Circumference of Circle with Uncertainty

[ELLE_AW]

Homework Statement

Calculate the circumference (including uncertainty) of a circle whose measured radius is r=7.3 ± 0.2cm.

2.Relevant equations & 3.The attempt at a solution

- Circumference of circle --> C = 2πr = 2π7.3 = 45.87 cm

- Exact constant error propagation --> z = kx

- Limit Error --> δz = kδx

- Therefore, δC = 2π(0.2 cm) = 1.257 cm

Final Answer = 46 ± 1 cmOR Should I be going about it like this:

- Circumference of circle --> C = 2πr = 2π7.5 = 47.124 cm = 47 cm

- Circumference of a circle --> C = 2πr = 2π7.1 = 44.611 cm = 45 cm

- Final Answer 46 ± 1 cmI was discussing this with someone else. I did it the first way and they did it the second way.

Also, my final answer has the correct significant figures right?

 

[kuruman]

You should do it the first way. Bracketing the calculated value with the minimum and maximum values using the given uncertainty is for people who are not conversant with calculus and do not understand where ΔC = 2πr Δr comes from. Yes, your final answer has the correct sig. figs.

 

[ELLE_AW]

You should do it the first way. Bracketing the calculated value with the minimum and maximum values using the given uncertainty is for people who are not conversant with calculus and do not understand where ΔC = 2πr Δr comes from. Yes, your final answer has the correct sig. figs.

Thank you! That's what I thought as well :)

 

[Orodruin]

Word of warning: You typically should not round errors down. This overrepresents the accuracy that you have. The typical thing to do when you have an error whose first non-zero digit is 1 or 2 is to include another digit to also avoid overstating the error.

The number of significant digits is not very relevant when you include the errors, the entire point of significant digits is that it is kind of a poor man's error analysis - letting you get a feeling for the kind of accuracy that you have from the number of digits you have included - but this is obsolete when you have the actual error!

In this case, I would answer 45.9±1.3 cm.