CHAPTER 1 : MEASUREMENTS SIGNIFICANT FIGURES AND CALCULATIONS.
Scientific Measurement and Significant Figures. Taking Measurements Need for Standards Basis of...
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Scientific Measurement and Significant Figures
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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
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SI Units – see page 26
Measurement Unit Abbreviation
Length Meter m
Mass Gram g
Volume Liter L
Temperature Kelvin (or Celcius)
K or (oC)
Number of Particles
Mole mol
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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
Small numbers – negative exponents 23000 2.3 X 104
0.0054 5.4 X 10-3
Proper Notation – One number to the left of the decimal
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Entering Scientific Notation into Your Calculator
Ex: 5.4 X1016
Step 1: Enter “5.4” Step 2: Hit “2nd” key Step 3: Hit “,” key (Second function is “EE”)
An “E” will appear Enter the exponent “16” Entered value should read “5.4E16” DO NOT USE “^” or “10^” or “10E”
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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 Symbol Value
kilo k 103
deci d 10-1
centi c 10-2
milli m 10-3
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Converting Units
DIMENSIONAL ANALYSIS Changing from one unit to another unit
requires: 1) Same type of measurement
- you cannot convert length into mass 2) A conversion factor
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Conversion Factors
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
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Conversion Examples
$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
48 quarters 168 feet 26.8 quarters 1.857 X 107 mg 6.047 m 12.45 L
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Multiple Dimensions The number of dimensions determines the
number of conversions 12.5 m2 to cm2
Area is two dimensions (length x width) so two conversions are needed
25.0 ft3 to cm3
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Conversions
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
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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
![Page 14: Scientific Measurement and Significant Figures. Taking Measurements Need for Standards Basis of comparison – allows for proper communication of information.](https://reader031.fdocuments.us/reader031/viewer/2022020721/56649db05503460f94a9ed65/html5/thumbnails/14.jpg)
Making Sense of Measurements
Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex:
Scientists want to be BOTH
![Page 15: Scientific Measurement and Significant Figures. Taking Measurements Need for Standards Basis of comparison – allows for proper communication of information.](https://reader031.fdocuments.us/reader031/viewer/2022020721/56649db05503460f94a9ed65/html5/thumbnails/15.jpg)
Making Sense of Measurements
Accuracy vs. Precision Accuracy = “Correctness” Precision = “Consistency” Ex:
Scientists want to be BOTH
![Page 16: Scientific Measurement and Significant Figures. Taking Measurements Need for Standards Basis of comparison – allows for proper communication of information.](https://reader031.fdocuments.us/reader031/viewer/2022020721/56649db05503460f94a9ed65/html5/thumbnails/16.jpg)
Reading for Significance
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Correct Measurement? 11.6 cm 11.6283476 cm 11.65 cm
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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.
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Rules for Determining the Number of Significant Figures in a Given Measurement
1) All non-zeros are significant
Ex: 23 m --- 2 sig figs.
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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
Zeros between two significant figures are significant
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Rules for Determining the Number of Significant Figures in a Given Measurement
3) Zeros after a decimal AND after a non-zero 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
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Rules for Determining the Number of Significant Figures in a Given Measurement
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
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Rules for Determining the Number of Significant Figures in a Given Measurement
5) Counting numbers, those that do not use a measuring device, are considered infinitely significant. Ex: 24 dogs Can’t get more accurate Only is important when they are used in a
calculation.
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SIG FIG Practice
Measurement # Significant Figures
10.01 m
10.0 m
10 m
50050 m
56.610 g
0.008910 km
23.010 L
56 crickets
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Math and Significant Figures
A calculation can only be as accurate as the least accurate part
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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. Ex. 1.34 m + 2.5678 m = 3.9078 m
Since 1.34 only has 2 decimal places, you must round your answer to 2 decimal places
ACTUAL ANSWER = 3.91 m
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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. 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
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PRACTICE
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 =
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)