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Measurement Unit
Unit Description:
• In this unit we will focus on the
mathematical tools we use in science,
especially chemistry – the metric system
and moles.
• We will also talk about how to gauge the
accuracy and precision of our
measurements.
Measurement Unit
The Big Questions
• How do we measure things in chemistry?
• Why are units so important?
• How accurate and precise are my
measurements and how can I show this in my
calculations?
• How can I move between different
measurement units?
• What the heck are moles and why are they
important?
Measurement Unit
Review Topics:
• scientific notation and exponents
• metric system
• algebra
• density calculations
• dimensional analysis – conversions
• temperature conversions
Measurement Unit
New Topics:
• rounding in chemistry – significant
figures
• determining uncertainty of a
measurement
• % error
• accuracy vs. precision
Measurement Unit
New Topics:
Moles!
and related topics…
Accuracy and Precision
• Accuracy = how close one comes to the
actual value (absolute error)
• Precision = the agreement of two or more
measurements that have been made in
the same way (reproducibility)
Accuracy and Precision
Can you have accuracy without precision?
Or precision without accuracy?
Why or why not?
What are significant figures
and why do we use them?
• Measurements are dependent on the
instruments we use.
• We round our measurements to reflect the
level of precision of these instruments.
• These are significant figures.
Rules for Recognizing
Significant Figures
1. Non-zero numbers are always
significant.
2. Zeros between non-zero numbers are
always significant.
3. All final zeros to the right of the
decimal place (i.e. after digits) are
significant.
Rules for Recognizing
Significant Figures
4. Zeros that act as placeholders are not
significant.
Convert quantities to scientific notation to
remove the placeholder zeros.
5. Counting numbers and defined constants
have an infinite/unlimited number of
significant figures.
How many sig figs are in the following measurements?
1.
46 g
7.
0.04066 g
2.
406 g
8.
0.00406600 g
3.
460 g
9.
1.04066 g
4.
460. g
10.
100.040660 g
5.
460.0 g
11.
1000466 g
6.
40660 g
12.
100046600 g
How many sig figs are in the following measurements?
1.
46 g
2
7.
0.04066 g
4
2.
406 g
3
8.
0.00406600 g 6
3.
460 g
2
9.
1.04066 g
4.
460. g
3
10.
100.040660 g 9
5.
460.0 g
4
11.
1000466 g
6.
40660 g
4
12.
100046600 g 7
6
7
Rules for Rounding Numbers
If the digit to the immediate right of the
last significant figure is
1. < 5, do not change the last significant
figure.
2. > 5, round up the last significant figure.
Rules for Rounding Numbers
If the digit to the immediate right of the
last significant figure is
3. = 5, and is followed by a nonzero digit,
round up the last significant figure.
4. = 5, and is not followed by a non-zero
digit, look at the last significant figure.
If it is an odd digit, round it up.
If it is an even digit, do not round up.
Rounding Practice:
Round the following measurements to two sig
figs:
13.4 g
13.5 g
13.51 g
14.5 g
14.51 g
14.500001 g
14.500000 g
10.5 g
Rounding Practice:
Round the following measurements to two sig
figs:
13.4 g
13 g
13.5 g
14 g
13.51 g
14 g
14.5 g
14 g
14.51 g
15 g
14.500001 g
15 g
14.500000 g
14 g
10.5 g
10. g
Significant Figures in
Measurement
consist of all parts of the measurement
that you know for sure
+ one estimated digit
e.g. metric ruler, thermometer
Significant Figures
What about electronic instruments?
e.g. electronic balances, digital
thermometers
The electronics within the instrument
estimate the last digit.
Addition and Subtraction
You cannot be more precise than your last
uncertain number. If the mass of
something weighed on a truck scale was
added to the mass of an object weighed
on one of our centigram balances, the sum
would NOT be precise to 0.01 g.
Addition and Subtraction
If you circle the uncertain number (which is
significant), it can be seen that in additions
and subtractions, you round off to the leftmost uncertain number.
Addition and Subtraction
e.g.
20.53
6.6
3.986
31.116  31.1
An answer is reported to ONE uncertain
number.
Therefore 31.116 is rounded off to 31.1.
Multiplication and Division
• The product or quotient is precise to the number
of significant figures contained in the least
precise factor.
e.g. 1:
63.2 cm x 5.1 cm = 322.3 cm2  320 cm2 (2 sfs)
e.g. 2:
5.30 m x 0.006 m = 0.0318 m2  0.03 m2 (1 sf)
Sig Fig Practice
Addition/Subtraction and Multiplication/Division
1.
Calculate and round to the correct number of sig figs.
a) 4.53 x 0.01 x 700 =
b) 2 x 4 x 50400 =
c) _0.01_ =
0.0001
d) 3211 + 0.1590 + 3.2 =
e) 45119.32 – 0.001530 =
2.
(8.7 + 15.43 + 19) =
(4.32 x 1.7)
Sig Fig Practice
Addition/Subtraction and Multiplication/Division
1.
Calculate and round to the correct number of sig figs.
a) 4.53 x 0.01 x 700 = 30
b) 2 x 4 x 50400 = 400,000
c) _0.01_ = 100
0.0001
d) 3211 + 0.1590 + 3.2 = 3214
e) 45119.32 – 0.001530 = 45119.32
2.
(8.7 + 15.43 + 19) = 5.9
(4.32 x 1.7)
More Sig Fig Practice
Addition/Subtraction and Multiplication/Division
Perform each of the following mathematical operations and
express each result to the correct number of significant figures.
1.
9.5 mL + 4.1 mL + 2.8 mL + 3.175 mL =
4
(this is an averaging calculation)
2.
(8.925 g – 8.804 g) x 100% =
8.925 g
3.
(9.025 g/mL – 9.024 g/mL) x 100% =
9.025 g/mL
More Sig Fig Practice
Addition/Subtraction and Multiplication/Division
Perform each of the following mathematical operations and
express each result to the correct number of significant figures.
1.
9.5 mL + 4.1 mL + 2.8 mL + 3.175 mL =
4
4.90 mL
(this is an averaging calculation)
2.
(8.925 g – 8.804 g) x 100% = 1.36%
8.925 g
3.
(9.025 g/mL – 9.024 g/mL) x 100% = 0.01%
9.025 g/mL
More Sig Fig Practice (Honors)
Addition/Subtraction and Multiplication/Division
Perform each of the following mathematical operations and
express each result to the correct number of significant figures.
4.
4.184 x 100.62 x (25.27-24.16) =
5.
(9.04 – 8.23 + 21.954 + 81.0) 3.1416 =
6.
8.27 (4.987 – 4.962) =
7.
1.285 x 10-2 + 1.24 x 10-3 + 1.879 x 10-1 =
8.
(1.0086 – 1.00728) =
6.02205 x 1023
More Sig Fig Practice (Honors)
Addition/Subtraction and Multiplication/Division
Perform each of the following mathematical operations and
express each result to the correct number of significant figures.
4.
4.184 x 100.62 x (25.27-24.16) = 467
5.
(9.04 – 8.23 + 21.954 + 81.0) 3.1416 = 33.04
6.
8.27 (4.987 – 4.962) = 0.21
7.
1.285 x 10-2 + 1.24 x 10-3 + 1.879 x 10-1 = 2.020 x 10-1
8.
(1.0086 – 1.00728) = 2.2 x 10-27
6.02205 x 1023
Uncertainty in Measurement
• The last place of a measurement is always
an estimate.
• The size of the estimate is based on the
reliability of the instrument
 range within which the measured value
probably lies
Uncertainty in Measurement
• Report to only one sig fig.
• That digit should be in the same decimal
place as the last sig fig of the measurement.
Correct
Incorrect
36.5 ± 0.5 m
36.5 ± 0.25 m
300.4 ± 0.2 g
300.4 ± 0.06 g
230 ± 10 s
232.4 ± 5 s
Uncertainty in Measurement
• Report to only one sig fig.
• That digit should be in the same decimal
place as the last sig fig of the measurement.
Correct
Incorrect
36.5 ± 0.5 m
36.5 ± 0.25 m
 36.5 ± 0.2 m
300.4 ± 0.2 g
300.4 ± 0.06 g
 300.4 ± 0.1 g
230 ± 10 s
232.4 ± 5 s
 232 ± 5 s
Percent Error
|theoretical – actual| x 100% = ___ %
theoretical
“what you should have got” – “what you got” x 100%
“what you should have got”