Significant Figures Lab
Purpose
To apply the rules of significant figures when measuring and predicting
experimental values.
Materials stopwatch
30 cm ruler (± 0.05 cm)
pennies (8) digital scale (200 ± 0.01g)
Safety
metrestick (± 0.001 m)
graduated cylinder (10±0.05 cm3)
The “blue water” contains dissolved chemicals including copper (II) ions; this
liquid is not highly toxic but students should avoid contact with their skin,
eyes, mouth, and nose. If any “blue water” is spilled, wipe up the spill
immediately and rinse thoroughly with water.
Procedure
Part 1 :
Time interval for heartbeats

To ensure similar conditions, all timings were conducted without delay in the same
location using the same subject, timers, and stopwatches.

Exactly ten (10) heartbeats were counted by the subject while the time interval for
those ten heartbeats was measured by three timers using stopwatches.

This procedure was repeated, providing a total of six data values for 10 heartbeats.

This procedure was performed once for 60 beats (3 data values for 60 heartbeats)

The data was recorded using ink in Table 1a.
Part 2 :
Dimensions of a penny

Two pennies were given to each group member

The diameter and height of each penny was measured using a 30-cm ruler

The height and length of all pennies together was measured using a 30-cm ruler.

The data was recorded using ink in Table 2a.
Part 3 :
Density of “blue water”

All objects were removed from the 200g digital scale and the scale was reset to zero.

A small graduated cylinder (10 mL) was placed on the scale and its mass was recorded.

Liquid that was labelled “blue water” was placed in the graduated cylinder until the
meniscus (lowest point on the top of the surface) was at the 10 mL mark.

The mass of the graduated cylinder and the 10-mL of “blue water” was measured using
the 200 g digital scale.

The same procedure was repeated using a 50-mL, then a 100-mL graduated cylinder
and the maximum volume of “blue water”

The data was recorded using ink in Table 3a.
Raw Data
Table 1a.
Time intervals, t, for 10 heartbeats and 60 heartbeats.
time interval, t / s
TRIAL
10 beats
60 beats
1
2
3
Table 2a.
Height and diameter of individual pennies and the combined height and length
for all pennies. (Indicate the number of pennies used in parentheses)
Single penny
A
B
C
D
all (
)
pennies
height,
h / cm
diamter,
d / cm
Table 3a.
Masses of empty and full graduated cylinders
volume of “blue water”,
V / mL
mass of graduated cylinder,
mgc / g
mass of graduated cylinder and
“blue water”, mgc+bw / g
Data Processing
Table 1b.
Analysis of time intervals for 10 beats and 60 beats
10 heartbeats
(measured)
mean time
interval,
x/s
Table 2b.
standard
deviation
s/s
60 heartbeats
(predicted)
relative
uncertainty
%
mean time
interval,
x/s
uncertainty
s
60 heartbeats
(measured)
mean time
interval,
x/s
standard
deviation
s/s
error
absolute
error / s
relative error
/%
Analysis of height and diameter of pennies
single penny (measured)
mean,
x / cm
standard
deviation
s / cm
relative
uncertainty
%
all ( ) pennies
(predicted)
mean
x / cm
uncertainty
all ( ) pennies
(measured)
mean
x / cm
standard
deviation
s / cm
error
absolute
error / cm
relative
error / %
height,
h
diamter,
d
Table 3b.
Density of “blue water”
volume of “blue water”
V/±
mL
mass of “blue water”,
mbw / ±
g
density of “blue water”
ρ / kg dm-3
absolute uncertainty
kg dm-3
relative uncertainty
%
Sample Calculations
 For each TYPE of calculation, ONE sample calculation must be shown
o Generally, the first set of data that uses the calculation is used to demonstrate
the calculation
o Communicate the variables and formula clearly for the reader
o Substitute using a designated sample set and solve
o Show proper number of significant digits and appropriate units in the final answer
 Sample calculations should be shown near the table where the data is presented
Calculations to be shown include, but are not limited to:
Mean Time Interval, x , for 10 heartbeats (from data in Table 1a)
x = (sum of all time intervals, xi ) ÷ (the number of samples taken, n)
x
xi

n
Sample Variance, s2, for 10 heartbeats (from data in Table 1a)
( x  xi ) 2
s 

n 1
2
Sample Standard Deviation, s, for 10 heartbeats (from data in Table 1a)
( x  xi )2
s s 

n 1
2
Relative Uncertainty for 10 heartbeats (from data in Table 1b)
relative uncertainty
= (absolute uncertainty of the measurement) ÷ (measurement value)
= (sample standard devaition) ÷ (sample mean)
=
s
 100% 
x
Absolute Error for 60 heartbeats
absolute error = difference between the experimental value and expected value
= (time for 60 heartbeats, t60) – (6 times the time for 10 heartbeats, 6 t10)
= | t60 – 6t10 |
=
Relative Error for 60 heartbeats
relative error = the ratio of the absolute error to the accepted value, expressed as a percent
= (absolute error for 60 heartbeats) ÷ (actual time interval for 60 heartbeats)
=
| t60  6t10 |
 100% 
t60
Conclusion and Evaluation







comment on the purpose / goals of the experiment
state the significant findings of the experiment
state the general relationships demonstrated in the experiment
comment on the possible implications of these conclusions
compare the measured and expected values
evaluate the random and systematic errors in the experiment
identify specific strategies to improve the investigation
Heartbeats
 Compare the actual (measured) time for 60 heartbeats and the expected time for 60
heartbeats based on the average time for 10 heartbeats.
 Evaluate the difference between these two values.
 Identify specific reasons why the expected value was higher/lower than the actual value
 Identify specific methods or materials that could improve the precision (reduce random
error), the accuracy (remove/reduce a source of systematic error), the efficiency, or the
meaning of this or a similar investigation.
Pennies
 Compare the actual (measured) height and diameter all of your pennies and the
expected height and diameter of an average penny.
 Evaluate the differences between these values.
 Identify specific reasons why the expected value was higher/lower than the actual value
 Identify specific methods or materials that could improve the precision, accuracy,
efficiency, or meaning of this or a similar investigation.
Density of Blue Water
 Compare the density of the “blue water” using each size of graduated cylinder
 Evaluate which graduated cylinder provides the best data for determining these values.
 State your concluded value and uncertainty (including relative uncertainty) for “blue
water”
 Compare this concluded value to the density of pure water (1.00 g / mL).
 Identify specific methods or materials that could improve the precision, accuracy,
efficiency, or meaning of this or a similar investigation.