Measurement, sigfigs, and
Scientific Notation
Many slides copied from:
http://www.unit5.org/chemistry/Intr
oduction.htm
100 mL
Graduated
Cylinder
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119
Instruments for Measuring Volume
Graduated
cylinder
Syringe
Buret
Pipet
Volumetric
flask
Units of Measuring Volume
1 L = 1000 mL
1 qt = 946 mL
Timberlake, Chemistry 7th Edition, page 3
Reading a Meniscus
10 mL
10
8
proper line of sight
reading correct
6
graduated
cylinder
Units for Measuring Mass
1 kg
(1000 g)
1 lb
1 lb
0.20 lb
Christopherson Scales
Made in Normal, Illinois USA
1 kg = 2.20 lb
1024 g
1021 g
Quantities of
Mass
1018 g
1015 g
1012 g
Giga-
109 g
Mega-
106 g
Kilo-
103 g
base
100 g
milli-
10-3 g
micro-
10-6 g
nano-
10-9 g
pico-
10-12 g
femto-
10-15 g
atomo-
10-18 g
Ocean liner
Indian elephant
Average human
1.0 liter of water
Grain of table salt
10-21 g
10-24 g
Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25
Earth’s atmosphere
to 2500 km
Typical protein
Uranium atom
Water molecule
Factor
Name
Symbol
Factor
Name
Symbol
10-1
decimeter
dm
101
decameter
dam
10-2
centimeter
cm
102
hectometer
hm
10-3
millimeter
mm
103
kilometer
km
10-6
micrometer
mm
106
megameter
Mm
10-9
nanometer
nm
109
gigameter
Gm
10-12
picometer
pm
1012
terameter
Tm
10-15
femtometer
fm
1015
petameter
Pm
10-18
attometer
am
1018
exameter
Em
10-21
zeptometer
zm
1021
zettameter
Zm
10-24
yoctometer
ym
1024
yottameter
Ym
Multiples of bytes
as defined by IEC 60027-2
SI prefix
Name
Symbol
Binary prefixes
Multiple
3
10
6
20
9
30
kilobyte
kB
10 (or 2 )
megabyte
MB
10 (or 2 )
gigabyte
GB
10 (or 2 )
terabyte
TB
10
petabyte
PB
10
exabyte
EB
10
zettabyte
ZB
10
yottabyte
YB
10
12
15
18
21
24
40
(or 2 )
50
(or 2 )
60
(or 2 )
Sy
mb
ol
Multiple
kibibyte
KiB
2
mebibyte
MiB
2
gibibyte
GiB
2
tebibyte
TiB
2
pebibyte
PiB
2
exbibyte
EiB
2
Name
10
20
30
40
50
60
70
(or 2 )
80
(or 2 )
A yottabyte (derived from the SI prefix )
SI-US Conversion Factors
Relationship
Conversion Factors
Length
2.54 cm = 1 in.
2.54 cm
1 in
and
1 m = 39.4 in.
39.4 in
1m
and
946 mL = 1 qt
946 mL
1 qt
and
1 qt
946 mL
1 L = 1.06 qt
1.06 qt
1L
and
1L
1.06 qt
and
1 lb
454 g
and
1 kg
2.20 lb
1 in
2.54 cm
1m
39.4 in.
Volume
Mass
454 g = 1 lb
1 kg = 2.20 lb
454 g
1 lb
2.20 lb
1 kg
Accuracy vs. Precision
Good accuracy
Good precision
Poor accuracy
Good precision
Poor accuracy
Poor precision
Systematic errors:
reduce accuracy
(instrument)
Random errors:
reduce precision
(person)
Precision
Accuracy
 reproducibility
 correctness
 check by
repeating
measurements
 check by using a
different method
 poor precision
results from poor
technique
 poor accuracy
results from
procedural or
equipment flaws.
SI Prefixes
kilocentimillinano-
1000
1/
100
1/
1000
1/
1 000 000 000
Also know…
1 mL = 1 cm3 = 1 cc
SI System for Measuring Length
The SI Units for Measuring Length
Unit
Symbol
Meter Equivalent
_______________________________________________________________________
1,000 m or 103 m
kilometer
km
meter
m
1
decimeter
dm
0.1 m or 10-1 m
centimeter
cm
0.01 m or 10-2 m
millimeter
mm
0.001 m or 10-3 m
micrometer
mm
0.000001 m or 10-6 m
nanometer
nm
0.000000001 m or 10-9 m
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118
m or 100 m
Comparison of English and
SI Units
1 inch
2.54 cm
1 inch = 2.54 cm
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119
Reporting Measurements
• Using significant figures
• Report what is known
with certainty
• Add ONE digit of
uncertainty (estimation)
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46
Measuring a Pin
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122
Practice Measuring
Timberlake, Chemistry 7th Edition, page 7
0
cm
1
2
3
4
5
4.5 cm
0
cm
1
2
3
4
5
4.54 cm
0
cm
1
2
3
4
5
3.0 cm
Implied Range of Uncertainty
3
4
5
6
Implied range of uncertainty in a measurement reported as 5 cm.
3
4
5
6
Implied range of uncertainty in a measurement reported as 5.0 cm.
3
4
5
6
Implied range of uncertainty in a measurement reported as 5.00 cm.
Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32
20
?
15
?1 mL
1.50
15.0
xmL
10
mL
10
How to Read a Thermometer
(Celcius)
4.0 oC
10
10
100
5
5
50
0
0
0
8.3 oC
64 oC
5
0
3.5 oC
Record the Temperature
A
(Celcius)
60oC
6oC
50oC
5oC
25oC
100oC
100oC
40oC
4oC
20oC
80oC
80oC
30oC
3oC
15oC
60oC
60oC
20oC
2oC
10oC
40oC
40oC
10oC
1oC
5oC
20oC
20oC
0oC
0oC
0oC
0oC
0oC
30.0oC
B
3.00oC
C
19.0oC
D
48oC
E
60.oC
Accuracy vs. Precision
 Accuracy - how close a measurement
is to the accepted value
 Precision - how close a series of
measurements are to each other
ACCURATE = Correct
PRECISE = Consistent
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Percent Error
 Indicates accuracy of a measurement
% error 
experimental  literature
literature
your value
accepted value
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
 100
Percent Error
 A student determines the density of a
substance to be 1.40 g/mL. Find the %
error if the accepted value of the density
is 1.36 g/mL.
% error 
1.40 g/mL  1.36 g/mL
1.36 g/mL
% error = 2.9 %
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
 100
Significant Figures
 Indicate precision of a measurement.
 Recording Sig Figs
 Sig figs in a measurement include the
known digits plus a final estimated digit
2.35 cm
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Significant Figures
 Counting Sig Figs (Table 2-5, p.47)
 Count all numbers EXCEPT:
 Leading
zeros -- 0.0025
 Trailing
zeros without
a decimal point -- 2,500
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Rules for Counting Significant Figures
1. Nonzero integers always count as significant figures.
2. Zeros: There are three classes of zeroes.
a.
Leading zeroes precede all the nonzero digits and DO NOT count as
2 significant figures.
significant figures. Example: 0.0025 has ____
b.
Captive zeroes are zeroes between nonzero numbers. These always
4 significant figures.
count as significant figures. Example: 1.008 has ____
c.
Trailing zeroes are zeroes at the right end of the number.
Trailing zeroes are only significant if the number contains a decimal point.
3 significant figures.
Example: 1.00 x 102 has ____
Trailing zeroes are not significant if the number does not contain a decimal
1 significant figure.
point. Example: 100 has ____
3.
Exact numbers, which can arise from counting or definitions such as 1 in
= 2.54 cm, never limit the number of significant figures in a calculation.
Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 53
Significant figures: Rules for zeros
Leading zeros are not significant.
Leading zero
0.421 – three significant figures
Captive zeros are significant.
Captive zero
4012 – four significant figures
Trailing zeros are significant.
Trailing zero
114.20 – five significant figures
Significant Figures
Counting Sig Fig Examples
1. 23.50
4 sig figs
2. 402
3 sig figs
3. 5,280
3 sig figs
4. 0.080
2 sig figs
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
 Calculating with Sig Figs
 Multiply/Divide - The # with the fewest
sig figs determines the # of sig figs in
the answer.
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
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Significant Figures
 Calculating with Sig Figs (con’t)
 Add/Subtract - The # with the lowest
decimal value determines the place of
the last sig fig in the answer.
3.75 mL
+ 4.1 mL
7.85 mL  7.9 mL
224 g
+ 130 g
354 g  350 g
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
 Calculating with Sig Figs (con’t)
 Exact Numbers do not limit the # of sig
figs in the answer.
 Counting
 Exact
 “1”
numbers: 12 students
conversions: 1 m = 100 cm
in any conversion: 1 in = 2.54 cm
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
Practice Problems
5. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL  2.4 g/mL
2 SF
6. 18.9 g
- 0.84 g
18.06 g  18.1 g
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Scientific Notation: Powers of Ten
Rules for writing numbers in scientific notation:
Write all significant figures but only the significant figures.
Place the decimal point after the first digit, making the number have a value between 1 and 10.
Use the correct power of ten to place the decimal point properly, as indicated below.
a) Positive exponents push the decimal point to the right. The number becomes larger.
It is multiplied by the power of 10.
b) Negative exponents push the decimal point to the left. The number becomes smaller.
It is divided by the power of 10.
c) 10o = 1
Examples:
3400 = 3.20 x 103
0.0120 = 1.20 x 10-2
Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!
Scientific Notation
65,000 kg  6.5 × 104 kg
 Converting into scientific notation:
 Move decimal until there’s 1 digit to
its left. Places moved = exponent.
 Large # (>1)  positive exponent
Small # (<1)  negative exponent
 Only include sig. figs.
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Scientific Notation
Practice Problems
7. 2,400,000 mg
2.4 
8. 0.00256 kg
2.56 
9. 7  10-5 km
0.00007 km
10. 6.2  104 mm
62,000 mm
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6
10
mg
-3
10
kg
Scientific Notation
 Calculating with scientific notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
5.44
EXP
EE
7
÷
8.1
EXP
EE
4
EXE
ENTER
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Proportions
 Direct Proportion
y x
y
x
 Inverse Proportion
1
y
x
y
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
x
The following slides are a more
detailed look at types of errors.
This is material you are NOT
responsible for.
Errors
Systematic
Errors in a single direction (high or low)
Can be corrected by proper calibration or
running controls and blanks.
Random
Errors in any direction.
Can’t be corrected. Can only be accounted
for by using statistics.
Accuracy Precision Resolution
time offset [arbitrary units]
3
not accurate, not precise
accurate, not precise
not accurate, precise
accurate and precise
accurate, low resolution
2
1
0
-1
-2
-3
subsequent samples
Types of errors
Systematic
• Instrument not ‘zeroed’ properly
• Reagents made at wrong concentration
Random
• Temperature in room varies ‘wildly’
• Person running test is not properly trained