1. Scientific Measurement and Significant Figures

2. 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

3. 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

4. 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
 5.4 X 10-3
Proper Notation – One number to the left of the decimal

5. 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”

6. Unit Multipliers Prefix Symbol Value kilo k 103 deci d 10-1 centi c
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

7. 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

8. 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 cm
2.54 cm in
Choose the conversion factor that puts what you are converting to over what you are converting from

9. Conversion Examples $12.00 to quarters 56 yards to feet
67 dimes to quarters
18.57 kg to mg
19.84 ft to m
mL to L
48 quarters
168 feet
26.8 quarters
1.857 X 107 mg
6.047 m
12.45 L

10. 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

11. 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

12. Making Sense of Measurements
Accuracy vs. Precision
Accuracy = “Correctness”
Precision = “Consistency”
Ex:
Scientists want to be BOTH

13. Making Sense of Measurements
Accuracy vs. Precision
Accuracy = “Correctness”
Precision = “Consistency”
Ex:
Scientists want to be BOTH

14. Making Sense of Measurements
Accuracy vs. Precision
Accuracy = “Correctness”
Precision = “Consistency”
Ex:
Scientists want to be BOTH

15. Making Sense of Measurements
Accuracy vs. Precision
Accuracy = “Correctness”
Precision = “Consistency”
Ex:
Scientists want to be BOTH

16. Reading for Significance

17. Correct Measurement?
11.6 cm cm
11.65 cm

18. 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.

19. 1) All non-zeros are significant Ex: 23 m --- 2 sig figs.
Rules for Determining the Number of Significant Figures in a Given Measurement
1) All non-zeros are significant
Ex: 23 m sig figs.

20. 2) Zeros between non-zeros are significant Ex: 203 m --- 3 sig figs.
Rules for Determining the Number of Significant Figures in a Given Measurement
2) Zeros between non-zeros are significant
Ex: 203 m sig figs.
SIGNIFICANCE SANDWICH
Zeros between two significant figures are significant

21. 3) Zeros after a decimal AND after a non-zero 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: m sig figs.
m sig figs.
m sig figs.
REASON: These zeros show SPECIFICITY of the measurement – they show the accuracy

22. 4) Zeros that act as PLACE HOLDERS only are NOT significant.
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
m --- only 3 sig figs
Both numbers can be written in a different form without sacrificing accuracy.
HOW?
Scientific Notation

23. 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.

24. SIG FIG Practice Measurement # Significant Figures 10.01 m 10.0 m 10 mkm L
56 crickets

25. Math and Significant Figures
A calculation can only be as accurate as the least accurate part

26. 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 m m = m
Since 1.34 only has 2 decimal places, you must round your answer to 2 decimal places
ACTUAL ANSWER = 3.91 m

27. 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 = 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

28. PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg =
25.0 m x m =
cm + 4 cm =
456 cm x 456 cm X 10.5 cm =
25.0 m km =
68.7 m
2.20 g/cm3
307 kg
2.50 X 103 m2
7 cm
cm3
25025 m OR 25.0 km
(must be same units)