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1 Standards for Measurement

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2 Mass and Weight

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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.

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4 Measurement and Significant Figures

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

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

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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

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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

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9 Significant Figures on Reading a Thermometer

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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.

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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.

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12 461 All nonzero numbers are significant. Significant Figures

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13 461 All nonzero numbers are significant. Significant Figures

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14 461 All nonzero numbers are significant. Significant Figures

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

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

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

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

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

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

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

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

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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

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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

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25 Scientific Notation of Numbers

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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.

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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

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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.

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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

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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

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31 Significant Figures in Calculations

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32 The Metric System

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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.

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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

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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

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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

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37 Problem Solving

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

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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.

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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

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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

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

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Temperature Conversions 43

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44 To convert between the scales use the following relationships.

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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 ?

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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 ?

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47 Density

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

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

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50 Density varies with temperature

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53 Examples

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

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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

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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.

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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

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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.

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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

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