Percentages Explained

I recieved a request for a tutorial Percentages recently. It's quite an odd tutorial to write, as you assume that most people are aware of how they work, but apparently it is a very common hangup for lots of people out there, especially when it comes to Excel and formulas etc.

What follows therefore isn't so much an Excel tutorial as one on how percentages work and how to use them.

So, what is a percentage? Well, in its basic form a percentage is a means of expressing a fraction in terms of what value that fraction would be if it were out of one hundred. Let me explain in more detail..

Let's say we're looking at three fractions; 3/5, 8/11 and 9/13. Which one is the largest? We're taught in maths when comparing fractions that to see which is the biggest you make the bottom number of the fraction the same and then multiply the top by the same amount so that they are all a fraction of the same number. That's what we do with percentages in a way.

Basically to convert these to percentages we divide the top number by the bottom number to get a decimal figure, as below:-

3/5 = 0.6
8/11 = 0.73 (rounded to two decimal places)
9/13 = 0.69 (again rounded to two decimal places)

Now that we have the numbers in decimals it's much easier to see how the three fractions relate to each other. To convert to a percentage we now simply multiply by 100:-

3/5 = 0.6 x 100 = 60%
8/11 = 0.73 x 100 = 73%
9/13 = 0.69 x 100 = 69%

It's now plain to see that 8/11ths is the largest of the fractions. So we can now say that 8 is 73% of 11, and so on for the same numbers.

Right then, here comes the next bit. What about all those bags of crisps, cans of juice and tins of food which claim to have 20% extra free. How is that worked out?

Well. Let's say that a standard tin of beans is 150g in weight. We want to find out what 20% of 150g is. We do this another way:-

1) First take the beginning value, in this case 150, and divide it by 100:-

150/100 = 1.5

By dividing by 100 we now know what 1% of the weight of the tin of beans is.

2) Now we just multiply by the percentage figure we want, in this case 20

1.5 * 20 = 30

So, we now know that 20% of 150g is 30g. If there is 20% extra free the tin of beans weighs 150 + 30 - 180g in weight.


Working backwards

Sometimes you may need to work backwards with percentages. Lets say again that you have bought a tin of beans that is 175g in weight and it tells you that you are getting 33% extra free. What's the weight of a normal can of beans then? How much are you getting for free?

Well, lets break it down:-

1) If you have 33% extra free, you need once again to suss out what 1% of the value is to work it backwards. In this case, however we don't divide the sum by 100, as what we have is a tin of beans which is 33% larger. What we need to do is divide by 133 to get the original value of 1%

175/133 = 1.32 (rounded to 2 decimal places).

2) Now, by multiplying the figure by 100 you will get the weight of a standard tin with no extras:-

1.32 * 100 = 132g

132g is the weight of a standard tin. If you work out 33% of this you'll find it is the 43g difference.

And that's about it. It might take a bit to get around your head, but it is really quite easy.


More hints

To quickly find out the percentage value of a number you can simply multlipy by a decimal. Let me show you how:-

Lets say you wanted to find out 17.5% of 100. Basically just convert 17.5% to a decimal. Its actually really easy. Just move the numbers two directions to the right of the decimal point:-

17.5% = 0.175
5% = 0.05
50% = 0.5

Now you can simply multiply your number, so 17.5% of 100 is 100*0.175 = 17.5.

You can do the same to find out what the percentage value on top of something is by adding a 1 before the decimal point:-

What's 250 + 23% ? :-

250 * 1.23 = 307.5

Anyway, that's it. Play around with it for a while. If you have any problems or suggestions for how this tutorial could be made better, or if you have any other ideas for tutorials please don't hesitate to leave a comment or get in touch by email.

Mat