# Homework Help: Calculating error in measurements w/ uncertainty

1. Jun 30, 2011

### Wa1337

1. The problem statement, all variables and given/known data
The radius of a circle is measured to be 2.4 cm +/- 0.1 cm.
Find the error in the area of the circle.
Find the error in the circumference.

2. Relevant equations
Have no idea but I'm taking a guess it could be multiplying fractional uncertainties?

3. The attempt at a solution
I got 18.09 for area and 15.08 for circumference...just need a way to go about calculating error

...really rusty in math and learning physics now, pardon the noob question.

2. Jun 30, 2011

### Staff: Mentor

A discussion of error analysis can be found here:

http://teacher.pas.rochester.edu/PHY_LABS/AppendixB/AppendixB.html

Near the end of the document is a table showing how to deal with the uncertainty values when performing various mathematical operations.

Keep in mind that constants (like 2 or π) are exact and have zero uncertainty.

3. Jun 30, 2011

### Wa1337

Thanks but I'm still a little confused...would I have to do the 0.1/2.4 twice and add them or what?

4. Jun 30, 2011

### Staff: Mentor

For what calculation?

You might want to ponder entry 5 in the table, which deals with numbers with uncertainties raised to a power.

5. Jun 30, 2011

### Wa1337

Well in that scenario delta Z would be the change in 2.4 + .1 and 2.4 -.1 right? What about delta A?

6. Jun 30, 2011

### Staff: Mentor

Z is the result. ΔZ is the uncertainty in the result. A is the number with uncertainty ΔA. So in the case of calculating Z = A2, n = 2 and
$$\frac{\Delta Z}{Z} = n \frac{\Delta A}{A}$$
giving
$$\Delta Z = 2 Z \frac{\Delta A}{A}$$
and since Z = A2, this yields
$$\Delta Z = 2 A^2 \frac{\Delta A}{A}$$
You could reach the same result using entry 3 in the table (for Z = A*B) by setting B = A and ΔB = ΔA.

7. Jun 30, 2011

### Wa1337

Ok thanks for clarifying.