Significant Figures: What is the Correct Number for g in Your Area?

[logans_run]

Homework Statement

Solve for g in your area with the correct number of significant figures.
Theta = latitude = 50.7 degrees
h = height = 518. m

Homework Equations

g = 9.80616 - 0.025928 cos2(theta) + .00068 cos^2(2*theta) - 0.000003h

The Attempt at a Solution

Well, I just plugged in the data and calculated it to receive 9.81 m/s^2 which sounds right.
The problem is, our teacher said she is really picky about sig figs, and only 4 students have ever gotten the sig figs right for this question.
I can't decide if the answer should be 3 sig figs, as the data with the lowest sig figs is 3.
Or if it should be 1 sig fig because of the term 0.000003h? Although I do not think you include the expression as a limiting factor for significant figures.
So 9.81 m/s^2 or 10 m/s^ or 1*10 m/s^2?
Any help would be greatly appreciated.

Thanks!

 

[Bystander]

Describe the equation for "g" term by term; that is, what each term means.

 

[logans_run]

Well our teacher only told us that it is an equation for gravity in out specific area. The terms are there to take into account latitude and height.

 

[Bystander]

Correct. Now, look at the terms, one at a time, and describe them. What each term means, and what each term does, or tells you.

 

[jbriggs444]

My take on the problem is somewhat different from Bystander's. It appears to be more an exercise in significant figures than a problem in geophysics.

The rule that I hear you using for significant figures is "the result has as many significant figures as the input with the fewest significant figures". That rule is correct and reasonable if you are multiplying a few numbers together. It is not the correct rule for adding a few numbers together.

If you go refer back to your notes, to your textbook or to Google, can you give us the rule for adding numbers? And how many digits are there in your value for theta?