# Significant figures question

Discussion in 'Mathematics' started by randomjames, Jul 1, 2011.

1. ### randomjames

Hello,

When rounding 0.009991 to 2 significant figures, would you give the answer as (a) 0.0100 or (b) 0.010?

(a) takes the fact that 2 s.f of the question goes to the 4th decimal place.

(b) takes the fact that 2 s.f. of the answer are given.

2. ### PaulDGOccasional commenter

OK... What you do is you have to think about what's meant by 2 significant figures...
It's about noting which figures in your original are the "most significant" and then finding the closet approximation, or if you like "preserving as best you can" that significance.
Here, the first 2 9s are the most significant so, one way or another, your answer must preserve as much of the truth as possible down to the 4th decimal place.
The nearest number you can get to 0.00999 to 4 decimal places is 0.0010. So that's the answer..
(But the real answer when teaching this is to avoid these dodgy boundary conditions. They'll never matter in "real life" and the examiners will avoid them too - as do most text books.
Perhaps they can make good extension questions for G&T kids who can be asked not just to give the answer but to make a case for their answer.)

3. ### valed

Yes - never mind them understanding - just teach to the exam!
Valed, blood boiling at the sheer .............. mutter mutter .....

4. ### salsamaths

I must be having a blonde moment! Surely 0.0100 is closer to 0.00999 than 0.0010?

5. ### salsamaths

.... and 0.0010 wasn't one of the original options either, it was 0.010. Hence the answer is 0.0100 because this takes into account, to which accuracy the measurement has been rounded.

6. ### PaulDGOccasional commenter

Yes, of course. Sorry. Typo.

A bit harsh, I think, Valed. I see this as more a question of convention rather than being a key part of mathematical understanding. Significant figures are a way of approximating accuracy, but only a shorthand and not as good as +/- x%. For example, according to the s.f counting method, 0.1000 (4 s.f) is more accurate than 0.0999 (3.s.f) but the implied accuracy is almost exactly the same. I see this as a "life's too short to worry about...l" rather than something they really need to know. That is probably why exam questions avoid the issue.

8. ### valed

Not really - you either teach or settle for what's needed in the exam - and I know where I stand on that!
Sadly [for that argument] they don't!
Just marked OCR and Edexcel A level S1 and, on both papers, candidates suffered because they could write answers as specified.

Valed, I meant that this particular issue strikes me as unimportant, not that we should always teach to the exam. My point here is that it is an argument about conventions rather than a real issue of understanding. I am not familiar with the papers you mention (we do MEI); did they demand rounding of a number in a way that could be seen as ambiguous?

10. ### afterdark

eh?
because they could? or could not?

11. ### erm

I suspect because they *can* but make a typo, which means they potentially lose lots of marks if not enough evidence is in their working.

Those that don't even attempt to round as requested can still get full marks for their answer.

It can be very frustrating to award full marks to those who haven't even attempted to approximate as requested when you have to dock marks from others for what is likely to be a silly slip when you know the approximation, though asked for, isn't worth any marks.

12. ### erm

Then again, maybe Piranha did make a typo and he is indeed frustrated by candidates who can't approximate by the time they get to A level. I'll get my coat.