m/s
and 3.00 x m/s 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.
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