Amarathon runner completes a 42.238 km course in 2 h, 31 min, and 46 s . there is an uncertainty of 29 m in the distance run and an uncertainty of 3 s in the elapsed time. what is the percent uncertainty in the average speed?

The percentage uncertainty in the average speed is 0.10% (2 sig. fig.)

Explanation:

Consider the formula for average speed .

,

where

The percentage uncertainty of a fraction is the sum of percentage uncertainties in

What are the percentage uncertainties in and in this question?

The unit of the absolute uncertainty in is meters. Thus, convert the unit of to meters:

.

.

The unit of the absolute uncertainty in is seconds. Convert the unit of to seconds:

Similarly,

.

The average speed here is a fraction of and . Both and come with uncertainty. The percentage uncertainty in will be the sum of percentage uncertainties in and . That is:

.

Generally, keep

The percentage uncertainty in here is less than 2%. Thus, keep two significant figures. However, keep more significant figures than that in calculations to make sure that the final result is accurate.

this is a good question! i'll do some research and come back when i have the answer!