Error analysis: significant figues

[armolinasf]

Homework Statement

I have three measurements for the L, W, H of a box: 40.4, 14.9, 17.0. the volume would then be 10233.32cm. each of my measurements has three sig figures, and it says in my book that with multiplication the product should have no more sig figures than the measurement with the fewest sig figures. So does this mean that my measurement would be 10200cm? thanks for the help

 

[AJKing]

So does this mean that my measurement would be 10200cm? thanks for the help

Exactly so.
If it helps, think of significant figures as your degree of accuracy in a question.

Edit: Just as a clarifying example,

If I want to multiply 4.8 m by 9.4854, my exact result will be 45.52992 m.

This result is extremely accurate. It's so precise that it takes into account all the units down to 20 micrometers.

But how could we know that it's the correct answer when your first measurement was only held 2 digits of information? Perhaps, if you measured closer, you would have found that it was 4.78923 m instead.

 

[Fewmet]

More precisely, it would be 10200 cm³.

I've seen some disagreement in texts about whether terminal zeroes are significant. It might be safer to write the answer as 1.02 x 10⁴ cm³.

 

[bingoboy]

I was always taught that terminal zeroes are only significant if it is noted that they are significant (i.e 345000m six sig figs is completely different to 34500 3 sig figs) but yes as the others have stated, keep as many figures as you can until you reach the final answer and then round to the specified significant figure

 

[technician]

I agree with these responses, you should round off to the lowest number of significant figures.
A good way, I find, to appreciate the meaning of significant figures is to realize what the number you write down is NOT telling you.
The length of your box is given as 40.4cm, this means it is NOT 40.3cm and it is NOT 40.5cm. This means you cannot calculate an answer with any knowledge of the number beyond 3 figures.
Significant figures are also closely related to the accuracy of measurement. If you quote a measurement to 3 significant figures it implies that the measurement was made to better than 1%. the 40.4cm measurement given implies that the measurement could be made to within +/- 0.1cm which is about 1/4%...very accurate