How do I estimate?

A reader asks:

There are some confusing questions in my maths textbooks. There is one question asking me to estimate the answers to the following maths problems but it doesn't say whether we need to round the numbers to decimal places, or significant figures.
So, I'd like to ask for these type of questions, do we use our common sense to solve it or do you have any tips?

Estimation, by its nature, is as much an art as a science. If you ask the Mathematical Ninja, he’ll keep track of approximate errors as he goes along, and then adjust his answer at the end; however, the Mathematical Ninja is a great big show-off.

Common sense really is the right answer: the typical way to approach this kind of question is to round everything to one significant figure, work out the sum, and round the answer to one significant figure again. (At GCSE, this -somewhat bizarrely - is the only acceptable form of estimation, so even if you work it out a little more accurately, you may not get any marks). Rob Eastaway has a good article on this kind of estimation - which he calls ‘zequals’ - here:

It’s probably also worth having a read of the textbook chapter before the questions to see exactly what the syllabus says you should be doing - different courses might have different ideas of the ‘right’ way to do it.


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

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