Explain the concept of significant figures?

[I'm]

Homework Statement

How many significant figures in each?:
-214
-81.60
-7.03
-.03
-0.0086
-3236
-8700

I don't quite understand this (I'm self studying, need a little help :) )

If got them all right then can someone explain the concept of significant figures?
I hate knowing only how to do a problem, I always need to know the concepts and such. Its annoying, I know.

Homework Equations

The Attempt at a Solution

I got

-3
-4
-2
-3
-2
-2
-2

 

[negitron]

http://en.wikipedia.org/wiki/Significant_figures

It's a well-written and clear article (somewhat unusual for Wiki) which explains the concept nicely. It should help you see where you went wrong in three of your examples.

 

[ideasrule]

Homework Statement

How many significant figures in each?:
-214
-81.60
-7.03
-.03
-0.0086
-3236
-8700

I don't quite understand this (I'm self studying, need a little help :) )

If got them all right then can someone explain the concept of significant figures?
I hate knowing only how to do a problem, I always need to know the concepts and such. Its annoying, I know.

Homework Equations

The Attempt at a Solution

I got

-3
-4
-2
-3
-2
-2
-2

The first two are right, but after that you seem to have gotten confused.

Anyways, the number of significant digits reflects the accuracy of the data. Suppose you measure an object and the balance says 43.1 g. The actual mass could be 43.13, 43.19, or 43.135839 g, but you have no way of knowing what it actually is because the balance is not accurate enough to discriminate between a 43.13 g object and a 43.19 g object. If another balance reports the mass as 43.13 g, you'd have one more significant digit because you'd know the mass with 10 times more precision.

A significant digit is just that: a digit that has physical significance. By physical significance, I mean that it actually tells you something about the object. Leading zeros are not significant because a 5.3 cm eraser could also be said to be a 0.053 m eraser; the 2 extra zeros result from unit conversation, and don't provide any information about the length of the eraser. All other digits are significant, however, because they tell you about the quantity being measured.

 

[ideasrule]

That said, I have to say that the concept of significant figures is just a rule of thumb, and not a good one at that. The number of significant digits a measurement has doesn't tell you anything about the errors that have nothing to do with the measurement device's precision. You use an ammeter and it changes the current through the circuit; the ammeter's # of sig figs doesn't reflect that. You do a blackbody experiment with a less-than-perfect black body; sig figs can't reflect the error that causes. You measure "g" and can't take friction into account; sig figs are once again useless. Worse, you switch to base 2 or base 20, apply the sig fig rules, and all of a sudden your data seems either 5 times less or 2 times more precise than it actually is.

Learn this rule of thumb, since it's useful in deciding how much rounding to use, but don't fool yourself into thinking it has any use in real data analysis.

 

[I'm]

Sorry, I got to re look at my posts haha. My apologies.



-214 (3 sig.)
-81.60 (4 sig.)
-7.03 (3 sig.)
-.03 (1. sig.)
-0.0086 (2 sig.)
-3236 (4 sig.)
-8700 (2 sig.) or 4? Someone explain this?

 

[negitron]

Nailed 'em all. The last one is 2 sig figs because there are trailing zeros but no decimal point. If it had been

-8700.

it would have been 4.

 

[I'm]

Awesome ! i think I get it now, thanks guys. :)