Chapter Menu Analyzing Data Section 2.1Section 2.1Units and Measurements Section 2.2Section 2.2 Scientific Notation and Dimensional Analysis Section 2.3Section 2.3 Uncertainty in Data Section 2.4Section 2.4 Representing Data Exit Click a hyperlink or folder tab to view the corresponding slides.

Section 2-1 Section 2.1 Units and Measurements Define SI base units for time, length, mass, and temperature. mass: a measurement that reflects the amount of matter an object contains Explain how adding a prefix changes a unit. Compare the derived units for volume and density.

Section 2-1 Section 2.1 Units and Measurements (cont.) base unit second meter kilogram Chemists use an internationally recognized system of units to communicate their findings. kelvin derived unit liter density

Section 2-1 Units Système Internationale d'Unités (SI) is an internationally agreed upon system of measurements. A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units.base unit

Section 2-1 Units (cont.)

Section 2-1 Units (cont.)

Section 2-1 Units (cont.) The SI base unit of temperature is the kelvin (K).kelvin Zero kelvin is the point where there is virtually no particle motion or kinetic energy, also known as absolute zero. Two other temperature scales are Celsius and Fahrenheit.

Section 2-1 Derived Units Not all quantities can be measured with SI base units. A unit that is defined by a combination of base units is called a derived unit.derived unit

Section 2-1 Derived Units (cont.) Volume is measured in cubic meters (m 3 ), but this is very large. A more convenient measure is the liter, or one cubic decimeter (dm 3 ).liter

Section 2-1 Derived Units (cont.) Density is a derived unit, g/cm 3, the amount of mass per unit volume.Density The density equation is density = mass/volume.

A.A B.B C.C D.D Section 2-1 Section 2.1 Assessment Which of the following is a derived unit? A.yard B.second C.liter D.kilogram

A.A B.B C.C D.D Section 2-1 Section 2.1 Assessment What is the relationship between mass and volume called? A.density B.space C.matter D.weight

Section 2-2 Section 2.2 Scientific Notation and Dimensional Analysis Express numbers in scientific notation. quantitative data: numerical information describing how much, how little, how big, how tall, how fast, and so on Convert between units using dimensional analysis.

Section 2-2 Section 2.2 Scientific Notation and Dimensional Analysis (cont.) scientific notation dimensional analysis conversion factor Scientists often express numbers in scientific notation and solve problems using dimensional analysis.

Section 2-2 Scientific Notation Scientific notation can be used to express any number as a number between 1 and 10 (the coefficient) multiplied by 10 raised to a power (the exponent).Scientific notation Count the number of places the decimal point must be moved to give a coefficient between 1 and 10.

Section 2-2 Scientific Notation (cont.) The number of places moved equals the value of the exponent. The exponent is positive when the decimal moves to the left 800 = 8.0  10 2 The exponent is negative when the decimal moves to the right = 3.43  10 –5

Section 2-2 Scientific Notation (cont.) Addition and subtraction –Exponents must be the same. –Rewrite values with the same exponent. –Add or subtract coefficients.

Section 2-2 Scientific Notation (cont.) Multiplication and division –To multiply, multiply the coefficients, then add the exponents. –To divide, divide the coefficients, then subtract the exponent of the divisor from the exponent of the dividend. –Homework – page 41 11, 12 – page 42 13, 14 – page 43 15, 16 – page – 79

Section 2-2 Dimensional Analysis Dimensional analysis is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another.Dimensional analysis A conversion factor is a ratio of equivalent values having different units.conversion factor

Section 2-2 Dimensional Analysis (cont.) Writing conversion factors –Conversion factors are derived from equality relationships, such as 1 dozen eggs = 12 eggs. –Percentages can also be used as conversion factors. They relate the number of parts of one component to 100 total parts.

Section 2-2 Dimensional Analysis (cont.) Using conversion factors –A conversion factor must cancel one unit and introduce a new one.

Steps to Problem Solving 1.Write down the given amount. Don’t forget the units! 2.Multiply by a fraction. 3.Use the fraction as a conversion factor. Determine if the top or the bottom should be the same unit as the given so that it will cancel. 4.Put a unit on the opposite side that will be the new unit. If you don’t know a conversion between those units directly, use one that you do know that is a step toward the one you want at the end. 5.Insert the numbers on the conversion so that the top and the bottom amounts are EQUAL, but in different units. 6.Multiply and divide the units (Cancel). 7.If the units are not the ones you want for your answer, make more conversions until you reach that point.

Metric Prefixes 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)

A.A B.B C.C D.D Section 2-2 Section 2.2 Assessment What is a systematic approach to problem solving that converts from one unit to another? A.conversion ratio B.conversion factor C.scientific notation D.dimensional analysis

A.A B.B C.C D.D Section 2-2 Section 2.2 Assessment Which of the following expresses 9,640,000 in the correct scientific notation? A.9.64  10 4 B.9.64  10 5 C.9.64 × 10 6 D.9.64  6 10

do the following problems: –Page 45 19, 20 –Page – 30 –Page

Section 2-3 Section 2.3 Uncertainty in Data Define and compare accuracy and precision. experiment: a set of controlled observations that test a hypothesis Describe the accuracy of experimental data using error and percent error. Apply rules for significant figures to express uncertainty in measured and calculated values.

Section 2-3 Section 2.3 Uncertainty in Data (cont.) accuracy precision error Measurements contain uncertainties that affect how a result is presented. percent error significant figures

Section 2-3 Accuracy and Precision Accuracy refers to how close a measured value is to an accepted value.Accuracy Precision refers to how close a series of measurements are to one another.Precision

Section 2-3 Accuracy and Precision (cont.) Error is defined as the difference between an experimental value and an accepted value.Error

Section 2-3 Accuracy and Precision (cont.) The error equation is error = experimental value – accepted value. Percent error expresses error as a percentage of the accepted value.Percent error

Section 2-3 Significant Figures Often, precision is limited by the tools available. Significant figures include all known digits plus one estimated digit.Significant figures

Significant Figures (cont.) –Rule 1: Any non-zero digit is significant. – 329 g –3 significant digits – x – 4 significant digits –Rule 2: Any zero stuck between other numbers is significant. – 2002 –4 sig figs – 3.09 x 10 – 3 sig figs

Section 2-3 Significant Figures (cont.) –Rule 3: Zeros to the left of all the other digits are NEVER significant – – 3 sig figs – – 4 sig figs

Section 2-3 Significant Figures (cont.) –Rule 4: Zeros to the right of all the other digits – a.) ARE significant if there is a decimal point – a decimal point TELLS us that the number is a measurement – – – a.) are NOT significant if there is no decimal point. – no decimal point means that the number is an estimate – 3900 –

Section 2-3 Rounding Numbers Calculators are not aware of significant figures. Answers should not have more significant figures than the original data with the fewest figures, and should be rounded.

Section 2-3 Rounding Numbers (cont.) Rules for rounding –Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure. –  4.56 –  36.5 –Rule 2: If the digit to the right of the last significant figure is greater than 5, round up to the last significant figure. –  23.6 –  6.56

Rounding Numbers (cont.) –Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up to the last significant figure. –  5.54 –Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up. –  2.54 –  2.52

Section 2-3 Rounding Numbers (cont.) Addition and subtraction –Round numbers so all numbers have the same number of digits to the right of the decimal. Multiplication and division –Round the answer to the same number of significant figures as the original measurement with the fewest significant figures.

A.A B.B C.C D.D Section 2-3 Section 2.3 Assessment Determine the number of significant figures in the following: 8,200, 723.0, and A.4, 4, and 3 B.4, 3, and 3 C.2, 3, and 1 D.2, 4, and 1

A.A B.B C.C D.D Section 2-3 Section 2.3 Assessment A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is the percent error? A.0.20 g/L B.–0.20 g/L C.0.10 g/L D.0.90 g/L

Homework – page 49 33, 34 – page – 37 – page – 41 – page – 44