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#1 2014-02-01 08:59:57

silverpuma
Member
Registered: 2011-06-19
Posts: 72

On a multi-part question when do you round to significant figure?

Hi folks,  I have a question to do that has a few parts but it states the answer is given to 3 significant figures.  I can do all the calculations but am wondering about the 3 significant figures (which I understand how to do as well).  The answer must be given in m^2

I'm given a square lawn 30m x 60m and inside the square lawn are 4 round paved areas, 2 have dia of 1.9m, one a dia of 2.2m and one a dia of 0.9m.

Do I do all my working out of all the circle areas, adding them together and subtracting from the 180 (area of lawn) and only when I get that final figure of do I consider the 3 significant figures? 

Its just for example the circle with a dia of 0.9m works out at

0.6361725124 m^2  as Im working through the question and the other circles do I need to use the 10 digits after the decimal point  or because I know I'm working towards 3 s.f. can I just use say 4 digits after the decimal point?

Hope Im making sense........thanks for your patience:)


“Men occasionally stumble over the truth, but most of them pick themselves up and hurry off as if nothing ever happened.”  ―  Winston Churchill

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#2 2014-02-01 12:07:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

Re: On a multi-part question when do you round to significant figure?

Hi;

Check this and your questions will be answered.

http://www.mathsisfun.com/algebra/appro … tions.html

I work with as many digits as I can for all calculations and then round at the end. Use this calculator to make sure you round correctly.

http://www.mathsisfun.com/rounding-numbers.html


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2014-02-01 15:30:53

silverpuma
Member
Registered: 2011-06-19
Posts: 72

Re: On a multi-part question when do you round to significant figure?

thanks for the links bobbym its appreciated.....


“Men occasionally stumble over the truth, but most of them pick themselves up and hurry off as if nothing ever happened.”  ―  Winston Churchill

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#4 2014-02-01 18:20:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,251

Re: On a multi-part question when do you round to significant figure?

Hi;

That significant digit calculator sure is a nifty program.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2014-02-01 21:16:50

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,269

Re: On a multi-part question when do you round to significant figure?

hi silverpuma,

Definitely leave the rounding until the end as each round off will introduce an error in the calculation.

If you're asked for an answer at each stage, calculate it and round it for answer purposes.  But use the most accurate value in the next calculation.

UK exam boards expect you to round off sensibly.  If, for example, you're asked for the diameter of a tree given its circumference, it would be silly to state the answer as 2.4567 m .  (i) You couldn't measure the circumference that accurately in the first place and (ii) tree trunks aren't perfectly circular anyway.

Here's an simple example that shows why 'over-acurate' answers are not appropriate.

eg.  What is the area of a rectangle 3.6 m by 4.2 m ?

The calculator gives the answer as 15.12  But are we justified in giving that as the answer?

A value of 3.6 suggests the measuring was only done to the nearest 0.1  So the true value could be anything from 3.55 to 3.65

Similarly the 4.2 could be anything from 4.15 to 4.25

Look what you get if you take the two smallest values and then the two largest values:

3.55 x 4.15 = 14.7325
3.65 x 4.25 = 15.5125

So the 'true' answer could lie anywhere in the range 14.7325 to 15.5125

That would suggest that a sensible answer after rounding would be 15 m^2

Sometimes, at GCSE, they ask for all the calculator figures (to show you have used the calc. correctly) and then expect you to decide on a sensible rounded figure.

I used to advise my students to write down the calculator answer in the working and then put the rounded answer in the answer space.  That way they were 'hedging their bets' about what was wanted.  Obviously. if you're asked for, say, 2dp, then anything else would be wrong.

On the exam board pages you can download mark schemes that show how markers are instructed to deal with answers.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2014-02-02 02:46:50

silverpuma
Member
Registered: 2011-06-19
Posts: 72

Re: On a multi-part question when do you round to significant figure?

Thanks Bob for the great answer and all makes perfect sense.....I suppose in maths like a lot of things in life there is a certain amount of "common" sense to be applied as well:-)


“Men occasionally stumble over the truth, but most of them pick themselves up and hurry off as if nothing ever happened.”  ―  Winston Churchill

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