Sciencemadness Discussion Board

Significant figures

thunderfvck - 13-3-2004 at 00:08

This stuff really gets me. I know how simple it is but I can't seem to master it. I've been to quite a few sites and in every case I always leave the site feeling confident. However, when it comes to me writing lab reports, or doing assignment questions, I ALWAYS lose points for significant figures.

Okay, this is my understanding of it:

1.01 three figures.
15.63, four figures
10.0, three

and I can go on and on. How I do this is I think, what would it look like if it were in scientific notation, then I count the numbers. When multiplying/dividing I write my final answer with the significant figures imposed by the lowest number digit.

Where is my thinking gone wrong?

Saerynide - 13-3-2004 at 03:30

Quote:
Originally posted by thunderfvck
How I do this is I think, what would it look like if it were in scientific notation, then I count the numbers. When multiplying/dividing I write my final answer with the significant figures imposed by the lowest number digit.


You mean you write your final answer according to the number of sigfigs in the number with least digits right?

You probably know this, but place-marking 0s do not count.
So 0.00002 only has 1 sigfig.

And when you add/subtract, you round the answer to the number of decimal places (irregardless of sigfigs) according to the number with the least decimal places.
So 0.081 + 5.6710 = 5.752, not 5.75

[Edited on 13-3-2004 by Saerynide]

thunderfvck - 13-3-2004 at 13:04

Quote:

You mean you write your final answer according to the number of sigfigs in the number with least digits right?


Yes, that's what I meant.
Quote:

So 0.081 + 5.6710 = 5.752, not 5.75


Isn't it 5.8? Because 0.081 has two significant figures? And about rounding, isn't there a rule with that, with 5 anyway? A simple search would answer this question but laziness is a terrible disease. Soemthing like, if the preceeding digit is odd, round down, if even, round up, I don't remember which it is...

I will post specific examples of questions I have made mistakes on once I get my lab book back from my teacher...

Ahah. I was going to post one example that I was boggled by, but on second look, he crossed it out! I guess he's so used to me screwing up the significant figures. HA!

axehandle - 13-3-2004 at 13:10

When I went through college, 0.081 had 3 significant <i>decimals</i>. So the answer to the addition would have 3 decimals as well.

These rules may be different in other places in the world.

Or perhaps I'm just confusing, I shouldn't post while drunk..... you know, "friends don't let friends derive while drunk..."

Edit: Murphy struck again, the correct quote is "friends don't let friends drink and derive".


[Edited on 2004-3-14 by axehandle]

Saerynide - 13-3-2004 at 17:08

Quote:
Originally posted by thunderfvck
Quote:

So 0.081 + 5.6710 = 5.752, not 5.75


Isn't it 5.8? Because 0.081 has two significant figures? And about rounding, isn't there a rule with that, with 5 anyway? A simple search would answer this question but laziness is a terrible disease. Soemthing like, if the preceeding digit is odd, round down, if even, round up, I don't remember which it is...


Yep Axehandle's right. Its 3 decimals because when you add, you dont look at the least sigfigs. Instead, you look at the least decimal places.

Maybe Im just not understanding your explanation of your rounding dilema. I dont get what you mean by even or odd preceding digits.

When you round, the preceeding digit gets rounded up if the digit after it is 5 or more. Otherwise, it gets rounded down.

So 1.234 rounded to 3 sigfigs (or 2 decimal places) is 1.23
but 1.235 would round to 1.24

axehandle - 13-3-2004 at 17:19

Thank you. I just couldn't put it into words, I know it more by intuition than by words.

thunderfvck - 15-3-2004 at 00:07

Quote:

Yep Axehandle's right. Its 3 decimals because when you add, you dont look at the least sigfigs. Instead, you look at the least decimal places.


So when you add/subtract, you must round off to the lowest possible number of decimal places.

So only when you multiply/divide do you really have to start worrying about the least number of sigfigs.

Right!

I was reading on the web. The rounding thing I was reffering to, when 5 is the number you have to round, you must round off to give you an even number. ie. 1.65 rounds to 1.6 and 1.75 rounds to 1.8. The idea is that if we round up half the time and round down the other half of the time, we're good.

NOW, I have completely mastered significant figures and should never lose 1/2 a mark AGAIN, EVER!!

Thanks for your help!

Uh?

axehandle - 15-3-2004 at 03:02

Now I'm really confused. I've always rounded UP when >= 5, down when <5. Rounding up half of the time and rounding down the other half is new to me. Could you give a reference?

Saerynide - 15-3-2004 at 03:34

Quote:
Originally posted by thunderfvck
The rounding thing I was reffering to, when 5 is the number you have to round, you must round off to give you an even number. ie. 1.65 rounds to 1.6 and 1.75 rounds to 1.8.


I'm lost too now.

How does 1.65 round to 1.6? Doesnt it round to 1.7? I dont understand the even numbers thing.

thunderfvck - 15-3-2004 at 08:43

Okay, it wouldn't be fair to be rounding up ALL the time. Because, for the same reasons we round up, we can also round down.

So, we always round to give the even number. That way, we will be rounding up half the time and rounding down the other half of the time. It's just to even things out.

axehandle - 15-3-2004 at 09:52

But you don't round up or down until you have your answer! The up/down/up/down..... etcetera would make sense if you were rounding, say, all the factors in a multiplication before actually multiplying them, but why would one do such a silly thing?

thunderfvck - 15-3-2004 at 12:03

Yeah, well it's not my rule. It's things I've read off the internet.

A few teachers of mine have also explained this to me.

It makes just as much sense to round it up OR down everytime. It's just a generalized rule, to try and balance it out.

Whatever. It's not like the stake of our lives depends on it anyway.

axehandle - 15-3-2004 at 13:53

Well, not our lives, but I've made it a rule of life to do as little work as possible. I still stand by my conclusion that you absolutely <b>don't</b> round things up or down or sideways or anyways until in the final answer.

The method would have some merit for head calculation though. And it's an old optimization technique when doing huge calculations on old computers. A "probable prime" finder algorith would be a good example. But I won't go into binary operations here, it's completely off topic.

Magpie - 15-3-2004 at 20:24

Axehandle I agree - never give up a hard earned digit until you have to - at the end where you keep as many significant digits as the factor with the least. I don't know if this is a published rule or not, it is just something a professor I respected said to me and it made sense. I don't round the last digit unless there is a good reason to do so.

t_Pyro - 16-3-2004 at 02:01

Rounding off is a rather dicey issue.

If you're going to raise a number like 3.21 to the fourth power (that's 106.17447681, before you get your calc out), the last few decimals are just there to test your patience. On the other hand, if you're going to subtract 106.17447671 from that number and use it for further calculations, you'll get 0 if you's rounded off the answer prematurely. The actual answer is 10<sup>-7</sup>.

Further, if you round off your answer at every step, the deviation from the actual value will increase art every stage. eg. a=3.274468 If you round off a to 4 decimal places initially, you get 3.2745. Round off the answer to 3 decimals again at the next step (assuming you get the same value again), and you get 3.275. Round it off again, you get 3.28, while it should have been 3.27 You get the idea.