Numerical reasoning is often a challenge, especially when percentages are involved. To start with “%” is very simple, but of course its use in context often makes things harder. Here we show how putting percentage expressions in Excel and seeing them visualised in EQUS helps their comprehension.
It may seem trivial, the “%” is used after a number to show it is a percentage value. However, it is in fact a postfix operator which means “… now divide by 100″, with the number before the operator. As an operator “%” can be used any formula just like you might use “-” in front of an expression to negate it. Here’s 9% and -9% with the EQUS visualisation:
A simple example of how this can be a bit confusing would be “2/3%”. Now does that mean “2 divided by 0.03” or is it “0.6666 as a percentage (that would be 0.006666)”?
You can see the “%” takes precedence. If you know BODMAS, you will see there is no “P” for percentage. In fact it could or should be BPODMAS! So, to get the other result you need brackets:
Not to mention as an operator something like “sqrt(81)%%%%” is a valid expression meaning “the square root of 9 times 10^-8”.
Try EQUS and see if it helps untangle percentages for you, and much more.