percentages greater than 100%. Percentage is just another way of writing a fraction with a denominator of 100. Just as you can have an improper fraction, (4/3) so you can have something like an "Improper Percentage" as well.

Think about how Google's Android Market can grow by 861.5% in year-over-year revenue, just to pick one example. It basically means that every year Google's Android Market's growth becomes 961.5/100 times the growth of the previous year.

Now to solve your case, we take a simpler example. Let A be 100 and B be 10. Now we need to find how much higher is A when compared to B. We continue with finding A-B = 100-10 =>90. Now when we express this in percentage we get (A-B/B)*100 that is 900%.

Now let's verify this. What is 900% of B. It's 9B. Now when you add 9B and B you get 10B which is A.

So to conclude, a percentage higher than 100 is alright.

Answer 2

When the percentage is higher than 100%, what does that exactly mean?

What does it mean that $A$ is 200% of $B$? This means that $\frac AB \cdot 100 = 200$, or equivalently $A=2B$. So it means that A is twice the size of B. It also means that $A= B + B$ or $A=B + \frac{100}{100} B$ which is the same as $A=B+100\% B$ which reads that $A$ is 100% greater than $B$, key word being greater.

Now if you apply the same reasoning to $\frac{A-B}{B}\cdot 100=168.269$, it follows that $A-B = 16.8269\cdot B$, and if we move $B$ to the right we get $A=B + 16.8269\cdot B$, or $A=17.8269\cdot B$

So, to answer

Does this mean the value A is 168.2690% higher than B?

yes, the key word being higher, or greater. While $A$ is 178.269% of $B$, it is 168.269% greater than $B$.

Answer 3

Lets do an easier example. Suppose $B = 100$ and suppose $A = 104$. Then $A$ is $4$ more than $B$. $4$ is $4\%$ of $100$. so $A$ is $4\%$ of $B$ higher than $B$. ANother way of saying this is $A$ is $104\%$ of $B$ which is $4\%$ higher than $100\%$ of $B$, which would be $B$.

And if $C = 160$ then $C$ is $60$ more than $B$. And $60$ is $60\%$ of $B$. So $C$ is $60\%$ of $B$ higher than $B$. And so $C$ is $160\%$ of $B$ which is $60\%$ more than $100\%$ of $B$.

And if $D = 200$ then $D$ is $100$ more than $B$. And $100$ is $100\%$ of $B$ so $D$ is $100\%$ higher than $B$. And $D$ is $200\%$ of $B$ which is $100\%$ more than $100\%$.

And if $E = 280$ then $E$ is $180$ more than $B$. And $180$ is $180\%$ of $B$ so $E$ is $180\%$ higher than $B$. And $E$ is $280\%$ of $B$ which is $180\%$ more than $100\%$.