What does the word “percent” actually mean?
One way to think of a percent is to think of it as being a proportion measured in hundredths. It is a sort of scale. 100 hundredths is all of something, 0 hundredths is none of something.
This may sound a bit strange, but if you imagine there are 100 pieces of chocolate on a table (my table) and 0 pieces of chocolate on another table (bad luck as that’s your table) I have 100% of the chocolate and you have 0%. I’m a reasonable person, and so I put 25 pieces on your table. I now have 75 hundredths of the chocolate and you have 25. I have 75 out of 100, and you have 25 out of 100. We write this 75% and 25%.
That is all well and good, but 2 of our friends appear, and I feel obliged to give them each 25% of the chocolate. Note that is of 25% of the total chocolate that I started with, not what I have now. That would be 25% of 75. For now we all have 25 pieces.
Percentages can also be written out as a decimal, which is very useful in doing calculations. We already said that 100% is the same as 1 of something. 1 can also be written out as 1.00 (this is 1 to 2 decimal places). To work out 75% as a decimal, you can move the decimal point 2 places to the left. So start with 75.0 and move the point two places to the left and you get 0.750. Similarly for 25% you get 0.25. That is the way it works for any percent to decimal.
It is a bit more complicated if you want to express 5% as a decimal. You still move the point 2 places to the left, but as there is a “space” in the tens bit, so you have put a zero. Therefore, 5% is 0.05 as a decimal.
To find out what a %age of something is, you can multiply by the decimal. For example 25% of 100 is 0.25*100. You can see this is 25.
Say you weren’t willing to share your 25 pieces chocolate. So I offered our friends 25% each of mine. How may would we each have? The maths is the same, except we are looking for 0.25 of 75, instead of 100. Use a calculator to work this out and you will see our friends have 18.75 pieces each. Ok you have to imagine that the chocolate gets cut, but you get the idea. I’m still ahead of the game as you have 25, friend 1 has 18.75 and Friend 2 has 18.75 means that I am left with the balance of 37.5.
This is all well and good, but in the real world no one has a table with a hundred pieces of chocolate on waiting to be divided between friends.
A common reason for using percentages is to work out sales taxes. When you go in to a retail hardware store and buy wood for a DIY project you get charged a retail price including sales tax (in the UK this is called VAT). However, if you go in to a trade hardware store, you’ll be charged a VAT exclusive price. Currently VAT is at 20%.
If you spend £237.39 VAT inclusive how much were the goods and how much did you pay in tax? VAT is currently 20% which can be written as 0.20 as a decimal. The cost of the goods is therefore 80% or 0.80 as a decimal.
To calculate this, you would multiply by 0.80 and 0.20 respectively. So 237.39*0.80=189.912 and 237.39*0.20=47.478 as we don’t have coins for tenths of a penny you, would round up. 189.91 + 47.48=237.39.
If you went in to a trade hardware store and bought £237.89 worth of goods, how much sales tax would you have to pay? As 100% of the goods is £237.39 what would 120% of this be? Perhaps the easiest way to calculate this is to multiply the value of the goods by 1.2.
This would be 237.39*1.2=284.868 Rounded this is £284.87