Scientific Measurement and Significant Figures

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

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 • 0.0054  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 • 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

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 2.54 cm 2.54 cm1 in Choose the conversion factor that puts what you are converting toover what you are converting from

9. $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 Conversion Examples

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 • 11.6283476 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. Rules for Determining the Number of Significant Figures in a Given Measurement 1) All non-zeros are significant Ex: 23 m --- 2 sig figs.

20. 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

21. 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

22. 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

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

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. 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

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 = 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

28. 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) PRACTICE