# 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. **

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