Physics IA Uncertainties Question

[ProjectFrostbite]

How do I work out the uncertainies in my IA?

I know about how to get them initially, but how do I handle them taking my IA to its conclusion?

Can I simply add the uncertainties if I am multiplying two numbers for a third, or do I need to add the percentage errors and then work out the actual error from this?

How many significant figures should I take my results to?

Help

[Guest B.E.P.]

Look:

If you are adding/subtracting two numbers, then you must add the absolute uncertainties:

(2.0 +- 0.3) + (0.3 +- 0.4) = 2.3 +- 0.7

(2.0 +- 0.3) - (0.3 +- 0.4) = 1.7 +- 0.7

If you are multiplying/diving two numbers, then you must add the percent uncertainties:

(2.0 +- 0.1) x (3.0 +- 0.3) = 6.0 (I will keep this as it is until I find out the absolute uncertainty

Percent uncertainties:

0.1/2.0 = 0.05x100 = 5%
0.3/3.0 = 0.10x100 = 10%

5% + 10% = 15%

Converting it back to absolute uncertainties:

15/100=0.15 x 6.0 = 0.9

Therefore, the answer is 6.0 +- 0.9

Concerning significant figures, these are the rules I follow:

Make sure your absolute uncertainty is to one significant figure.

Make sure your uncertainties and your values are to the same decimal point.

For example, if this question:

(2.0 +- 0.2) x (3.0 +- 0.3) = 6.0 (I will keep this as it is until I find out the absolute uncertainty)

Percent uncertainties:

0.2/2.0 = 0.10x100 = 10%
0.3/3.0 = 0.10x100 = 10%

10% + 10% = 20%

Converting it back to absolute uncertainties:

20/100=0.20 x 6.0 = 1.2

Since uncertainties must be to one significant figure, then the uncertainty will be reported as 1

Therefore, the answer is 6 +- 1

I hope this is clear enough!