scientific measurement and significant figures. taking measurements need for standards basis of...
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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)
K or (oC)
Number of Particles
Mole 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
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
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”
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
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
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
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
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
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
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
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
Reading for Significance
Correct Measurement? 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
Zeros between two significant figures are significant
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
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
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.
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
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. 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
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
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)