http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/
Rounding Rules
less than 5 round down
e.g: 4.62 = 4.6
5 round to nearest even number e.g: 4.65 = 4.6, 4.75 = 4.8
More than 5 round up
e.g: 4.67 = 4.7, 4.651 = 4.7
Significant figures and scientific notation
3.563 ( 2 sig fig) = 3.6
0.000047236 ( 3 sig figs) = 0.0000472 = 4.72 x 10-5
32000000 ( 3 sig fig) = 3.20 x 107
When doing calculations do not round until the end.
Round your final answer to the smallest number of significant
figures given in the question.
Eg. 3.92 x 5.7 = 22.344 = 22
Web site
Problem sheet
Uncertainties
Shape of Time in seconds
boat
Average time (s)

3.2
3.4
2.9
3.2

1.7
1.7
1.9

4.2
2.1
2.0
1.8
2.8

1.5
1.4
1.3
1.4
There is a mistake in one of the times.
This is not an uncertainty.
Results from three experiments to find the speed of
sound.
(a) (240  100) m/s
(b) (48  500) m/s
(c) (333  2) m/s

absolute uncertainty
Example: Find the speed.
d = (50  1) m
t = (0.033  0.002) s
Percentage uncertainty =
absolute x 100%
mean value or reading
Use the biggest percentage uncertainty to calculate the
absolute uncertainty in the final answer.
The three types of uncertainties.
Systematic.
Reading.
Random.
Systematic uncertainty Reduce this and to get an accurate result.
– zero uncertainty
- design of experiment
Reading uncertainty – chose the correct measuring
instrument for that reading.
i.e.. You can measure a distance using trundle wheel, a metre
stick or a micrometre
Analogue – ½ least unit
Digital – least unit
14.2
ammeter
Least unit is 1 N
Least unit is 0.1 A
F = (18 ± 0.5)N
I = (14.2 ± 0.1)A
Find out which of the following you can measure most
accurately.
1.The temperature of running water from the cold tap.
2.The volume of water in bottle A.
3.The current through a 2.5V bulb connected to 3V.
4.The length of the lab bench.
5.The time for 10 swings of a 50 cm long pendulum.
6.The inside and outside diameters of a boiling tube.
7.The diameter of a golf ball.
For each of the above you should note:
(a) The measuring instrument used.
(b) The measurement.
(c) The reading uncertainty.
(d) Your answer in the form
(measurement + absolute uncertainty)
(e) The percentage uncertainty.
Random uncertainties – caused by random changes in
temperature, air movements etc.
Repeat readings will improve the reliability and make the
mean reading more precise
Mean = sum of readings ÷ number of readings
Random uncertainty
= (max value – min value) ÷ number of values
Example: Find the average distance travelled.
distances (m) 23.4
21.3
22.5
23.5
22.1
22.8
Experiment:
•Find the time it takes a trolley to travel 50 cm down a slope
with an angle of 150.
•Repeat at least 5 times and find the mean and random
uncertainty in the time.
•Find the reading uncertainty for time.
•Calculate the percentage uncertainty in time using the
largest absolute uncertainty (reading or random)
•Find the reading uncertainty and percentage uncertainty in
distance.
•Calculate the average speed and the absolute uncertainty
in it.
2010 paper Qu 24
An experiment is carried out to measure the time taken of a
steel ball to fall vertically through a fixed distance using
an electronic timer.
(a)The experiment is repeated and the following values for
time recorded.
0.49s 0.53s 0.50s 0.50s 0.55s 0.51s
Calculate:
(i) The mean value of the time;
(ii) the approximate random uncertainty in the mean value of
the time.
Answers (i) 0.51s
(ii) 0.02s (0.012 acceptable)