# Using Uncertainties to Get the Range of Possible Values

Problem: You measure a time to have a value of (9.22 ± 0.09) s. Your friend measures the time to be (9.385 ± 0.002) s. The accepted value of the time is 9.37 s. Does your time agree with the accepted? Does your friend's time agree with the accepted?

We look within 2 deviations of your value, that is between 9.22 - 2(0.09) = 9.04 s and 9.22 + 2(0.09) = 9.40 s. The accepted value is within this range of 9.04 to 9.40 s, so your experiment agrees with the accepted.

The news is not so good for your friend. 9.385 - 2(0.002) = 9.381 s and 9.385 + 2(0.002) = 9.389 s. The range of answers for your friend, 9.381 to 9.389 s, does not include the accepted value, so your friend's time does not agree with the accepted value.

## Return (or use Browser "back" function)

Problem: Are the following numbers equal within the expected range of values?

(i) (3.42 ± 0.04) m/s and 3.48 m/s?

The 2-deviation range is 3.34 to 3.50 m/s.  Yes the numbers are equal.

(ii) (13.106 ± 0.014) grams and 13.206 grams?

The 2-deviation range is 13.078 to 13.134 grams.  No the numbers are not equal.

(iii) (2.95 ± 0.03) x m/s and 3.00 x m/s

The 2-deviation range is 2.89  x to 3.01 x m/s.  Yes the numbers are equal.