Maths - Pivotal precision

24th August 2012 at 01:00
Inexact working can mean your answer is way out

A maths teacher's tombstone should read something like this: "J.G. died after 79.1 years (3sf)". Most of our waking lives, after all, are spent telling our students to round that final answer to some suitable level of precision, and "three significant figures" is often our mantra. And yet we have all seen workings where the precision is to 3sf, only for the answer to be given to 5sf.

Perhaps the best way to get our young disciples to take sensible precision on board is to show them an example where things go wrong. A student of mine (let's call him John) once produced the following. John's starting question was "Find the angle between the vectors and ." He began promisingly:

John has dutifully followed what he believes the 3sf rule to be, working to this precision as he goes along. Apart from this, his method is fine. He continues:

When I present this to my A2 group, they follow with interest. "He should be giving more accuracy in his working, but he can't be that much out," says Rachel, and this is the general view.

But when they work out the percentage error they discover he is 20 per cent out. Indeed, the exact value for Ois , which is 7.13 degs (3sf).

John has, to be fair, been unlucky here, in that square root 5 rounds up to 2.24, square root 13 rounds up to 3.61, and 2.24x3.61 rounds up to 8.09 (you might hope for the ups and downs to balance out). But why rely on luck, when a tiny amount of extra work makes you secure? Work to 4 or 5sf and then round your final answer to 3.

This example comes from an A-level study of vectors, but similar ones can be produced whatever your level of study - in fact, asking students to construct a good demonstration of this principle for themselves might be a lesson very well spent.

Jonny Griffiths teaches maths at a sixth-form college.


Test pupils' skills at rounding up and down with jmillsdadson's millionaire game.

Or try Not_Just_Sums' rounding and estimation practice questions pack.


Maths teachers are in planning mode, already thinking about displays for their new classrooms. What will you be putting on your walls?

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