# Why your calculations are always wrong, even though you did them ‘right’

I`m willing to bet that on more than one occasion you`ve struggled to figure out why your answer is wrong when you`re pretty sure that you`ve done everything right.

Obviously, what you`re likely to have done wrong depends on the calculation you are doing. But there are lots of common mistakes that everyone makes at some point. The list below will give you some ideas about why your calculations are often wrong.

You probably got your relative formula mass wrong.

This is one of those things that`s so simple that people go on autopilot when they do it and so often it`s the thing that messes up the calculation. I see this all the time. Always, always, always double check your relative formula mass and always look things up on the periodic table rather than just freestyling and hoping you`ve remembered it right. And watch out for Oxygen – you know you`ve been sat their going “is it 8, 16 or 32” more than once.

The other thing you may have done is got your formula upside down. Did you do moles over mass instead of mass/ moles? Again this is really common. If you know you do this jot down your formulae on the side of the exam paper before you even start reading the question. This gives you time to focus and check it’s correct before you have the “Oh no, I`m not sure how to do that” panic.

If you had to do unit conversions (for example converting volume in cm3 to volume in dm3) it`s probably this – especially if you can see your answer is out by a factor of a 1000.

Unit conversions can really catch you out because they are sort of counter-intuitive. For instance, when you`re converting milligrams to grams its easy to think “oh, grams is bigger than milligrams so I must multiply by 1000”. This is the classic mistake – it`s easy to see it`s wrong when it`s written down like this but I even catch myself doing this sometimes.

The correct way to think about unit conversions is this:

If you`re starting with the bigger unit (e.g. grams) and you want to convert to a smaller unit (e.g. mg) then you will multiply. This is because you will have a lot more of the smaller unit than of the larger unit.

For example – if you were converting metres to millimetres you would have a lot more millimetres than metres.

For example, if you have 2 metres, you would x 1000, giving you 2000 mm.

Conversely – if you are converting from a small unit to a large unit you will have a lot less of the small one than the large one so you need to divide.

So, if you have 50 mm and you want to convert to metres you would divide by 1000, giving you 0.050 m.

When I`m doing unit conversions this is what I repeat in my head:

‘large to small multiply, small to large divide’

Also if you`re measuring length never use cm. Not only is it more awkward to convert (mm -> um for instance is a lot easier than cm -> um) but there is also more of a tendency to round up. I`ve seen students measure, say 0.9 cm but round it up to 1 cm all the time, but I`ve never seen anyone round 9mm to 10mm.

It will be your significant figures that are the problem giving you a rounding error.

Remember: the significant figures are all the numbers after the first 0 (Yes, I know this is an oversimplification but it will do for now).

Take a look at these numbers:

a) 1.05 b) 0.001 c) 0.00105 d) 0.00100

a) has 3 significant figures 1.05

b) only has 1 significant figure – all the 0s at the beginning are not significant 0.001

c) has 3 significant figures – the first 3 0s are not significant but the following 1,0,5 are all significant 0.00105

d) has 3 significant figures – the first 3 0s are not significant and but the 1 and the following 00s are significant 0.00100

You need to be really careful how you use your significant figures. When doing a calculation, your answer needs to have the same number of significant figures as the value with the fewest significant figures.

Let me explain: Let`s say you are asked to calculate the moles NaOH in a solution. You are given the volume and concentration.

If the volume is 30 cm3 and the concentration is 0.125 mol dm-3. The value for volume has 2 significant figures, whereas the concentration has 3 significant figures. Your answer should therefore have 2 significant figures.

Watch out for multi-step calculations (particularly in chemistry).

In multistep calculations it is the final answer than needs to have the same number of significant figures as the value with the fewest significant figures. For the rest of the steps in your calculation follow this rule: you answer at each step should have one more significant figure than you need for your final answer.

So, if you are aiming for 3 significant figures keep 4 significant figures in at each step. If you are aiming for 2 keep 3. Then round up at the end – you are less likely to end up with an error if you round up at the end than if you round up too early.