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1.2 Measurement & Scientific 1.2 Measurement & Scientific NotationNotation

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MeasurementMeasurement

You make a You make a measurement measurement every time youevery time you

Measure your Measure your height. height.

Read your watch.Read your watch. Take your Take your

temperature.temperature. Weigh a Weigh a

cantaloupe.cantaloupe.

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Measurement in ScienceMeasurement in Science

In science and allied health weIn science and allied health we Measure quantities.Measure quantities. Do experiments.Do experiments. Calculate results. Calculate results. Use numbers to report Use numbers to report

measurements.measurements. Compare results to standards.Compare results to standards.

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Standards of MeasurementStandards of Measurement

When we When we measure, we use measure, we use a measuring tool a measuring tool to compare some to compare some dimension of an dimension of an object to a object to a standard.standard.

Calipers are used Calipers are used to measure the to measure the thickness of the thickness of the skin fold at the skin fold at the waist.waist.

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Stating a MeasurementStating a Measurement

In every measurement, a In every measurement, a number number is is followed by afollowed by a unitunit..

Observe the following examples of Observe the following examples of measurements:measurements:

number + unitnumber + unit

35 m35 m

0.25 L0.25 L

225 lb225 lb

3.4 hr 3.4 hr

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The Metric System (SI)The Metric System (SI)

The metric system The metric system isis

A decimal system A decimal system based on 10.based on 10.

Used in most of Used in most of the world.the world.

Used by scientists Used by scientists

and in hospitals.and in hospitals.

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Units in the Metric SystemUnits in the Metric System

In the metric and SI systems, a In the metric and SI systems, a basic unit identifies each type of basic unit identifies each type of measurement:measurement:

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Length MeasurementLength Measurement In the metric system, length is In the metric system, length is

measured in meters using a meter measured in meters using a meter stick.stick.

The metric unit for length is the The metric unit for length is the meter (m).meter (m).

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Volume MeasurementVolume Measurement

Volume is the space Volume is the space occupied by a occupied by a substance.substance.

The metric unit of The metric unit of volume is thevolume is the liter liter (L).(L).

The liter is slightly The liter is slightly bigger than a quart.bigger than a quart.

A graduated cylinder A graduated cylinder is used to measure is used to measure the volume of a the volume of a liquid.liquid.

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Mass MeasurementMass Measurement

The mass of an The mass of an object is the object is the quantity of material quantity of material it contains.it contains.

A balance is used to A balance is used to measure mass.measure mass.

The metric unit for The metric unit for mass is themass is the gram gram (g).(g).

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Temperature MeasurementTemperature Measurement

The temperature of a The temperature of a substances indicates substances indicates how hot or cold it is.how hot or cold it is.

In the metric system, In the metric system, temperature is temperature is measured on the measured on the Celsius scale. Celsius scale.

On this thermometer,On this thermometer, the temperature isthe temperature is 1919ººC or 66C or 66ºF.ºF.

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Scientific NotationScientific Notation A number in scientific notation contains a A number in scientific notation contains a

coefficient and a power of 10.coefficient and a power of 10. coefficient power of ten coefficient power of ten coefficient power of coefficient power of

tenten 1.5 x 101.5 x 1022 7.35 x 107.35 x 10-4-4

Place the decimal point after the first digit. Place the decimal point after the first digit. Indicate the spaces moved as a power of ten.Indicate the spaces moved as a power of ten.

52 000 = 5.2 x 1052 000 = 5.2 x 1044 0.00378 = 3.78 x 0.00378 = 3.78 x 1010-3-3

4 spaces left4 spaces left 3 spaces 3 spaces rightright

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1.3 Measured and Exact 1.3 Measured and Exact NumbersNumbers

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Measured NumbersMeasured Numbers

You use a You use a measuring tool to measuring tool to determine a determine a quantity such as quantity such as your height or the your height or the mass of an object.mass of an object.

The numbers you The numbers you obtain are called obtain are called measured measured numbers.numbers.

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. l. l22. . . . l . . . . l. . . . l . . . . l33 . . . . l . . . . l . . . . l . . . . l44. . . . cmcm

To measure the length of the blue To measure the length of the blue line, we read the markings on the line, we read the markings on the meter stick. meter stick.

The first digit The first digit 2 2 plus the second digit plus the second digit 2.7 2.7

EstimatingEstimating the third digit between the third digit between 2.7–2.82.7–2.8gives a final length reported asgives a final length reported as

2.72.755 cm cm oror 2.7 2.76 6 cm cm

Reading a Meter Stick Reading a Meter Stick

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Known + Estimated DigitsKnown + Estimated Digits

In the length measurement of 2.76 cm,In the length measurement of 2.76 cm,

the digits 2 and 7 are certain (the digits 2 and 7 are certain (knownknown).).

the third digit the third digit 5(or 6)5(or 6) is is estimated estimated

((uncertainuncertain).). all three digits (2.76) are all three digits (2.76) are significantsignificant

including the including the estimated digitestimated digit..

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. l. l33. . . . l . . . . l. . . . l . . . . l44. . . . l . . . . . . . . l . . . . ll55. . . . cmcm

The first and second digits are 4.5.The first and second digits are 4.5. In this example, the line ends on a In this example, the line ends on a

mark.mark. Then the Then the estimatedestimated digit for the digit for the

hundredths place is hundredths place is 00.. We would report this measurement We would report this measurement

as 4.5as 4.500 cm.cm.

Zero as a Measured Zero as a Measured NumberNumber

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Exact NumbersExact Numbers

An An exact numberexact number is obtained when is obtained when you you count objectscount objects or use a or use a defined defined relationshiprelationship..Counting objectsCounting objects

2 soccer balls2 soccer balls4 pizzas4 pizzas

Defined relationshipsDefined relationships1 foot = 12 inches1 foot = 12 inches1 meter = 100 cm1 meter = 100 cm

An An exact numberexact number is is not not obtainedobtained with a with a measuring toolmeasuring tool..

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1.4 Significant Figures in 1.4 Significant Figures in CalculationsCalculations

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Significant Figures in Significant Figures in MeasurementMeasurement

The numbers reported The numbers reported in a measurement in a measurement depend on the depend on the measuring tool.measuring tool.

Measurements are not Measurements are not exact; they have exact; they have uncertainty.uncertainty.

The significant figures The significant figures for a measurement for a measurement include all of the known include all of the known digits plus one digits plus one estimated digit.estimated digit.

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All non-zero numbersAll non-zero numbers in a in a measuredmeasured number are number are significantsignificant. . MeasurementMeasurement Number of Number of Significant Significant

FiguresFigures

38.15 cm38.15 cm 44

5.6 ft5.6 ft 22

65.6 lb65.6 lb 33

122.55 m122.55 m 55

Counting Significant Counting Significant FiguresFigures

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Leading zerosLeading zeros precede non-zero digits precede non-zero digits in a decimal number. in a decimal number.

Leading zerosLeading zeros in decimal numbers are in decimal numbers are not significant.not significant.

MeasurementMeasurement Number of Number of Significant Significant FiguresFigures

0.008 mm0.008 mm 11 0.0156 oz0.0156 oz 33 0.0042 lb0.0042 lb 22 0.000262 mL 0.000262 mL 33

Leading ZerosLeading Zeros

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Sandwiched zerosSandwiched zeros occur between occur between nonzero numbers.nonzero numbers.

Sandwiched zeros Sandwiched zeros are significantare significant.. MeasurementMeasurement Number of Number of

Significant Significant FiguresFigures 50.8 mm50.8 mm 33 2001 min2001 min 44 0.0702 lb0.0702 lb 33 0.40505 m0.40505 m 5 5

Sandwiched ZerosSandwiched Zeros

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In numbers without decimal points, In numbers without decimal points, trailing zeros trailing zeros follow non-zero numbers. follow non-zero numbers.

Trailing zeros are usually place holders Trailing zeros are usually place holders and and not significantnot significant..

MeasurementMeasurement Number of Number of Significant Significant Figures Figures

25 000 cm 25 000 cm 22 200 kg200 kg 11 48 600 mL48 600 mL 33 25 005 000 g 25 005 000 g 55

Trailing ZerosTrailing Zeros

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Significant Figures in Significant Figures in Scientific NotationScientific Notation

All digits including zeros that appear All digits including zeros that appear in the coefficient of a number written in the coefficient of a number written in scientific notation are significantin scientific notation are significant..

Scientific NotationScientific Notation Number of Number of Significant Significant FiguresFigures

8 x 108 x 104 4 mm 11

8.0 x 108.0 x 1044 m m 22

8.00 x 108.00 x 1044 m m 33

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A calculated answer must relate to A calculated answer must relate to the measured values used in the the measured values used in the calculation. calculation.

In calculations involving addition In calculations involving addition or subtraction, the number of or subtraction, the number of decimal places are counted.decimal places are counted.

In calculations involving In calculations involving multiplication or division, multiplication or division, significant figures are counted to significant figures are counted to determine final answers. determine final answers.

Significant Numbers in Significant Numbers in CalculationsCalculations

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Rules for Rounding Off Rules for Rounding Off Calculated AnswersCalculated Answers

To obtain the correct number of significant To obtain the correct number of significant figures, an answer may be rounded off.figures, an answer may be rounded off.

When digits of 4 or less are dropped, the When digits of 4 or less are dropped, the rest of the numbers are the same. For rest of the numbers are the same. For example, rounding 45.832 to 3 significant example, rounding 45.832 to 3 significant figures givesfigures gives

45.832 rounds to 45.8 (3 SF)45.832 rounds to 45.8 (3 SF) When digits of 5 or greater dropped, the When digits of 5 or greater dropped, the

last retained digit is increased by 1. For last retained digit is increased by 1. For example, rounding 2.4884 to 2 significant example, rounding 2.4884 to 2 significant figures givesfigures gives

2.4884 rounds to 2.5 (2 SF)2.4884 rounds to 2.5 (2 SF)

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Adding Significant ZerosAdding Significant Zeros

When a calculated answer requires When a calculated answer requires more significant digits, zeros are more significant digits, zeros are addedadded..

Calculated answerCalculated answer Zeros added to Zeros added to give 3 significant give 3 significant figuresfigures

44 4.4.00001.51.5 1.51.5000.20.2 0.20.20000

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An answer obtained by adding or An answer obtained by adding or subtracting has the same number of subtracting has the same number of decimal places as the measurement with decimal places as the measurement with the fewest decimal placesthe fewest decimal places..

Proper rules of rounding are used to Proper rules of rounding are used to adjust the number of digits in the answer.adjust the number of digits in the answer.

25.25.2 2 one decimal placeone decimal place

+ 1.+ 1.3434 two decimal placestwo decimal places

26.5426.54 calculated answercalculated answer

26.5 26.5 answer withanswer with one decimal one decimal placeplace

Adding and SubtractingAdding and Subtracting

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An answer obtained by multiplying or An answer obtained by multiplying or dividing has the same number of dividing has the same number of significant figures as the significant figures as the measurement with the fewest measurement with the fewest significant figuressignificant figures..

Use rounding to limit the number of Use rounding to limit the number of digits in the answer.digits in the answer.

110.5 x 0.048 = 5.304 110.5 x 0.048 = 5.304

(calculator)(calculator) 4 SF 2 SF 4 SF 2 SF The final answer is rounded off to give The final answer is rounded off to give

2 significant figures = 2 significant figures = 5.35.3 (2 SF)(2 SF)

Multiplying and DividingMultiplying and Dividing

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1.6 1.6 SI and Metric SI and Metric PrefixesPrefixes

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PrefixesPrefixes

A prefix in front of a unit increases A prefix in front of a unit increases or decreases the size of that unit. or decreases the size of that unit.

The new units are larger or smaller The new units are larger or smaller that the initial unit by one or more that the initial unit by one or more factors of 10. factors of 10.

A prefix indicates a numerical value.A prefix indicates a numerical value.

prefixprefix == valuevalue

1 1 kilokilometermeter == 10001000 meters meters

1 1 kilokilogramgram == 10001000 grams grams

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Metric and SI PrefixesMetric and SI Prefixes

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An equality states the same An equality states the same measurement in two different units.measurement in two different units.

Equalities are written using the Equalities are written using the relationships between two metric relationships between two metric units.units.

For example, 1 meter can be For example, 1 meter can be expressed as 100 cm or as 1000 expressed as 100 cm or as 1000 mm.mm.

1 m1 m == 100 cm100 cm

1 m1 m == 1000 mm1000 mm

Metric EqualitiesMetric Equalities

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Metric Equalities for LengthMetric Equalities for Length

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Metric Equalities for VolumeMetric Equalities for Volume

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Metric Equalities for MassMetric Equalities for Mass

Several equalities can be Several equalities can be written for mass in the written for mass in the metric systemmetric system

1 kg1 kg == 1000 g1000 g

1 g1 g == 1000 mg1000 mg

1 mg1 mg = = 0.001 g0.001 g

1 mg1 mg == 1000 1000 µgµg

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1.6 Writing Conversion 1.6 Writing Conversion FactorsFactors

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The quantities in an equality use two The quantities in an equality use two different units to describe the same different units to describe the same measured amount. measured amount.

Equalities are written for Equalities are written for relationships between units of the relationships between units of the metric system, U.S. units or between metric system, U.S. units or between metric and U.S. units. For example, metric and U.S. units. For example,

1 m 1 m = = 1000 mm1000 mm1 lb 1 lb = 16 oz = 16 oz2.20 lb = 1 kg2.20 lb = 1 kg

EqualitiesEqualities

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Exact and Measured Exact and Measured Numbers in EqualitiesNumbers in Equalities

Equalities written between units Equalities written between units of the of the samesame system are system are definitions; they are exact definitions; they are exact numbers.numbers.

Equalities written between Equalities written between metric-U.S. units, which are in metric-U.S. units, which are in different systems, represent different systems, represent measured numbers and must be measured numbers and must be counted as significant figures.counted as significant figures.

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Some Common EqualitiesSome Common Equalities

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Equalities on Food LabelsEqualities on Food Labels

The contents of packaged foods The contents of packaged foods in the U.S. are listed as both in the U.S. are listed as both metric and U.S. units.metric and U.S. units.

The content values indicate the The content values indicate the same amount of substance in two same amount of substance in two different units.different units.

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A conversion factor is a fraction in A conversion factor is a fraction in which the quantities in an equality are which the quantities in an equality are written as the numerator and written as the numerator and denominator.denominator.Equality: 1 in. = 2.54 cmEquality: 1 in. = 2.54 cm

Each unit can be written as the Each unit can be written as the numerator or denominator. Thus, two numerator or denominator. Thus, two conversion factors are possible for conversion factors are possible for every equality.every equality.1 in. 1 in. and and 2.54 cm 2.54 cm 2.54 cm2.54 cm 1 in. 1 in.

Conversion FactorsConversion Factors

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A word problem may contain information A word problem may contain information that can be used to write conversion that can be used to write conversion factors.factors.

Example 1Example 1: : At the store, the price of At the store, the price of one one poundpound of red peppers is of red peppers is $2.39.$2.39.1 lb red peppers1 lb red peppers $2.39$2.39

$2.39$2.39 1 lb red peppers1 lb red peppers

Example 2:Example 2: At the gas station, At the gas station, one gallonone gallon of gas is of gas is $1.34$1.34..1 gallon of gas1 gallon of gas $1.34$1.34

$1.34$1.34 1 gallon of gas1 gallon of gas

Conversion Factors in a Conversion Factors in a ProblemProblem

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To start solving a problem, it is To start solving a problem, it is important to identify the initial and important to identify the initial and final units. A person has a height of final units. A person has a height of 2.0 meters. What is that height in 2.0 meters. What is that height in inches?inches?

The The initial unitinitial unit is the unit of the given is the unit of the given height. The height. The final unit final unit is the unit is the unit needed for the answer.needed for the answer.

Initial unit = meters (m)Initial unit = meters (m)

Final unit = inches (in.)Final unit = inches (in.)

Initial and Final UnitsInitial and Final Units

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In working a problem, start with the In working a problem, start with the initial unit.initial unit.

Write a unit plan that converts the Write a unit plan that converts the initial unit to the final unit.initial unit to the final unit.

Unit 1 Unit 2Unit 1 Unit 2 Select conversion factors that cancel Select conversion factors that cancel

the initial unit and give the final unit.the initial unit and give the final unit.Initial Initial x x ConversionConversion = = FinalFinal

unit unit factor factor unitunitUnit 1 x Unit 1 x Unit 2Unit 2 == Unit 2Unit 2

Unit 1Unit 1

Problem SetupProblem Setup

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Setting up a ProblemSetting up a Problem

How many minutes are 2.5 hours?How many minutes are 2.5 hours?Solution: Solution: Initial unitInitial unit = = 2.5 hr2.5 hrFinal unitFinal unit == ? min? minUnit PlanUnit Plan == hrhr min min

Setup problem to cancel hours (hr). Setup problem to cancel hours (hr). InitalInital ConversionConversion Final Final

unitunit factor factor unit unit

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min (2 SF (2 SF)) 1 hr1 hr

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Often, two or more conversion factors Often, two or more conversion factors are required to obtain the unit of the are required to obtain the unit of the answer.answer.

Unit 1 Unit 1 Unit 2Unit 2 Unit 3Unit 3 Additional conversion factors are Additional conversion factors are

placed in the setup to cancel the placed in the setup to cancel the preceding unitpreceding unit

Initial unit Initial unit x x factor 1 factor 1 xx factor 2 = factor 2 = Final unitFinal unitUnit 1 x Unit 1 x Unit 2Unit 2 x x Unit 3Unit 3 = = Unit 3Unit 3

Unit 1Unit 1 Unit 2 Unit 2

Using Two or More FactorsUsing Two or More Factors

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How many minutes are in 1.4 days?How many minutes are in 1.4 days?

Initial unit:Initial unit: 1.4 days 1.4 days

Unit planUnit plan: days hr min: days hr minSet up problem:Set up problem:

1.4 days 1.4 days x x 24 hr24 hr x x 60 min60 min = 2.0 = 2.0 x 10x 103 3 minmin

1 day 1 hr1 day 1 hr

2 SF Exact2 SF Exact Exact = 2 SF Exact = 2 SF

Example: Problem SolvingExample: Problem Solving

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Be sure to check your unit cancellation in the Be sure to check your unit cancellation in the setup.setup.

What is wrong with the following setup?What is wrong with the following setup?1.4 day x 1.4 day x 1 day 1 day x x 1 hr 1 hr

24 hr 60 min 24 hr 60 min

Units = Units = dayday22/min/min is is Not the final unit neededNot the final unit needed

Units don’t cancel properly.Units don’t cancel properly.

The units in the conversion factors must The units in the conversion factors must cancel to give the correct unit for the answer.cancel to give the correct unit for the answer.

Check the Unit CancellationCheck the Unit Cancellation

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Identify the initial and final units. Identify the initial and final units. Write out a unit plan. Write out a unit plan. Select appropriate conversion factors.Select appropriate conversion factors. Convert the initial unit to the final unit.Convert the initial unit to the final unit. Cancel the units and check the final Cancel the units and check the final

unit.unit. Do the math on a calculator. Do the math on a calculator. Give an answer using significant figures.Give an answer using significant figures.

Typical Steps in Problem Typical Steps in Problem SolvingSolving

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Clinical FactorsClinical Factors

Conversion factors are also possible Conversion factors are also possible when working with medications. when working with medications.

A drug dosage such as 20 mg A drug dosage such as 20 mg Prednisone per tablet can be Prednisone per tablet can be written aswritten as

20 mg Prednisone20 mg Prednisone and and 1 1 tablet tablet 1 tablet 1 tablet

20 mg Prednisone20 mg Prednisone

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A percent refers to a ratio of the parts to A percent refers to a ratio of the parts to the whole.the whole.

%% = = Parts Parts x 100 x 100 WholeWhole

A percent factor is written by choosing a A percent factor is written by choosing a unit to express the percent. unit to express the percent.

Write 100 of the same unit in the Write 100 of the same unit in the denominator.denominator.

The second factor is the inverse of the The second factor is the inverse of the first. For example, a food contains 30% first. For example, a food contains 30% (by mass) fat. (by mass) fat.

30 g fat30 g fat and and 100 g of food100 g of food100 g of food100 g of food 30 g fat 30 g fat

Percent as a Conversion Percent as a Conversion FactorFactor

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1.81.8 Density Density

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Density compares the mass of an Density compares the mass of an object to its volume.object to its volume.

In the density expression, the mass of In the density expression, the mass of an object or substance is written in an object or substance is written in the numerator and its volume in the the numerator and its volume in the denominator.denominator.D = D = mass mass = = g g or or g g = = g/cmg/cm33

volume mL cmvolume mL cm33

Note: 1 mL = 1 cmNote: 1 mL = 1 cm33

DensityDensity

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Volume by DisplacementVolume by Displacement

A solid displaces its volume of water A solid displaces its volume of water when the solid is placed in water.when the solid is placed in water.

Therefore the volume of the solid is Therefore the volume of the solid is calculated from the volume calculated from the volume difference.difference.

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Density Using Volume Density Using Volume DisplacementDisplacement

The volume of zinc is calculated from The volume of zinc is calculated from the displaced volumethe displaced volume

45.0 mL - 35.5 mL = 9.5 mL = 45.0 mL - 35.5 mL = 9.5 mL = 9.5 cm9.5 cm33

Density zinc = Density zinc = massmass = = 68.60 g68.60 g = 7.2 g/cm= 7.2 g/cm33 volume volume 9.5 cm9.5 cm33

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Sink or FloatSink or FloatIce floats in water because the Ice floats in water because the density of ice is less than the density of ice is less than the density of water. Aluminum sinks density of water. Aluminum sinks because it has a density greater because it has a density greater that the density of water.that the density of water.

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Density represents an equality for a Density represents an equality for a substance. The mass in grams is for 1 substance. The mass in grams is for 1 mL. For a substance with a density of mL. For a substance with a density of 3.8 g/mL, the equality is: 3.8 g/mL, the equality is: 3.8 g = 1 mL3.8 g = 1 mL

For this equality, we can write two For this equality, we can write two conversion factors. conversion factors.

Conversion Conversion 3.8 g 3.8 g and and 1 mL 1 mL factorsfactors 1 mL 3.8 g1 mL 3.8 g

Density as a Conversion Density as a Conversion FactorFactor

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Specific GravitySpecific Gravity

Specific gravity compares the density of a Specific gravity compares the density of a substance to the density of water (1.00 substance to the density of water (1.00 g/mL).g/mL).Specific gravity = Specific gravity = density of substancedensity of substance

density of waterdensity of water For example, the density of mercury is For example, the density of mercury is

13.6 g/mL.13.6 g/mL.Specific gravity = Specific gravity = 13.6 g/mL13.6 g/mL = = 13.613.6

1.00 g/mL1.00 g/mL The units cancel. Thus specific gravity has The units cancel. Thus specific gravity has

no units.no units.

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1.91.9 TemperatureTemperature

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Temperature is a measure of how Temperature is a measure of how hot or coldhot or cold an object is. an object is.

Temperature is determined by Temperature is determined by using a thermometer.using a thermometer.

Some thermometers contain a Some thermometers contain a liquid that expands with heat and liquid that expands with heat and contracts with cooling. Other contracts with cooling. Other types of thermometers are types of thermometers are electronic.electronic.

TemperatureTemperature

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Temperature ScalesTemperature Scales

Temperature is Temperature is measured using measured using the Fahrenheit, the Fahrenheit, Celsius, and Kelvin Celsius, and Kelvin temperature temperature scales.scales.

The reference The reference points are the points are the boiling and boiling and freezing points of freezing points of water.water.

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On the Fahrenheit scale, there are are 180On the Fahrenheit scale, there are are 180°F °F between the freezing and boiling pointsbetween the freezing and boiling points and and on the Celsius scale, there are on the Celsius scale, there are 100 100 °C. °C.

180°F180°F = = 9°F 9°F == 1.8°F 1.8°F 100°C 100°C 5°C 5°C 1°C1°C

In the In the formula for Fahrenheit, tformula for Fahrenheit, the value of he value of 32 adjusts the zero point of water from 032 adjusts the zero point of water from 0°C °C to to 3232°F.°F.

°F = 9/5 T°C + 32 °F = 9/5 T°C + 32 oror °F = 1.8 T°C + 32°F = 1.8 T°C + 32

Fahrenheit FormulaFahrenheit Formula

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The equation for Fahrenheit is The equation for Fahrenheit is rearranged to calculate T°C.rearranged to calculate T°C.

°F °F = = 1.8 T°C + 321.8 T°C + 32 Subtract 32 from both sides and Subtract 32 from both sides and

divide by 1.8.divide by 1.8.

°F - 32 = °F - 32 = 1.8 T°C ( +32 - 32)1.8 T°C ( +32 - 32)°F - 32°F - 32 = = 1.8 T°C1.8 T°C

1.8 1.8 1.8 1.8°F - 32 °F - 32 = = T°C T°C

1.81.8

Celsius FormulaCelsius Formula

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A person with hypothermia A person with hypothermia has a body temperature of has a body temperature of 34.8°C. What is that 34.8°C. What is that temperature in °F? temperature in °F? °F °F = 1.8 (= 1.8 (34.8°C34.8°C) + 32) + 32 exact tenth's exact tenth's exactexact

= = 62.6 + 3262.6 + 32= = 94.6°F 94.6°F

tenth’stenth’s

Solving A Temperature Solving A Temperature ProblemProblem

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On the Kelvin Scale, the lowest possible On the Kelvin Scale, the lowest possible temperature is 0 K called temperature is 0 K called absolute zero.absolute zero.0 K 0 K == –273–273 °C °C

On both K and °C scales, there are 100 On both K and °C scales, there are 100 units between freezing and boiling. units between freezing and boiling. 100 K 100 K = 100°C= 100°C or or 1 K = 1 °C1 K = 1 °C

The Kelvin temperature is obtained by The Kelvin temperature is obtained by adding 273 to the Celsius temperature.adding 273 to the Celsius temperature.K = °C + 273K = °C + 273

Kelvin Temperature ScaleKelvin Temperature Scale

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Some Temperature Some Temperature ComparisonsComparisons