Types of measurement

1. Types of measurement • Quantitative- use numbers to describe • Qualitative- use description without numbers *Scientists prefer: • Quantitative - easy to check • Easy to agree upon, no personal bias • The measuring instrument limits how good the measurement is.

2. QUANTITATIVE MEASUREMENTS • -“Derived vs. Measured” • Measured – acquired directly from a measuring instrument. • EX: ruler, balance, scale, graduated cylinder • Derived – calculated or determined from Measured values using formulas • EX: area of a square or circle, volume of a cylinder, • density of an object

3. Quantitative Measurements • 2) Temperature • Celcius (Centigrade) -- 00 C – Freezing Point of water • Fahrenheit -- 320 F – Freezing Point of water • Kelvin-------- SI Unit of temperature with 00K absolute zero, and 273.16 0 K equal to the triple point of water (the point at which all three phases of water are at equilibrium) • Kelvin = 0C + 273 • Celcius = K -273 • Farenheit = 0C(1.8 F/1 0C) + 32 • 0C = F - 32 (1 0C/1.8 F)

4. Quantitative Measurements • 3) Time • Fundamental unit is …..SECONDS • 4) Volume – 3-D space that matter occupies • Liquids are defined (measured) or derived • solids -- regular shapes – formulas (derived value) -- irregular shapes – displacement of another liquid, usually water • gases – formulas (derived values) • UNITS OF VOLUME??????????????

5. SI UNIT IS 1 LITER • Meters X Meters X Meters = 1 m3 = 1000 liters OR • .1m X.1m X .1m = .001 m3 1 = 1000ml = 1 liter • 5) Mass • matter • weight – the gravitational pull on an object (related to its mass) • SI Units • UNITS OF MASS????????????? • 6) Density • Mass/Volume • A derived quantity • Grams/cm3

6. Kilo- means 1000 of that unit • 1 kilometer (km) = 1000 meters (m) • Centi- means 1/100 of that unit • 1 meter (m) = 100 centimeters (cm) • 1 dollar = 100 cents • Milli- means 1/1000 of that unit • 1 Liter (L) = 1000 milliliters (mL)

7. PROBLEM SOLVING STEPS • Read problem • Identify data • Make a unit plan from the initial unit to the desired unit • Select conversion factors • Change initial unit to desired unit • Cancel units and check • Do math on calculator • Give an answer using significant figures

8. How many minutes in 2.5 hours? 2.5 hr X 60min/1 hr = 150 min By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers! You have $7.25 in your pocket in quarters. How many quarters do you have? 7.25 $ X 4 quarters/1 $ = 29 quarters

9. WHAT’S WRONG WITH THIS? • How many seconds in 1.4 days? • 1.4 day X 1 day/24 hr X 60 min/1 hr X 60 sec/1 min

10. What about Square and Cubic units? • Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also! • Best way: Square or cube the ENITRE conversion factor • Example: Convert 4.3 cm3 to mm3 • 4.3 cm3 (10 mm/ 1 cm)3 = 4.3 cm3 X 103 mm3/ 13 cm3 = 4300 mm3

11. SCIENTIFIC NOTATION Technique Used to Express Very Large or Very Small Numbers • Based on Powers of 10 • Errors are less likely when using scientific notation • To Compare Numbers Written in Scientific Notation • First Compare Exponents of 10 (order of magnitude) • Then Compare Numbers

12. SCIENTIFIC NOTATION deals with numbers that are really small….. The electrical charge on one electron: 0.0000000000000000001602 = 1.602 X 10-19 C

13. Or numbers that are really big!! The mass of the moon: 73,600,000,000,000,000,000,000 kg = 7.36 X 1022kg

14. Unit Symbol Meter Equivalent kilometer km 1,000 m or 103 m meter m 1 m or 100 m decimeter dm 0.1 m or 10-1 m centimeter cm 0.01 m or 10-2 m millimeter mm 0.001 m or 10-3 m micrometer mm 0.000001 m or 10-6 m nanometer nm 0.000000001 m or 10-9 m SI System for Measuring Length

15. Comparison of English and SI Units 1 inch 2.54 cm 1 inch = 2.54 cm Zumdahl, Zumdahl, DeCoste, World of Chemistry2002, page 119

16. SCIENTIFIC NOTATION • Writing Numbers in Scientific Notation • Locate the Decimal Point • Move the decimal point to the right of the non-zero digit in the largest place • The new number is now between 1 and 10 • Multiply the new number by 10n • where n is the number of places you moved the decimal point • Determine the sign on the exponent, n • If the decimal point was moved left, n is + • If the decimal point was moved right, n is – • If the decimal point was not moved, n is 0

17. SCIENTIFIC NOTATION • Writing Numbers in Standard Form • Determine the sign of n of 10n • If n is + the decimal point will move to the right • If n is – the decimal point will move to the left • Determine the value of the exponent of 10 • Tells the number of places to move the decimal point • Move the decimal point and rewrite the number

18. How good are the measurements? (that’s where sig fig’s come in!) • Scientists use two word to describe how good the measurements are • Accuracy- how close the measurement is to the actual value • Precision- how well can the measurement be repeated • In short, when you plug these three numbers into your calculator, remember your calculator neither knows nor cares about how good (significant) the numbers it’s working with are. However, to you, the taker of data, these three numbers tell you whether or not your data is good enough to pay attention to.

19. Significant Figures are concerned with Accuracy vs. Precision in measurement Poor accuracy Poor precision Good accuracy Good precision Poor accuracy Good precision Random errors: reduce precision Systematic errors: reduce accuracy

20. Differences • Accuracy can be true of an individual measurement or the average of several • Precision requires several measurements before anything can be said about it

21. Let’s use a golf analogy

22. Accurate? No Precise? Yes 10

23. Precise? Yes Accurate? Yes 12

24. Accurate? Maybe? Precise? No 13

25. Precise? We cant say! Accurate? Yes 18

26. Precise? We cant say! Accurate? Yes 18

27. Precise? We cant say! Accurate? Yes 18

28. not accurate, not precise accurate, not precise not accurate, precise accurate and precise accurate, low resolution 3 2 1 time offset [arbitrary units] 0 -1 -2 -3 Accuracy Precision Resolution subsequent samples

29. In terms of measurement • Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. • Were they precise? • Were they accurate?

30. Making Measurements in the Lab:Recording Thermometer Data to the Correct Number of Significant Figures 23°C 23°C The number of SFs in a measured value is equal to the number of known digits plus one uncertain digit. 22°C 22°C 21°C 21°C you record 21.6°C you record 21.68°C

31. Making Measurements in the Lab:Recording Volumetric Data to the Correct Number of Significant Figures - Glassware with Graduations Example B Example A 1. If the glassware is marked every 10 mLs, the volume you record should be in mLs. (Example A) 2. If the glassware is marked every 1 mL, the volume you record should be in tenths of mLs. 3. If the glassware is marked every 0.1 mL, the volume you record should be in hundredths of mLs. (Example B) 0 mL 30 mL 20 mL 1 mL 10 mL 30-mL beaker: the volume you write in your lab report should be 13 mL 2 mL Buret marked in 0.1 mL: you record volume as 0.67 mL

32. Reporting Measurements • Using significant figures • Report what is known with certainty • Add ONE digit of uncertainty (estimation) Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

33. 1 2 3 4 5 0 cm 1 2 3 4 5 0 cm 1 2 3 4 5 0 cm Practice Measuring 4.5 cm 4.54 cm 3.0 cm Timberlake, Chemistry 7th Edition, page 7

34. SIG FIG’s • Rules: • All non zero numbers are significant • All zeros between significant figures are significant • All zeros following a decimal AND, are at the end of number, or a significant figure (ex: 42.0 g), are significant -when adding or subtracting, certainty is in the least “place” of the values being added or subtracted -when multiplying or dividing, the derived value must have the least number of sig fig’s as is found in the numbers being multiplied or divided

35. Cheap balance measurements are trustworthy to the nearest gram. Measurement = 25 g, so implied precision is +/-1g. Standard lab balance are trustworthy to the nearest milligram (0.001g) measurement: 25.000g, so implied precision is +/-0.001g The analytical balance is very precise. Measurements are trustworthy to the nearest 0.1mg. Measurement:25.0000 implied precision: +/-0001g

36. Significant Figures • What is the smallest mark on the ruler that measures 142.15 cm? • 142 cm? • 140 cm? • Here there’s a problem, does the zero count or not? • They needed a set of rules to decide which zeros count. • All other numbers do count

37. Which zeros count? • Those at the end of a number before the decimal point don’t count • 12400 • If the number is smaller than one, zeros before the first number don’t count • 0.045

38. Which zeros count? • Zeros between other sig figs do. • 1002 • zeroes at the end of a number after the decimal point do count • 45.8300 • If they are holding places, they don’t. • If they are measured (or estimated) they do

39. Sig Figs • Only measurements have sig figs. • Counted numbers are exact • Ex: • A dozen is exactly 12 • A piece of paper is measured 11 inches tall. • Being able to locate, and count significant figures is an important skill.

40. Sig figs. • How many sig figs in the following measurements? • 458 g • 4085 g • 4850 g • 0.0485 g • 0.004085 g • 40.004085 g

41. Sig Figs. • 405.0 g • 4050 g • 0.450 g • 4050.05 g • 0.0500060 g • Next we learn the rules for calculations

42. More Sig Figs How to Round

43. Problems • 50 is only 1 significant figure • if it really has two, how can I write it? • A zero at the end only counts after the decimal place • Scientific notation • 5.0 x 101 • now the zero counts.

44. Adding and subtracting with sig figs • The last sig fig in a measurement is an estimate. • Your answer when you add or subtract can not be better than your worst estimate. • have to round it to the least place of the measurement in the problem

45. Maintain the Correct Number of SFs When Performing Calculations Involving Measured Data • Addition/Subtraction: The answer contains the same number of digits to the right of the decimal as that of the measurement with the fewest number of decimal places. 33.14159 - 33.04 0.10159 0.10 (correct answer) 2 SFs 3.14159 + 25.2 28.34159 28.3 (correct answer) 3 SFs • Calculators do NOT know these rules. It’s up to you to apply them!

46. 27.93 + 6.4 27.93 27.93 + 6.4 6.4 For example • First line up the decimal places Then do the adding Find the estimated numbers in the problem 34.33 This answer must be rounded to the tenths place

47. Rounding rules • look at the number behind the one you’re rounding. • If it is 0 to 4 don’t change it • If it is 5 to 9 make it one bigger • round 45.462 to four sig figs • to three sig figs • to two sig figs • to one sig fig

48. Practice • 4.8 + 6.8765 • 520 + 94.98 • 0.0045 + 2.113 • 6.0 x 102 - 3.8 x 103 • 5.4 - 3.28 • 6.7 - .542 • 500 -126 • 6.0 x 10-2 - 3.8 x 10-3

49. Multiplication and Division • Rule is simpler • Same number of sig figs in the answer as the least in the question • 3.6 x 653 • 2350.8 • 3.6 has 2 s.f. 653 has 3 s.f. • answer can only have 2 s.f. • 2400

50. Maintain the Correct Number of SFs Multiplying or Dividing Measured Data • The answer contains the same number of SFs as the measurement with the fewest SFs. 25.2 x 6.1 = 153.72 (on my calculator) = 1.5 x 102 (correct answer) 25.2 ------------ = 7.3122535 (on my calculator) 3.44627 = 7.31 (correct answer) (6.626 x 10-34)(3 x 108) ------------------------------- = 3.06759 x 10-2 (on my calculator) 6.48 x 10-24 = 0.03 (correct answer)