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To show how very large or very small numbers can be expressed in scientific notation To learn the English, metric, and SI systems of measurement To use the metric system to measure length, volume and mass Objectives 5.1Scientific Notation and UnitsMeasurements and Calculations1Measurement A quantitative observation Consists of 2 parts Number Unit tells the scale being used

Measurements and Calculations2A. Scientific Notation Very large or very small numbers can be expressed using scientific notation The number is written as a number between 1 and 10 multiplied by 10 raised to a power. The power of 10 depends on:The number of places the decimal point is moved. The direction the decimal point is moved.Left Positive exponentRight Negative exponent Measurements and Calculations3A. Scientific Notation Representing Large Numbers Representing Small Numbers0.000167To obtain a number between 1 and 10 we must move the decimal point. 0.000167 = 1.67 10-4

Measurements and Calculations4B. Units Units provide a scale on which to represent the results of a measurement.

Measurements and Calculations5B. Units There are 3 commonly used unit systems.

English (used in the United States)Metric (uses prefixes to change the size of the unit) SI (uses prefixes to change the size of the unit)Measurements and Calculations6C. Measurements of Length, Volume and Mass LengthFundamental unit is meter 1 meter = 39.37 inchesComparing English and metric systems

Measurements and Calculations7C. Measurements of Length, Volume and Mass

Measurements and Calculations8C. Measurements of Length, Volume and Mass Volume Amount of 3-D space occupied by a substance Fundamental unit is meter3 (m3)

Measurements and Calculations9C. Measurements of Length, Volume and Mass Mass Quantity of matter in an object Fundamental unit is kilogram

Measurements and Calculations10C. Measurements of Length, Volume and Mass

Measurements and Calculations11To learn how uncertainty in a measurement arises To learn to indicate a measurements uncertainty by using significant figures To learn to determine the number of significant figures in a calculated result Objectives 5.2Uncertainty in Measurements and Significant FiguresMeasurements and Calculations12A. Uncertainty in Measurement A measurement always has some degree of uncertainty.

Measurements and Calculations13A. Uncertainty in Measurement Different people estimate differently. Record all certain numbers and one estimated number.

Measurements and Calculations14B. Significant Figures Numbers recorded in a measurement. All the certain numbers plus first estimated number Measurements and Calculations15B. Significant Figures Rules for Counting Significant Figures Nonzero integers always count as significant figures. 1457 4 significant figures Measurements and Calculations16B. Significant Figures Rules for Counting Significant Figures ZerosLeading zeros - never count0.0025 2 significant figures Captive zeros - always count 1.008 4 significant figures Trailing zeros - count only if the number is written with a decimal point 100 1 significant figure 100. 3 significant figures 120.0 4 significant figuresMeasurements and Calculations17B. Significant Figures Rules for Counting Significant Figures Exact numbers - unlimited significant figures Not obtained by measurement Determined by counting3 apples Determined by definition1 in. = 2.54 cmMeasurements and Calculations18B. Significant Figures

Measurements and Calculations19A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.Record the certain digits and the first uncertain digit (the estimated number).Copyright Cengage Learning. All rights reservedMeasurements and Calculations20Measurement of Volume Using a BuretThe volume is read at the bottom of the liquid curve (meniscus).Meniscus of the liquid occurs at about 20.15 mL.Certain digits: 20.15Uncertain digit: 20.15Copyright Cengage Learning. All rights reserved

Measurements and Calculations21Significant Figures in Measurements

Measurements and Calculations22Three differently calibrated meter sticks are used to measure the length of a board. a) A meter stick calibrated in a 1-m interval. b) A meter stick calibrated in 0.1-m intervals. c) A meter stick calibrated in 0.01-m intervals. Measuring How many significant figures are reported in each measurement?

Precision and AccuracyAccuracyCopyright Cengage Learning. All rights reservedAgreement of a particular value with the true value. PrecisionDegree of agreement among several measurements of the same quantity. Measurements and Calculations23Precision and AccuracyCopyright Cengage Learning. All rights reserved

Measurements and Calculations24

Measurements and Calculations25The distribution of darts illustrates the difference between accuracy and precision. a) Good accuracy and good precision: The darts are close to the bulls-eye and to one another. b) Poor accuracy and good precision: The darts are far from the bulls-eye but close to one another. c) Poor accuracy and poor precision: The darts are far from the bulls-eye and from one another.ErrorDetermining ErrorThe accepted value is the correct value based on reliable references. The experimental value is the value measured in the lab. The difference between the experimental value and the accepted value is called the error.

Measurements and Calculations26ErrorThe percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.

Measurements and Calculations27Expressing very large numbers, such as the estimated number of stars in a galaxy, is easier if scientific notation is used.B. Significant Figures Rules for Multiplication and Division The number of significant figures in the result is the same as in the measurement with the smallest number of significant figures.

Measurements and Calculations28B. Significant Figures Rules for Addition and Subtraction The number of significant figures in the result is the same as in the measurement with the smallest number of decimal places.

Measurements and Calculations29To learn how dimensional analysis can be used to solve problems To learn the three temperature scales To learn to convert from one temperature scale to another To practice using problem solving techniques To define density and its units Objectives 5.3Problem Solving and Unit ConversionsMeasurements and Calculations30A. Tools for Problem Solving Be systematic Ask yourself these questions Where do we want to go? What do we know? How do we get there?Does it make sense? Measurements and Calculations31A. Tools for Problem Solving We can convert from one system of units to another by a method called dimensional analysis using conversion factors. Unit1 conversion factor = Unit2 Converting Units of Measurement Measurements and Calculations32A. Tools for Problem Solving Conversion factors are built from an equivalence statement which shows the relationship between the units in different systems.Conversion factors are ratios of the two parts of the equivalence statement that relate the two units.Converting Units of Measurement Measurements and Calculations33A. Tools for Problem Solving 2.85 cm = ? in.2.85 cm conversion factor = ? in. Equivalence statement2.54 cm = 1 in. Possible conversion factors Converting Units of MeasureDoes this answer make sense?

Measurements and Calculations34A. Tools for Problem Solving Tools for Converting from One Unit to Another Step 1 Find an equivalence statement that relates the 2 units.Step 2 Choose the conversion factor by looking at the direction of the required change (cancel the unwanted units).Step 3 Multiply the original quantity by the conversion factor. Step 4 Make sure you have the correct number of significant figures. Measurements and Calculations35B. Temperature Conversions There are three commonly used temperature scales, Fahrenheit, Celsius and Kelvin.

Measurements and Calculations36B. Temperature Conversions Note that The temperature unit is the same size. The zero points are different. To convert from Celsius to Kelvin we need to adjust for the difference in zero points. Converting Between the Kelvin and Celsius Scales

Measurements and Calculations37B. Temperature Conversions 70. oC = ? KTC + 273 = TK Converting Between the Kelvin and Celsius Scales 70. + 273 = 343 K

Measurements and Calculations38B. Temperature Conversions NoteConverting Between the Fahrenheit and Celsius Scales The different size unitsThe different zero points To convert between Fahrenheit and Celsius we need to make 2 adjustments.

Measurements and Calculations39C. Density Density is the amount of matter present in a given volume of substance.

Measurements and Calculations40C. Density

Measurements and Calculations41