Transcript 1.2 Uncertainties and Errors

1.2 Measurement and
Uncertainties
The
SI system of fundamental and derived units
Uncertainty and error in measurement
Uncertainties in calculated results
Uncertainties in graphs
The Nature of Measurement

Consider the following reading on a meter
stick:
1
cm
2
3
4
5
6
7
8
Fundamental Units of Measure
These seven units measure fundamental
physical properties of nature.
 They are not composed of other units.

1. Distance
the meter (m)
 1 m = the distance traveled by light in a
vacuum in a time of 1/299,792,458 s.
 Common measuring instruments:


Meter stick, tape measure
2. Mass
the kilogram (kg)
 1 kg = the mass of a certain quantity of a
platinum-iridium alloy kept at the Bureau
International des Poids et Mesures in
France
 Common measuring instruments:


Scale, Ohaus balance
3. Time
the second (s)
 1 s = the duration of 9,192,631,770 full
oscillations of the electromagnetic
radiation emitted in a transition between
the two hyperfine energy levels in the
ground state of a cesium-133 atom.
 Common measuring instrument:


Stopwatch
4. Electric Current
the ampere (A)
 1 A = defined as the amount of current
needed to induce a force of 2 x 10-7 N on
a pair of parallel conductors 1 m in length.
 Common measuring instrument:


Ammeter
5. Temperature
the kelvin (K)
 1 K = 1/273.16 of the thermodynamic
temperature of the triple point of water.
 Common measuring instruments:


Thermometer, temperature probe,
thermocouple
6. Amount of substance
the mole (mol)
 1 mol = 6.02 x 1023 molecules
(Avogadro’s number, the number of
molecules in 12 g of carbon-12.).
 This is calculated: not a directly measured
value.

7. Luminous Intensity
the candela (cd)
 1 cd = intensity of a source of frequency
5.4 x 1014 Hz emitting 1/683 W per
steradian.
 Common measuring instruments:
 Not needed for IB exam

Derived Units

these units are composed of other units
 examples:
velocity = m s-1 (or m/s)
power = watts (kg m2 s-3 or kg m2/s3 )
A note on convention…
 IB
& Most Publishers prefer inverse
units be expressed with a negative
exponent rather than in the
denominator of a fraction
m s-1 instead of m/s, but still read
“meters per second”
ex:
Dimensional Analysis
How many meters tall are you?
 Find a conversion factor to get you from
your current units to your desired units.


1 meter = ?? inches
Consistency of Units


Equations must result in the same units on both
sides of equation.
Example:
 Formula for period of a pendulum
 T = 2π √(l/g)
 T = period (s)
 l = length (m)
 g = gravitational acceleration (m s-2)
 Reduces into seconds on both sides!!!
Stop to Think…

Which of the following cannot be
measured in fundamental units?
Area of a football field
 Acceleration due to gravity on Mars
 Velocity of a coconut-carrying swallow
 Weight of above-mentioned coconut
 Power used by the Griswold Family Christmas
Exterior Illumination

Scientific Notation

Is there an easier way to express large
numbers?

Ex)
2 3471693273 x. 10
23,471,693,273
10 places
This
Count
number
the
Move
the
becomes
number of
the so
decimal
point
exponent
decimal
of
that
thereplaces
is ten.
only
Moving
you moved
the decimal
the
one
non-zero
left
decimal
makes
point.
itleft of
digit
on the
positive,
right
it.
makes negative.
Stop to Think…

Place the following numbers into scientific
notation.
Metric Prefixes
Power
10-18
10-15
10-12
10-9
10-6
10-3
10-2
10-1
Prefix
attofemtopiconanomicromillicentideci-
* rarely used
Symbol
a
f
p
n
µ
m
c
d
Power
101
102
103
106
109
1012
1015
1018
Prefix
dekahectokilomegagigaterapetaexa-
Symbol
da*
h*
k
M
G
T
P*
E*
Stop to Think…

Use scientific notation and metric prefixes
to state the given measurements in a
briefer expression.
Error

Random


can be reduced with repeated readings
Systematic

cannot be reduced with repeated readings
Precision vs. Accuracy
Accuracy is how close readings or
calculations are to the true or accepted
value.
 Precision is how many decimal places an
instrument resolves.
 To illustrate this…. a challenge of
archery!!!!

Precision vs. Accuracy
x xxx
xxx
True or
accepted
value
Precise, but not accurate!
Precision vs. Accuracy
x
x
x
x
x
x
x
x
Accurate, but not precise!
Precision vs. Accuracy
x
x
x
x
x
x
x
Neither accurate nor precise!
Precision vs. Accuracy
xxx
xxxx
Both accurate and precise!
Stop to Think…
Which is more precise, the metric side of a
meter stick or the inches side?
 What could affect the accuracy of a meter
stick?

Significant Figures
Think about our definition of precision…
 I want to measure a mile with a meter
stick…
 Does it make sense to record to the
millimeters place if I haphazardly
measured a mile?
 The number of significant digits clues you
in to the precision of the measurement.

Rules for determining sigfigs

This will be a separate PowerPoint
Presentation – Stay Tuned
Sigfigs in Calculations

This will be a separate PowerPoint
Presentation – Stay Tuned
Stop to Think…

How many sigfigs are in the following
measurements?
How to state uncertainties
Absolute
 Fractional
 Percentage

Standards Achieved
1.2.1 – State the fundamental units in the
SI system.
 1.2.2 – Distinguish between fundamental
and derived units and give examples of
derived units.
 1.2.3 – Convert between different units of
quantities.
 1.2.4 – State units in accepted SI format.
 1.2.5 – State values in scientific notation
and in multiples of units with appropriate
prefixes.

Standards Achieved
1.2.6 – Describe and give examples of
random and systematic error.
 1.2.7 – Distinguish between precision and
accuracy.
 1.2.8 – Explain how the effects of random
errors may be reduced.
 1.2.9 – Calculate quantities and results of
calculations to the appropriate number of
significant figures.

Standards Achieved
1.2.10 – State uncertainties as absolute,
fractional and percentage uncertainties.
 1.2.11 – Determine the uncertainties in
results.

Standards Achieved
1.2.12 – Identify uncertainties as error
bars in graphs.
 1.2.13 – State random uncertainty as an
uncertainty range (±) and represent it
graphically as on “error bar.”
 1.2.14 – Determine the uncertainties in the
gradient and intercepts of a straight-line
graph.
