Chapter 3 Scientific Measurement

1. Chapter 3 Scientific Measurement Anything in black letters = write it in your notes (‘knowts’)

2. 3.1 – Using & Expressing Measurements Measurements without units are useless! “I walked 5 today.” “The speed of light is 186,000 “I weigh 890” “20 of water” All measurements need units!

3. We will often work with really large or really small numbers in this class. Standard Notation Scientific Notation 872,000,000 grams 0.0000056 moles = 8.72 x 108 grams = 5.6 x 10-6 moles exponent coefficient 6.02 x 1023 The coefficient must be a single, nonzero digit, exponent must be an integer.

4. Multiplication and Division To multiply numbers written in scientific notation, multiply the coefficients and add the exponents. (3 x 104) x (2 x 102) = (3 x 2) x 104+2 = 6 x 106 (2.1 x 103) x (4.0 x 10–7) = (2.1 x 4.0) x 103+(–7) = 8.4 x 10–4

5. To divide numbers written in scientific notation, divide the coefficients and subtract the bottom exponent from the top exponent. Coefficient needs to be between 1 and 10

6. Addition and Subtraction When adding or subtracting in Sci. Not., the exponents must be the same. Not the same, need to adjust one of the exponents (5.4 x 103) + (8.0 x 102) = (5.4 x 103) + (0.80 x 103) = (5.4 + 0.80) x 103 = 6.2 x 103

7. Example • Solve each problem and express the answer in scientific notation. • a. (8.0 x 10–2) x (7.0 x 10–5) • b. (7.1 x 10–2) + (5 x 10–3)

8. a. Multiply the coefficients and add the exponents. (8.0 x 10–2) x (7.0 x 10–5) = (8.0 x 7.0) x 10–2 + (–5) = 56 x 10–7 = 5.6 x 10–6

9. b. Rewrite one of the numbers so that the exponents match. Then add the coefficients (7.1 x 10–2) + (5 x 10–3) = (7.1 x 10–2) + (0.5 x 10–2) = (7.1 + 0.5) x 10–2 = 7.6 x 10–2

10. Accuracy - closeness of a measurement to the actual or accepted value. Precision - closeness of repeated measurements to each other

11. Accuracy and Precision Darts on a dartboard illustrate the difference between accuracy and precision. Poor Accuracy, Poor Precision Good Accuracy, Good Precision Poor Accuracy, Good Precision The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.

12. Error = experimental value – accepted value Error Suppose you measured the melting point of a compound to be 78°C Suppose also, that the actual melting point value (from reference books) is 76°C. The error in your measurement would be 2°C. Error is the difference between the actual (accepted) and experimental value

13. How far off you are in a measurement doesn’t tell you much. For example, lets say you have $1,000,000 in your checking account. When you balance your checkbook at the end of the month, you find that you are off by $175; error = $175 Now, lets be more realistic, you have $225 in your checking account and after balancing you are off by $175!

14. error x 100% Percent error = accepted value In both cases, there is an error of $175. But in the first, the error is such a small portion of the total that it doesn’t matter as much as the second. So, instead of error, percent error is more valuable. Percent error compares the error to the size of the measurements.

15. ASSIGN: Chapter 3 Worksheet #1

16. Significant Figures In any measurement, the last digit is estimated 30.2°C The 2 is estimated (uncertain) by the experimenter, another person may say 30.1 or 30.3

17. 9.3 mL 0.72 cm

18. Increasing Precision

19. The significant figures in a measurement include all of the digits that are known, plus the last digit that is estimated. Numbers that are NOT significant are called placeholders.

20. Rules for determining Significant Figures (p. 67) 1. Every nonzero digit in a reported measurement is assumed to be significant. 2. Zeros appearing between nonzero digits are significant. 3. Leftmost zeros appearing in front of nonzero digits are not significant. They act as placeholders. By writing the measurements in scientific notation, you can eliminate such placeholding zeros. 4. Zeros at the end of a number and to the right of a decimal point are always significant. 5. Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number. 5 (continued). If such zeros were known measured values, then they would be significant. Writing the value in scientific notation makes it clear that these zeros are significant. 6. There are two situations in which numbers have an unlimited number of significant figures. The first involves counting. A number that is counted is exact. 6 (continued). The second situation involves exactly defined quantities such as those found within a system of measurement. HOLY SMOKES!!

21. A shorter method for determining which numbers are significant in a measurement. • All nonzero numbers are significant. • Zeros are also significant if they are NOT placeholder zeros. • Counted and exact numbers have an unlimited number of sig figs. The Tischer Method!™ A placeholder is a zero that ‘holds place’; it is only there to show how big or small a number is.

22. Underline the zeros that are placeholders • 100 1.00 0.23 • 0.0034 1.01 1005.4 • 0.10 100.0 54.0 A placeholder is a zero that ‘holds place’; it is only there to show how big or small a number is. Zeros to the right of a number & after the decimal are more than placeholders, they are part of the measurement and are significant.

23. How many significant digits are in the following measurements? a) 150.31 grams b) 10.03 mL c) 0.045 cm d) 4.00 lbs e) 0.01040 m f) 100.10 cm g) 100 grams h) 1.00 x 102 grams i) 11 cars j) 2 molecules • All nonzero numbers are significant. • Zeros are also significant if they are NOT placeholders. • Counted and exact numbers have an unlimited number of sig. figs.

24. “Box and Dot” Method for Counting Sig Figs 1. Draw a box around all digits from the 1st nonzero digit on left to last nonzero digit on the right. 2. If a dot is present, draw a box around any trailing zeros. 3. Any boxed digit is significant. Another Shorter Method SOURCE: JCE Vol 86 No 8 (Aug ‘09) W. Kirk Stephenson

25. An answer can’t be more accurate than the measurements it was calculated from

26. Rules for Add/Subtracting Sig Figs The answer to an +/- calculation should be rounded to the same number of decimal places as the measurement with the least number of decimal places. 3.2 cm 37.10 g

27. Rules for Mult/Division Sig Figs The answer to a x/÷ calculation should be rounded to the same number of sig figs as the measurement with the least number of sig figs. 3.8 cm2

28. Always round your finalanswer off to the correct number of significant digits. ASSIGN: Chapter 3 Worksheet #2

29. 3.2 – Units of Measurement SI – International System of Units We will use all of these in this class How is Mass different from Amount of Substance?

31. Volume - Amount of space occupied by an object (remember?) Normal units used for volume: Solids – m3or cm3 Liquids & Gases – liters (L) or milliliters (mL) 1 L = 1000 mL 1 mL = 1 cm3 The volume of a material changes with temperature, especially for gases.

32. Mass - Measure of inertia (remember?) Weight - Force of gravity on a mass; measured in pounds (lbs) or Newtons. Weight can change with location, mass does not

33. Energy – Ability to do work or produce heat. Normal units used for energy: SI – joule (J) non-SI – calorie (cal) 1 cal = 4.184 J How many joules are in a kilojoule? How many calories are in a kilocalorie?

34. Temperature – measure of how cold or hot an object is.

35. K = °C + 273 Temperature – measure of the average kinetic energy of molecules. Normal units used for temp: SI – kelvin (K) non-SI – celsius (°C) or Fahrenheit (°F) yucky!

36. Celsius 100 divisions 100°C Boiling point of water 373.15 K 0°C Freezing point of water 273.15 K 100 divisions Kelvin

37. mass Density = volume Density is an intensive property Normal units for density: g/cm3, g/mL, g/L

39. ASSIGN: Read 3.2 Lesson Check 3.2; #23-35 (page 82)

40. 3.3 – Solving Conversion Problems 12 inches = ______ foot 1 minute = _____ seconds 10 cents = _______ dime 24 hours = ______ day 1 km = ________meters 4.184 Joules = _______ calorie Fill in the blanks… These can all be used as conversion factors

41. Conversion Factors Any measurement that equals another measurement is a conversion factor

42. How to use conversion factors…to convert measurements… • Place the measurement you want to convert over 1. • Multiply by a conversion factor to cancel units.

43. Example 1 • How many seconds are in 8 hours? • Start with given information. • Use conversion factors to cancel units until desired unit is left. • 60 min = 1 hr; 60 sec = 1 min • Multiply across the top, • divide along the bottom of the conversion factors.

44. Example 2 • How many km are in 25 miles? • Start with given information. • Use conversion factors to cancel units until desired unit is left. • 1.6 km = 1 mile • Multiply across the top, • divide along the bottom of the conversion factors.

45. Example 3 – TRY IT! 5.26 mumu = 8 nunu; 1.76 nunu = 12 fufu; 0.826 fufu = 1000 bubu. 1. How many mumus are in 10 bubus?

46. Example 4 – TRY IT! 5.26 mumu = 8 nunu; 1.76 nunu = 12 fufu; 0.826 fufu = 1000 bubu. 2. How many fufus are in 26 mumus?

47. A student converted 10.1 feet as follows: How many significant digits should the answer have? Why not 1?

48. ASSIGN: Chapter 3 Worksheet 3

49. Conversion Factor Quiz Show your WORK for credit. 1 horsepower = 745.7 W 2.54 cm = 1 inch LEFT: 1. Convert 6.5 horsepower into watts RIGHT: 1. Convert 100 watts into horsepower LEFT: 2. How many cm are in 12 miles? RIGHT: 2. How many cm are in 20 miles

50. Practice With Conversions Show your WORK for credit. 1 horsepower = 745.7 W 2.54 cm = 1 inch LEFT: 1. Convert 6.5 horsepower into watts RIGHT: 1. Convert 100 watts into horsepower LEFT: 2. How many cm are in 12 miles? RIGHT: 2. How many cm are in 20 miles