1.2.6-11Uncertainty and error
1.2.7 Distinguish between precision and accuracy
 Accuracy is how close to the “correct” value
 Precision is being able to repeatedly get the same
value
 Measurements are accurate if the systematic error is
small
 Measurements are precise if the random error is
small.
Examples: groupings on targets
Example of precision and accuracy
 A voltmeter is being used to measure the potential
difference across an electrical component. If the
voltmeter is faulty in some way, such that it produces
a widely scattered set of results when measuring the
same potential difference, the meter would have low
precision. If the meter had not been calibrated
correctly and consistently measured 0.1V higher than
the true reading (zero offset error), it would be in
accurate.
1.2.6 Describe and give examples of random and systematic
errors.
1.2.8 Explain how the effects of random errors may be reduced.
There are two types of error, random and systematic.
 Random Errors - occur when you measure a
quantity many times and get lots of slightly different
readings.
 Examples - misreading apparatus, Errors made with
calculations, Errors made when copying collected
raw data to the lab report
 Can be reduced by repeating measurements many
times.
 Measurements are precise if the random error is
small
1.2.6 Describe and give examples of random and systematic
errors.
1.2.8 Explain how the effects of random errors may be reduced.
There are two types of error, random and systematic.
 Systematic error – when there is something
wrong with the measuring device or method
 Examples – poor calibration, a consistently bad
reaction time on the part of the recorder, parallax
error
 Can be reduced by repeating measurements using a
different method, or different apparatus and
comparing the results, or recalibrating a piece of
apparatus
 Measurements are accurate if the systematic error is
small.
 Graphs can be used to help us identify different types
of error.
 Low precision is represented by a wide spread of
points around an expected value.
 Low accuracy is represented by an unexpected
intercept on the y-axis. Low accuracy gives rise to
systematic errors.
Accurate or Precise?
Accurate or Precise?
Accurate or Precise?
Accurate or Precise?
1.2.9 Calculate quantities and results of calculations
to the appropriate number of significant figures
 The number of sig figs should reflect the precision of
the value of the input data.
 If the precision of the measuring instrument is not
known then as a general rule, give your answer to 3
sig figs.
 You may be penalized on the IB exam if you
round your answer off to too few sig figs or if
you give to many.
Three Basic Rules
 Non-zero digits are always
significant.
 523.7
has ____ significant figures
 Any zeros between two significant digits
are significant.

23.07 has ____ significant figures
 A final zero or trailing zeros if it has a
decimal, ONLY, are significant.


3.200 has ____ significant figures
200 has ____ significant figures
1.2.9 Calculate quantities and results of calculations
to the appropriate number of significant figures
 One rule: for multiplication and division, the number
of significant digits in a result should not exceed that
of the least precise value upon which it depends.
1.2.9 Practice 13(Dickinson)
 A meter rule was used to measure the length, height
and thickness of a house brick and a digital balance
was used to measure its mass. The following data
were obtained.
Length = 20.5cm, height = 8.4cm, thickness 10.2cm,
mass = 3217.94g
 Calculate the density of the house brick and give your
answer to an appropriate number of sig figs.
1.2.9 Practice 13(Dickinson)
Solution
 Density = (mass/volume)
 Density = (3217.94/1756.44)
 Density = 1.8320808 g cm-3
 Density = 1.8 g cm-3
1.2.10 State uncertainties as absolute, fractional and
percentage uncertainties.
 Random uncertainties(errors) due to the precision of
a piece of apparatus can be represented in the form
of an uncertainty range.
 Experimental work requires individuals to judge and
record the numerical uncertainty of recorded data
and to propagate this to achieve a statement of
uncertainty in the calculated results.
1.2.10 State uncertainties as absolute, fractional and
percentage uncertainties.
Rule of Thumb
 Analogue instruments = +/- half of the limit of
reading

Ex. Meter stick’s limit of reading is 1mm so it’s uncertainty
range is +/- 0.5mm
 Digital instruments = +/- the limit of the reading
 Ex. Digital Stopwatch’s limit of reading is 0.01s so it’s
uncertainty range is +/- 0.01s
 We can express this uncertainty in one of three ways-
using absolute, fractional, or percentage uncertainties



Absolute uncertainties are constants associated with a particular
measuring device.
(Ratio) Fractional uncertainty = absolute uncertainty
measurement
Percentage uncertainties = fractional x 100%
Example
A meter rule measures a block of wood 28mm long.
 Absolute =
28mm +/- 0.5mm
 Fractional = 0.5mm = 28mm +/- 0.0179
28mm
 Percentage = 0.0179 x 100% =
28mm +/- 1.79%
1.2.10 State uncertainties as absolute, fractional and
percentage uncertainties.
 Random uncertainties(errors) due to the precision of
a piece of apparatus can be represented in the form
of an uncertainty range.
 Experimental work requires individuals to judge and
record the numerical uncertainty of recorded data
and to propagate this to achieve a statement of
uncertainty in the calculated results.