Parts of a Measurement
1. The value (numerical portion)
2. The unit (describes what units)
3. The name of substance being measured
EX:
1 teaspoon salt
2 liters of pop
1
Uncertainty in Measurement
• No matter how careful you are
• No matter how carefully you read the
measuring instrument
• No measurement is perfectly accurate
• The quality of our measurements are
stated in terms of accuracy and precision
2
Uncertainty in Measurement
Measured numbers
-are an estimated amount
-measured to a certain number of significant
figures
-a numerical value with attached units that
expresses a physical quantity such as length,
mass, volume, time or temperature.
3
Uncertainty in Measurements
•Accuracy: is the degree of agreement between the
true value and the measured value.
•Precision: is a measure of the agreement of
replicate measurements
•Uncertainty: is the degree of doubt in a single
measurement.
4
Accuracy
= of a measurement is how close that
measurement is to the true or “exact”
value
EX: Standard weight = 5.00g
4.98g more accurate than 5.12 g
5
Accuracy
• Also subject to the
reliability of the
measuring instrument
• The smaller the
increments of units on
the instrument, the
more accurate
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Length Measurements
Measuring the length of a
metal rod
• Ruler A has more
uncertainty and gives
less precise
measurements.
Metric Rulers for Measuring
Length.
• Ruler B has less
uncertainty and gives
more precise
measurements.
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Precision
• Precision = making reproducible or
repetitive measurements of the same
quantity
• How fine the divisions are
• There will always be some uncertainty
because of the limits in the accuracy of
your instruments
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Precision versus Accuracy
Precise and
accurate
Imprecise and
inaccurate
Precise but
inaccurate
It is also possible
to have an
accurate
measurement
without being
precise.
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“Accuracy is telling the truth…..
Precision is telling the same story over
and over again.”
Yiding Wang
yiang@mtu.edu
10
• Strive for measurements that are accurate
and precise
• Measurements you perform will be used in
subsequent calculations
• In scientific measurements all the digits
known w/certainty, plus the one estimated
digit, are known as significant figures or
significant digits.
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Significant Figures
Significant figures: is defined to be all digits in a
number representing data or results that are known
with certainty plus the first uncertain digit.
5.4 cm
0
1
2
3
4
5
6
7
8
9
10 cm
9
10 cm
5.48 cm
0
1
2
3
4
5
6
7
8
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Significant figures or
Significant digits
• ANY numbers generated by means of a
measurement (length, volume, time, etc)
should be expressed in the correct number
of significant figures.
• This reflects how close the measured
values are to the true values.
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Significant Figures (digits)
= reliable figures obtained by
measurement
= all digits known with certainty plus
one estimated digit
Taking the measurement
• Is always some uncertainty
• Because of the limits of the instrument you
are using
EXAMPLE: mm ruler
Is the length of the line between 4 and 5 cm?
Yes, definitely.
Is the length between 4.0 and 4.5 cm? Yes, it
looks that way.
But is the length 4.3 cm? Is it 4.4 cm?
• It is important to be honest when reporting
a measurement, so that it does not appear
to be more accurate than the equipment
used to make the measurement allows.
• We can achieve this by controlling the
number of digits, or significant figures,
used to report the measurement.
As we improve the sensitivity of the
equipment used to make a measurement,
the number of significant figures increases.
Postage Scale
3g
1g
1 significant
figure
Two-pan
balance
2.53 g
0.01 g
3 significant
figures
Analytical
balance
2.531 g
0.001g
4 significant
figures
Which numbers are
Significant?
How to count them!
Non-Zero integers
• Always count as significant figures
1235 has 4 significant digits
Zeros – there are 3 types
Leading zeros (place holders)
The first significant figure in a
measurement is the first digit other than
zero counting from left to right
0.0045g
(4 is the 1st sig. fig.)
“0.00” are place holders.
The zeros are not significant
Captive zeros
Zeros within a number at always significant
–
30.0809 g
All digits are significant
Trailing zeros – at the end of numbers but to the right of the
decimal point
2.00 g - has 3 sig. digits (what this means is
that the measuring instrument can measure exactly to
two decimal places.
100 m has 1 sig. digit
Zeros are significant if a number contains decimals
Exact Numbers
Are numbers that are not obtained by
measuring
Referred to as counting numbers
EX : 12 apples, 100 people
Exact Numbers
Also arise by definition
1” = 2.54 cm
or
12 in. = 1 foot
Are referred to as conversion factors that
allow for the expression of a value using
two different units
Significant Figures
Rules for sig figs.:
•Count the number of digits in a measurement from left to
right:
•Start with the first nonzero digit
•Do not count place-holder zeros.
•The rules for significant digits apply only to
measurements and not to exact numbers
Sig figs is short for significant figures.
Determining Significant Figures
State the number of significant figures in the following measurements:
2005 cm
4
0.050 cm
2
25,000 g
2
0.0280 g
3
25.0 ml
3
50.00 ml
4
0.25 s
2
1000 s
1
0.00250 mol
3
1000. mol
4
Rounding Numbers
• To express answer in correctly
• Only use the first number to the right of the
last significant digit
Rounding
• Always carry the extra digits through to the
final result
• Then round
EX:
Answer is 1.331 rounds to 1.3
OR
1.356 rounds to 1.4
Significant Figures
Rounding off sig figs (significant figures):
Rule 1: If the first non-sig fig is less than 5, drop all non-sig
fig.
Rule 2: If the first sig fig is 5, or greater that 5, increase the
last sig fig by 1 and drop all non-sig figs.
Round off each of the following to 3 significant figures:
12.514748
12.5
192.49032
192
0.6015261
14652.832
0.602
14,700
Measurements With a Ruler or
Meter Stick – Look at it FIRST! –
Where is “0”
31
Protractor for Measuring Angles
32
Measuring Angles
Units are degrees (º)
33
Practice Time
34
Using a Vernier Caliper
http://phoenix.phys.clemson.edu/labs/cupol/vernier
/
•Used to accurately determine the fraction part of the
least count division.
•Length of an object, the outer diameter (OD) of a
round or cylindrical object, the inner diameter (ID) of a
pipe, and the depth of a hole.
35
Parts of a Caliper
36
Main scale
Auxillary
(Venier) Scale
• The caliper consists of a main scale engraved on a fixed ruler and
an auxiliary caliper scale engraved on a movable jaw
• The movable auxiliary scale is free to slide along the length of the
fixed ruler.
• The main scale is calibrated in centimeters with the smallest division
in millimeters.
• The auxiliary scale has 10 divisions that cover the same distance as
9 divisions on the main scale. Therefore, the length of the auxiliary
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scale is 9.0 mm.
• When the caliper is closed and properly zeroed
the first mark (zero) on the main scale is aligned
with the first mark on the auxiliary scale.
• The last mark on the auxiliary scale will then
coincide with the 9 mm-mark on the main scale.
• This is read 0.00 cm.
38
39
40
• Once the caliper is positioned to make a
reading, make a note of where the first mark on
the auxiliary scale falls on the main scale.
• We see that the object's length is between 1.2
cm and 1.3 cm because the first auxiliary mark is
between these two values on the main scale. 41
• The last digit (tenths of a millimeter) is found by
noting which line on the auxiliary scale coincides
with a mark on the main scale.
• The last digit is 3 because the third auxiliary
mark lines up with a mark on the main scale. T
• The length of the object is 1.23 cm.
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Practice Time!
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44
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