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

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Section 2.1Units and Measurements

Section 2.2Scientific Notation and Dimensional Analysis

Section 2.3Uncertainty in Data

Section 2.4Representing Data

Click a hyperlink or folder tab to view the corresponding slides.

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• Define SI base units for time, length, mass, and temperature.

• Explain how adding a prefix changes a unit.

• Compare the derived units for volume and density.

mass: a measurement that reflects the amount of matter an object contains

Section 2-1

base unit

second

meter

kilogram

kelvin

derived unit

liter

density

Chemists use an internationally recognized system of units to communicate their findings.

Section 2-1

• 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.

Section 2-1

Units (cont.)

Section 2-1

Units (cont.)

Section 2-1

Units (cont.)

• The SI base unit of time is the second (s), based on the frequency of radiation given off by a cesium-133 atom.

• The SI base unit for length is the meter (m), the distance light travels in a vacuum in 1/299,792,458th of a second.

• The SI base unit of mass is the kilogram (kg), about 2.2 pounds

Section 2-1

Units (cont.)

• The SI base unit of temperature is the kelvin(K).

• 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

• 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.

Section 2-1

Derived Units (cont.)

• Volume is measured in cubic meters (m3), but this is very large. A more convenient measure is the liter, or one cubic decimeter (dm3).

Section 2-1

Derived Units (cont.)

• Density is a derived unit, g/cm3, the amount of mass per unit volume.

• The density equation is density = mass/volume.

Section 2-1

B

C

D

Section 2.1 Assessment

Which of the following is a derived unit?

A.yard

B.second

C.liter

D.kilogram

Section 2-1

B

C

D

Section 2.1 Assessment

What is the relationship between mass and volume called?

A.density

B.space

C.matter

D.weight

Section 2-1

• Express numbers in scientific notation.

• Convert between units using dimensional analysis.

quantitative data: numerical information describing how much, how little, how big, how tall, how fast, and so on

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 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).

• 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 and negative when the decimal moves to the right.

800 = 8.0  102

0.0000343 = 3.43  10–5

Section 2-2

Scientific Notation (cont.)

• Exponents must be the same.

• Rewrite values with the same exponent.

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.

Section 2-2

• Dimensional analysis is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another.

• A conversion factor is a ratio of equivalent values having different units.

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.

Section 2-2

B

C

D

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

Section 2-2

B

C

D

Section 2.2 Assessment

Which of the following expresses 9,640,000 in the correct scientific notation?

A.9.64  104

B.9.64  105

C.9.64 × 106

D.9.64  610

Section 2-2

• Define and compare accuracy and precision.

• Describe the accuracy of experimental data using error and percent error.

• Apply rules for significant figures to express uncertainty in measured and calculated values.

experiment: a set of controlled observations that test a hypothesis

Section 2-3

accuracy

precision

error

percent error

significant figures

Measurements contain uncertainties that affect how a result is presented.

Section 2-3

• Accuracy refers to how close a measured value is to an accepted value.

• Precision refers to how close a series of measurements are to one another.

Section 2-3

Accuracy and Precision (cont.)

• Erroris defined as the difference between and experimental value and an accepted value.

Section 2-3

Accuracy and Precision (cont.)

• The error equation is error = experimental value – accepted value.

• Percent errorexpresses error as a percentage of the accepted value.

Section 2-3

• Often, precision is limited by the tools available.

• Significant figures include all known digits plus one estimated digit.

Section 2-3

Significant Figures (cont.)

• Rules for significant figures

• Rule 1: Nonzero numbers are always significant.

• Rule 2: Zeros between nonzero numbers are always significant.

• Rule 3: All final zeros to the right of the decimal are significant.

• Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation.

• Rule 5: Counting numbers and defined constants have an infinite number of significant figures.

Section 2-3

• 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.

• Rule 2: If the digit to the right of the last significant figure is greater than 5, round up to the last significant figure.

• 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.

Section 2-3

Rounding Numbers (cont.)

• Rules for rounding (cont.)

• 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.

Section 2-3

Rounding Numbers (cont.)

• 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.

Section 2-3

B

C

D

Section 2.3 Assessment

Determine the number of significant figures in the following: 8,200, 723.0, and 0.01.

A.4, 4, and 3

B.4, 3, and 3

C.2, 3, and 1

D.2, 4, and 1

Section 2-3

B

C

D

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

Section 2-3

• Create graphics to reveal patterns in data.

independent variable: the variable that is changed during an experiment

• Interpret graphs.

graph

Graphs visually depict data, making it easier to see patterns and trends.

Section 2-4

• A graphis a visual display of data that makes trends easier to see than in a table.

Section 2-4

Graphing (cont.)

• A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.

Section 2-4

Graphing (cont.)

• Bar graphs are often used to show how a quantity varies across categories.

Section 2-4

Graphing (cont.)

• On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis.

Section 2-4

Graphing (cont.)

• If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope.

Section 2-4

• Interpolation is reading and estimating values falling between points on the graph.

• Extrapolation is estimating values outside the points by extending the line.

Section 2-4

Interpreting Graphs (cont.)

• This graph shows important ozone measurements and helps the viewer visualize a trend from two different time periods.

Section 2-4

B

C

D

Section 2.4 Assessment

____ variables are plotted on the ____-axis in a line graph.

A.independent, x

B.independent, y

C.dependent, x

D.dependent, z

Section 2-4

B

C

D

Section 2.4 Assessment

What kind of graph shows how quantities vary across categories?

A.pie charts

B.line graphs

C.Venn diagrams

D.bar graphs

Section 2-4

Study Guide

Chapter Assessment

Standardized Test Practice

Image Bank

Concepts in Motion

Key Concepts

• SI measurement units allow scientists to report data to other scientists.

• Adding prefixes to SI units extends the range of possible measurements.

• To convert to Kelvin temperature, add 273 to the Celsius temperature. K = °C + 273

• Volume and density have derived units. Density, which is a ratio of mass to volume, can be used to identify an unknown sample of matter.

Study Guide 1

Section 2.2 Scientific Notation and Dimensional Analysis

Key Concepts

• A number expressed in scientific notation is written as a coefficient between 1 and 10 multiplied by 10 raised to a power.

• To add or subtract numbers in scientific notation, the numbers must have the same exponent.

• To multiply or divide numbers in scientific notation, multiply or divide the coefficients and then add or subtract the exponents, respectively.

• Dimensional analysis uses conversion factors to solve problems.

Study Guide 2

Key Concepts

• An accurate measurement is close to the accepted value. A set of precise measurements shows little variation.

• The measurement device determines the degree of precision possible.

• Error is the difference between the measured value and the accepted value. Percent error gives the percent deviation from the accepted value.

• error = experimental value – accepted value

Study Guide 3

Key Concepts

• The number of significant figures reflects the precision of reported data.

• Calculations should be rounded to the correct number of significant figures.

Study Guide 3

Key Concepts

• Circle graphs show parts of a whole. Bar graphs show how a factor varies with time, location, or temperature.

• Independent (x-axis) variables and dependent (y-axis) variables can be related in a linear or a nonlinear manner. The slope of a straight line is defined as rise/run, or ∆y/∆x.

• Because line graph data are considered continuous, you can interpolate between data points or extrapolate beyond them.

Study Guide 4

B

C

D

Which of the following is the SI derived unit of volume?

A.gallon

B.quart

C.m3

D.kilogram

Chapter Assessment 1

B

C

D

Which prefix means 1/10th?

A.deci-

B.hemi-

C.kilo-

D.centi-

Chapter Assessment 2

B

C

D

Divide 6.0  109 by 1.5  103.

A.4.0  106

B.4.5  103

C.4.0  103

D.4.5  106

Chapter Assessment 3

B

C

D

Round the following to 3 significant figures 2.3450.

A.2.35

B.2.345

C.2.34

D.2.40

Chapter Assessment 4

B

C

D

The rise divided by the run on a line graph is the ____.

A.x-axis

B.slope

C.y-axis

D.y-intercept

Chapter Assessment 5

B

C

D

Which is NOT an SI base unit?

A.meter

B.second

C.liter

D.kelvin

STP 1

B

C

D

Which value is NOT equivalent to the others?

A.800 m

B.0.8 km

C.80 dm

D.8.0 x 105 cm

STP 2

B

C

D

Find the solution with the correct number of significant figures:25  0.25

A.6.25

B.6.2

C.6.3

D.6.250

STP 3

B

C

D

How many significant figures are there in 0.0000245010 meters?

A.4

B.5

C.6

D.11

STP 4

B

C

D

Which is NOT a quantitative measurement of a liquid?

A.color

B.volume

C.mass

D.density

STP 5

Figure 2.10 Accuracy and Precision

CIM

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