Uncertainties

Question 1

A digital multimeter reads 0.818 V and has an absolute uncertainty of ± 0.001 V . This is
written as 0.818 ± 0.001 V
Calculate percentage uncertainty

Answer 1

δ% = absolute uncertainty (δ)
_____________________ observed measurement (O) × 100%
=
_δ
O × 100%
=
______
0.001
0.818 × 100%

= 0.12%
This would be written as 0.818 V ± 0.12%

Question 2

A voltmeter reading of 0.75 ± 0.05 V
Calculate percentage uncertainty

Answer 2

bserved measurement (O) × 100%
=
_δ
O × 100%
=
_
0.05
0.75 × 100%

= 6.7%
This would be written as 0.75 V ± 6.7%

Question 3

The winning time for the 100 m sprint in the 2016 Rio Olympic Games was 9.81 s. Assuming
the time was 9 . 81 ± 0.01 s and the distance was 100.0 ± 0.1 m, calculate the average speed.

Answer 3

Distance = 100.0 ± 0.1 m
= 100.0 ± (
_0.1
100.0 × 100 ) %
= 100.0 ± 0.1 % (converted to % uncertainty)
Time = 9.81 ± 0.1 s
= 9.81 ± (
_
0.1
9.81 × 100 ) %
= 9.81 ± 1.02 % (converted to % uncertainty)
Average speed =
_
100.0
9.81 ± (0.1 + 1.02 ) % (add percentage uncertainties)

= 10 .194 m s−1 ± 1.12 % (result)
= 10.194 ±
_
1.12
100 × 10.194 (convert back to absolute uncertainty)
= 10.194 ± 0 .114 m s−1

= 10.2 ± 0.1 m s−1 (correct significant figures)

Question 4

A student measured the acceleration due to gravity as 9.73 m s– 2 whereas the accepted
value at their location is 9.813 m s– 2. Calculate the:
a absolute error
b percentage error.

Answer 4

a Ea = |O − A|
= |9.73 − 9.813|
= 0.08 m s−2 (to the correct number of significant figures

b E% =
E_a
A × 100%
= _
0.08
9.813 × 100%
= 0.8%