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Can someone explain significant figures to my 11 year old?
By Maggie Jones (P3415) on Tuesday, December 5, 2000 - 09:13 am:

My daughter is struggling to understand what a significant figure is and left for school in tears today can somebody help?

By Tim Martin (Tam31) on Tuesday, December 5, 2000 - 10:56 am:

Firstly, I will say that I had trouble with sig figs at that age - it isn't a difficult concept but can be taught very badly.

The idea of significant figures is just an extension of the process of rounding decimals to a certain level of accuracy - eg. taking 1.0634 and writing it as 1.06 to 2 decimal places. I assume your daughter is already familiar with this, if not ask and I will attempt to explain it.

The problem with specifying accuracy in terms of decimal places is that it leads to a different level of accuracy for different numbers, for example if I measure my height in millimeters I get a value of 1750mm, which is 1750.00mm to 2d.p. If I measure my height in kilometers I get a figure of 0.00175km, which is 0km to 2d.p. Both these figures represent the same piece of information (my height) but rounding them to a particular number of decimal places results in a figure which is too accurate in one case and not accurate enough in the other case.

The solution to this is to round up at a point which depends on the number itself. For example, 6 and 6.000000000 are the same number, since the zeros at the end have no effect on the number. Neither to zeros to the right of the number, for example 000006 is still just 6. Therefore if we want to round a number, it makes sense to take into account which figures are significant (ie. which ones have an effect on the value of the number) and which ones don't. Numbers are significant if they are non-zero, but they are also significant if they are between two non-zero numbers (eg. 1001 is different from 11 - the zeros are significant).

Therefore if you need to round a value (say 0.0001353) to a certain number of significant figures (say 2 in this example) then you first work out which digit is the first significant one - in this case the 1, since it has only zeros to the left of it. You then count to the right by the necessary number of significant figures, in this case 2, and round the number at that point, in this case giving 0.00014 (since the 5 rounds upwards).

Hope this makes some sort of sense, ask if you're still not sure,

Tim

By Dave Sheridan (Dms22) on Tuesday, December 5, 2000 - 10:56 am:

It's a strange concept at first but quite simple when you get the hang of it. If I tell you that a football match had 20,354 people attending it, how much of that information is useful? Well, knowing that it was "roughly 20,000" is quite helpful. Knowing that it wasn't 20,353 or 20,355 isn't too helpful in most situations though - people can be notoriously difficult to count in crowds or by ticket returns.

The idea of a significant figure generalises what I've said above.

So 20,354 to 1 SF (significant figure) is 20,000. To 2 SF it is 20,000 (remember, 0 is still a number!). To 3 SF it is 20,400. Why? Because I rounded up. 354 is closer to 400 than 300. To 4SF it is 20,350. Finally, to 5SF it is 20,354.

So each SF adds another bit of detail, and we have to round up if necessary. This is demonstration by example rather than an actual definition, which would be more complicated to write.

Can you (and your daughter) write out 2,745 to 1, 2, 3 and 4 SF?

There's only one place where it gets different, and that's with numbers smaller than zero. I'll explain those when you've got the hang of this.

-Dave

By Vicky Smith (P3369) on Tuesday, December 5, 2000 - 12:42 pm:

Hi, I'm an A Level student doing Maths, here's an idea. If I set a test of 20 questions on significant figures, you can print it off and give it to your daughter, then if she answers them and you put the answers on here, I will check them and tell you how she has done, then you will know how she is doing now! It may take a couple of days for me to get back to you on this though!

1) 7856 to 3 sf
2) 59056 to 2 sf
3) 134 to 1 sf
4) 547324 to 4 sf
5) 503 to 1 sf
6) 8964 to 2 sf
7) 521 to 2 sf
8) 94532 to 3 sf
9) 32 to 1 sf
10) 4572974 to 5 sf
11) 1.457 to 2 sf
12) 5.08 to 2 sf
13) 3.56 to 1 sf
14) 12.57 to 1 sf
15) 7.3425 to 3 sf
16) 367.4 to 2 sf
17) 45.924 to 4 sf
18) 0.675 to 2 sf
19) 68.305 to 4 sf
20) 0.074 to 1 sf

Right, they get a little more difficult towards the end, but if she gets stuck, I'll do my best to explain it in simple terms so that she can understand! I'll check this again in a day or two and then send you the answers if you decide to give her the test.

Vicky

Good luck!

By Maggie Jones (P3415) on Tuesday, December 5, 2000 - 09:39 pm:

First from maggie and myself thank you to Tim, Dave and Vicky for responding. We are really grateful it may seem a trivial question that we posted but she had worked herself up. She is a set one student who worries at the thought of not understanding a topic and I didn't hold out much hope of getting any help she feels she has made 3 new friends today and no doubt will visit this site time and time again when in difficulty.

In answer to vicky thanks for taking the time to set the questions here follows her answers
1) 7860
2) 59000
3) 100
4) 547300
5) 500
6) 9000
7) 520
8) 94500
9) 30
10) 4573000
11) 1.500
12) 5.10
13) 4.00
14) 10.00
15) 7.3400
16) 370.0
17) 45.920
18) 0.680
19) 68.310
20) 0.070
Love Mags and Debs
xxx

By Susan Langley (Sml30) on Tuesday, December 5, 2000 - 10:16 pm:

Generally they are all correct. There is one consistent error though, which I don't think that anyone has explained. When, after the decimal you round to a certain number of significant figures, you do not retain zero's for all the numbers which are set to zero. Doing as she has indicates an accuracy to the end of the string of zeros. For instance in 20 the answer is 0.07 as 0.070 indicates an accuracy to 2 significant figures.
I hope that makes sense.
Otherwise, all the answers are correct.
Susan

By Vicky Smith (P3369) on Thursday, December 7, 2000 - 10:37 am:

It seems that Susan has already checked the answers although I said I would check. i can second her that the answers are correct and that the point about the extra 0 is true but if she takes this on board, she will be fine. Please tell her well done from me.

Vicky