chapter menu analyzing data section 2.1section 2.1units and measurements section 2.2section 2.2...

Chapter Menu

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

ExitClick 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.

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

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.

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 2-2

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).

• 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.)

800 = 8.0 102

0.0000343 = 3.43 10–5

• 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.

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.

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.

• 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 2-3

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.

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

Section 2-3

Accuracy and Precision (cont.)

• Error is 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 error expresses error as a percentage of the accepted value.

Section 2-3

Significant Figures

• 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

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.

– 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.)

• 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.

Section 2-4

Section 2.4 Representing Data

• Create graphics to reveal patterns in data.

independent variable: the variable that is changed during an experiment

graph

• Interpret graphs.

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

Section 2-4

Graphing

• A graph is 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

Interpreting Graphs

• 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.