# 1 Standards for Measurement. 2 Mass and Weight 3 Matter: Anything that has mass and occupies space. Mass : The quantity or amount of matter that an object.

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1 Standards for Measurement

2 Mass and Weight

3 Matter: Anything that has mass and occupies space. Mass : The quantity or amount of matter that an object possesses. –Fixed –Independent of the object’s location Weight: A measure of the earth’s gravitational attraction for an object. –Not fixed –Depends on the object’s location.

4 Measurement and Significant Figures

5 Measurements Experiments are performed. Numerical values or data are obtained from these measurements.

6 Form of a Measurement 70 kilograms = 154 pounds numerical value unit

7 Significant Figures The number of digits that are known plus one estimated digit are considered significant in a measured quantity estimated 5.16143 known

8 estimated 6.06320 Significant Figures The number of digits that are known plus one estimated digit are considered significant in a measured quantity known

9 Significant Figures on Reading a Thermometer

10 Temperature is estimated to be 21.2 o C. The last 2 is uncertain. The temperature 21.2 o C is expressed to 3 significant figures.

11 Temperature is estimated to be 22.0 o C. The last 0 is uncertain. The temperature 22.0 o C is expressed to 3 significant figures.

12 461 All nonzero numbers are significant. Significant Figures

13 461 All nonzero numbers are significant. Significant Figures

14 461 All nonzero numbers are significant. Significant Figures

15 461 3 Significant Figures All nonzero numbers are significant. Significant Figures

16 401 3 Significant Figures A zero is significant when it is between nonzero digits. Significant Figures

17 A zero is significant when it is between nonzero digits. 5 Significant Figures 600. 39 Significant Figures

18 3 Significant Figures 30.9 A zero is significant when it is between nonzero digits. Significant Figures

19 A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 000. 55 Significant Figures

20 A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 0391.2 Significant Figures

21 A zero is not significant when it is before the first nonzero digit. 1 Significant Figure 600. 0 Significant Figures

22 A zero is not significant when it is before the first nonzero digit. 3 Significant Figures 907. 0 Significant Figures

23 A zero is not significant when it is at the end of a number without a decimal point. 1 Significant Figure 0000 5 Significant Figures

24 A zero is not significant when it is at the end of a number without a decimal point. 4 Significant Figures 0178 6 Significant Figures

25 Scientific Notation of Numbers

26 Very large and very small numbers are often encountered in science. 602200000000000000000000 0.00000000000000000000625 Very large and very small numbers like these are awkward and difficult to work with.

27 602200000000000000000000 A method for representing these numbers in a simpler form is scientific notation. 0.00000000000000000000625 6.022 x 10 23 6.25 x 10 -21

28 Scientific Notation Write a number as a power of 10 Move the decimal point in the original number so that it is located after the first nonzero digit. Follow the new number by a multiplication sign and 10 with an exponent (power). The exponent is equal to the number of places that the decimal point was shifted.

29 Write 6419 in scientific notation. 64196419.641.9x10 1 64.19x10 2 6.419 x 10 3 decimal after first nonzero digit power of 10

30 Write 0.000654 in scientific notation. 0.0006540.00654 x 10 -1 0.0654 x 10 -2 0.654 x 10 -3 6.54 x 10 -4 decimal after first nonzero digit power of 10

31 Significant Figures in Calculations

32 The Metric System

33 The metric or International System (SI, Systeme International) is a decimal system of units. It is built around standard units. It uses prefixes representing powers of 10 to express quantities that are larger or smaller than the standard units.

34 International System’s Standard Units of Measurement Quantity Name of Unit Abbreviation Lengthmeterm Masskilogramkg TemperatureKelvinK Timesecond s Amount of substancemolemol Electric CurrentampereA Luminous Intensitycandelacd

35 Prefixes and Numerical Values for SI Units Power of 10 Prefix SymbolNumerical Value Equivalent exaE 1,000,000,000,000,000,00010 18 petaP 1,000,000,000,000,00010 15 teraT 1,000,000,000,00010 12 gigaG1,000,000,00010 9 megaM 1,000,00010 6 kilok 1,00010 3 hectoh 10010 2 decada 1010 1 —— 110 0

36 Prefixes and Numerical Values for SI Units decid 0.110 -1 centic0.0110 -2 millim 0.00110 -3 micro  0.00000110 -6 nanon 0.00000000110 -9 picop0.00000000000110 -12 femtof 0.0000000000000110 -15 attoa 0.00000000000000000110 -18 Power of 10 Prefix SymbolNumerical Value Equivalent

37 Problem Solving

38 Dimensional Analysis Dimensional analysis converts one unit to another by using conversion factors. unit 1 x conversion factor = unit 2

39 Basic Steps 1.Read the problem carefully. Determine what is to be solved for and write it down. 2.Tabulate the data given in the problem. –Label all factors and measurements with the proper units.

40 3.Determine which principles are involved and which unit relationships are needed to solve the problem. –You may need to refer to tables for needed data. 4.Set up the problem in a neat, organized and logical fashion. –Make sure unwanted units cancel. –Use sample problems in the text as guides for setting up the problem. Basic Steps

41 5.Proceed with the necessary mathematical operations. –Make certain that your answer contains the proper number of significant figures. 6. Check the answer to make sure it is reasonable. Basic Steps

42 Degree Symbols degrees Celsius = o C Kelvin (absolute) = K degrees Fahrenheit = o F

Temperature Conversions 43

44 To convert between the scales use the following relationships.

45 It is not uncommon for temperatures in the Canadian planes to reach –60 o F and below during the winter. What is this temperature in o C and K ?

46 It is not uncommon for temperatures in the Canadian planes to reach –60 o F and below during the winter. What is this temperature in o C and K ?

47 Density

48 Density is the ratio of the mass of a substance to the volume occupied by that substance.

49 Mass is usually expressed in grams and volume in ml or cm 3. The density of gases is expressed in grams per liter.

50 Density varies with temperature

51

52

53 Examples

54 A 13.5 mL sample of an unknown liquid has a mass of 12.4 g. What is the density of the liquid?

55 46.0 mL 98.1 g A graduated cylinder is filled to the 35.0 mL mark with water. A copper nugget weighing 98.1 grams is immersed into the cylinder and the water level rises to the 46.0 mL. What is the volume of the copper nugget? What is the density of copper? 35.0 mL

56 The density of ether is 0.714 g/mL. What is the mass of 25.0 milliliters of ether? Method 1 (a) Solve the density equation for mass. (b) Substitute the data and calculate.

57 The density of ether is 0.714 g/mL. What is the mass of 25.0 milliliters of ether? Method 2 Dimensional Analysis. Use density as a conversion factor. Convert: mL → g The conversion of units is

58 The density of oxygen at 0 o C is 1.429 g/L. What is the volume of 32.00 grams of oxygen at this temperature? Method 1 (a) Solve the density equation for volume. (b) Substitute the data and calculate.

59 The density of oxygen at 0 o C is 1.429 g/L. What is the volume of 32.00 grams of oxygen at this temperature? Method 2 Dimensional Analysis. Use density as a conversion factor. Convert: g → L The conversion of units is

60

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