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CH-2ANALYZING DATA

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.

PREFIXES USED IN THE SI SYSTEM

dreamy, Hungarian kings, make great, tantalizing powerful exclamations

dreadful, caped mighty men need plenty fearless aides

• 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

TEMPERATURE

• In scientific measurements, the Celsius and Kelvin scales are most often used.

• The Celsius scale is based on the properties of water.

• 0 C is the freezing point of water.

• 100 C is the boiling point of water.

• The kelvin is the SI unit of temperature.

• It is based on the properties of gases.

• There are no negative Kelvin temperatures.

• The lowest possible temperature is called absolute zero (0 K).

• K = C + 273.15

• 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.

• The equations below allow for conversion between the Fahrenheit and Celsius scales:

• °F = 1.8(°C) + 32

• °C = (°F − 32)/1.8

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.

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

The density equation is density = mass/volume.

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

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.

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.

• Addition and subtraction

– Exponents must be the same.

– Rewrite values with the same exponent.

– Add or subtract coefficients.

• 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.

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.

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

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

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

SIGNIFICANT FIGURES• Often, precision is limited by the tools available.

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

MEASUREMENT OF VOLUME USING A BURET

• The volume is read at the bottom of the

liquid curve (meniscus).

•Meniscus of the liquid occurs at about

20.15 mL.

• Certain digits: 20.15

• Uncertain digit: 20.15

20

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.

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.

RULES FOR ROUNDINGRule 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.

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

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.

SIG FIG PRACTICE • 1.0070 m

• 17.10 kg

• 100890 L

• 3.29 x 103

• 0.0054 cm

• 1 in

• 3,200,000 ns

• 35 students

• 200 ml

• 0.040 g

• 1.60 m

• 12 in

• 5 sig figs

• 4 sig figs

• 5 sig figs

• 3 sig figs

• 2 sig figs

• Unlimited

• 2 sig figs

• Unlimited

• 1 sig figs

• 2 sig figs

• 3 sig figs

• Unlimited

SIG FIG PRACTICE 1

SIG FIG PRACTICE 2

You have water in each graduated

cylinder shown. You then add both

samples to a beaker (assume that

all of the liquid is transferred).

How would you write the number

describing the total volume?

3.1 mL

What limits the precision of the

total volume?

CONCEPT CHECK!

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.

• 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.

DIMENSIONAL ANALYSIS

• We use dimensional analysis to convert one quantity to another.

• Most commonly, dimensional analysis utilizes conversion factors (e.g., 1 in. = 2.54 cm).

• We can set up a ratio of comparison for the equality either 1 in/2.54 cm or 2.54 cm/1 in.

• We use the ratio which allows us to change units (puts the units we have in the denominator to cancel).

1 ft 12 in and

12 in 1 ft

A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?

• To convert from one unit to another, use the equivalence statement that relates the two units.

1 ft = 12 in

The two unit factors are:

An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams?

(1 kg = 2.2046 lbs; 1 kg = 1000 g)

What data would you need to estimate the money you

would spend on gasoline to drive your car from New

York to Los Angeles? Provide estimates of values and

a sample calculation.

CONCEPT CHECK!

GRAPHING

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

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

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

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

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

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.

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

HOMEWORK ASSIGNMENT

• Pages 62-63

• Problems

65-69, 71, 73, 76-98