Transcript File - Honors Chemistry

Scientific Measurement
and Significant Figures
Taking Measurements

Need for Standards

Basis of comparison – allows for proper
communication of information if all are using the
same system
Le Systeme International d’Unite’s (SI)
- International System
aka – The Metric System
SI Units – see page 26
Measurement
Unit
Abbreviation
Length
Meter
m
Mass
Gram
g
Volume
Liter
L
Temperature
Kelvin (or
Celcius)
Mole
K or (oC)
Number of
Particles
mol
Dealing With Very Large or Very Small Numbers
Scientific Notation
 Uses powers of 10 to represent the
magnitude of the number but keeping the
same unit
 BIG NUMBERS – positive exponents
– negative exponents
 23000  2.3 X 104
 0.0054  5.4 X 10-3
 Proper Notation – One number to the left of
the decimal

Small numbers
Entering Scientific Notation
into Your Calculator
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Ex: 5.4 X1016
Step 1: Enter “5.4”
Step 2: Hit “2nd” key
Step 3: Hit “,” key (Second function is “EE”)
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An “E” will appear
Enter the exponent “16”
Entered value should read “5.4E16”
DO NOT USE “^” or “10^” or “10E”
Unit Multipliers

Purpose: allow the measurement to use reasonable
numbers – make the numbers smaller or larger with a
prefix in front of the unit to represent the magnitude
(size) of the measurement

Ex. Measuring the mass of a whale
Prefix
kilo
deci
centi
milli
Symbol
k
d
c
m
Value
103
10-1
10-2
10-3
Converting Units
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DIMENSIONAL ANALYSIS
Changing from one unit to another unit
requires:
1) Same type of measurement

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- you cannot convert length into mass
2) A conversion factor
Conversion Factors

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Mathematical Ratio of the two units you are
converting
Ex: Conversion of inches to centimeters
1 inch = 2.54 cm
Possible Conversion Factors

1 in
or
2.54 cm
2.54 cm
1 in
Choose the conversion factor that puts what you are
converting to over what you are converting from

Conversion Examples
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$12.00 to quarters
56 yards to feet
67 dimes to quarters
18.57 kg to mg
19.84 ft to m
12 450 mL to L
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48 quarters
168 feet
26.8 quarters
1.857 X 107 mg
6.047 m
12.45 L
Multiple Dimensions
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The number of dimensions determines the
number of conversions
12.5 m2 to cm2
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Area is two dimensions (length x width) so two
conversions are needed
25.0 ft3 to cm3
Conversions
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1 L = 1000 mL
1 mL = 1 cm3; If its water, 1 mL = 1 g
1 Kg = 1000 g
1 g = 1000 mg
1 in = 2.54 cm
Making Sense of Measurements

Accuracy vs. Precision
Accuracy = “Correctness”
Precision = “Consistency”
Ex:

Scientists want to be BOTH
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Making Sense of Measurements

Accuracy vs. Precision
Accuracy = “Correctness”
Precision = “Consistency”
Ex:

Scientists want to be BOTH

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
Making Sense of Measurements

Accuracy vs. Precision
Accuracy = “Correctness”
Precision = “Consistency”
Ex:

Scientists want to be BOTH



Making Sense of Measurements

Accuracy vs. Precision
Accuracy = “Correctness”
Precision = “Consistency”
Ex:

Scientists want to be BOTH
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
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Reading for Significance
Correct Measurement?
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11.6 cm
11.6283476 cm
11.65 cm
Significance of a Measurement
A Measurement can only be as accurate as
the tool used to make it
 A tool will allow for exact numbers plus one
decimal place of estimation
 These are known as
SIGNIFICANT FIGURES
These determine the basis of your calculations
– the more accurate your measurement, the
more accurate your calculations.

Rules for Determining the Number of Significant
Figures in a Given Measurement
1) All non-zeros are significant
Ex: 23 m --- 2 sig figs.
Rules for Determining the Number of Significant
Figures in a Given Measurement
2) Zeros between non-zeros are significant
Ex: 203 m --- 3 sig figs.
 SIGNIFICANCE SANDWICH
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Zeros between two significant figures are
significant
Rules for Determining the Number of Significant
Figures in a Given Measurement
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3) Zeros after a decimal AND after a nonzero are significant

Ex: 203.0 m --- 4 sig figs.
203.00 m --- 5 sig figs.
203.000000000 m --- 12 sig figs.
REASON: These zeros show SPECIFICITY of the
measurement – they show the accuracy
Rules for Determining the Number of Significant
Figures in a Given Measurement
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4) Zeros that act as PLACE HOLDERS only
are NOT significant.
EX: 2030 m --- only 3 sig figs
0.00203 m --- only 3 sig figs
Both numbers can be written in a different form
without sacrificing accuracy.
HOW?
Scientific Notation
Rules for Determining the Number of Significant
Figures in a Given Measurement
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5) Counting numbers, those that do not use a
measuring device, are considered infinitely
significant.
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Ex: 24 dogs
Can’t get more accurate
Only is important when they are used in a
calculation.
SIG FIG Practice
Measurement
10.01 m
10.0 m
10 m
50050 m
56.610 g
0.008910 km
23.010 L
56 crickets
# Significant Figures
Math and Significant Figures

A calculation can only be as accurate as the
least accurate part
Addition and Subtraction
Rules for Sig Figs.

RULE: The answer can only have as many
decimal places as the number with the
fewest decimal places.
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Ex. 1.34 m + 2.5678 m = 3.9078 m
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Since 1.34 only has 2 decimal places, you must round
your answer to 2 decimal places
ACTUAL ANSWER = 3.91 m
Multiplication and Division
Rules for Sig Figs.

RULE: The answer can only have as many
significant figures as the number with the
fewest significant figures.
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Ex: 8.97 m X 5.2 m = 46.644 m2
Since 5.2 m only has 2 significant figures, you
must express your answer with the first two
significant figures beginning from the left hand
side.
ACTUAL ANSWER = 47 m2
PRACTICE
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23.0 m + 45.678 m =
56.20 g / 25.6 cm3 =
12 dogs X 25.6 kg =
25.0 m x 100.0 m =
2.589542 cm + 4 cm =
456 cm x 456 cm X
10.5 cm =
25.0 m + 25.0 km =
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68.7 m
2.20 g/cm3
307 kg
2.50 X 103 m2
7 cm
2180000 cm3
25025 m OR 25.0 km
(must be same units)