3.3 solving conversion problems > 1 unit conversion and dimensional analysis notes copyright ©...

3.3 Solving Conversion Problems >3.3 Solving Conversion Problems >

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Unit Conversion and Unit Conversion and Dimensional Analysis NotesDimensional Analysis Notes

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.


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Quantity Base Unit Symbol

Length metermeter mm

Mass gramgram gg

Volume literliter LL

Temperature Kelvin or CelsiusKelvin or Celsius K or °CK or °C

Time secondsseconds ss

Energy joules or caloriesjoules or calories J or calJ or cal

Density grams per cubic grams per cubic centimetercentimeter

g/cmg/cm33

Units of MeasurementsUnits of Measurements

K = °C + 273°C = K – 273

TemperatureTemperature

massvolume

Density =

DensityDensity


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Volume can be measured by the length, width and height of an object:

Volume (cmVolume (cm33) = Length x width x height) = Length x width x height

2 main units for volume: mL and cm2 main units for volume: mL and cm33

conversion factor conversion factor 1 mL = 1 cm 1 mL = 1 cm33

Units of VolumeVolume

• 1 J = 0.2390 cal1 J = 0.2390 cal• 1 cal = 4.184 J1 cal = 4.184 J

Units of EnergyEnergy



The table below lists the prefixes in common use.

Metric PrefixesMetric Prefixes

Commonly Used Metric Prefixes

Prefix Symbol Meaning Factor

mega M 1 million times larger than the unit it precedes 106

kilo k 1000 times larger than the unit it precedes 103

deci d 10 times smaller than the unit it precedes 10-1

centi c 100 times smaller than the unit it precedes 10-2

milli m 1000 times smaller than the unit it precedes 10-3

micro μ 1 million times smaller than the unit it precedes 10-6

nano n 1 billion times smaller than the unit it precedes 10-9

pico p 1 trillion times smaller than the unit it precedes 10-12



CHEMISTRY & YOUCHEMISTRY & YOU

How can you convert U.S. dollars to euros?UNIT CONVERSIONUNIT CONVERSION


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Conversion Factors

• For example:• 1 dollar = 4 quarters = 10 dimes = 20 nickels

= 100 pennies

• For example:• 1 meter = 10 decimeters = 100 centimeters =

1000 millimeters

Conversion FactorsConversion Factors

1 m1 m

= 100 cm1 m

= 1 or 1 m100 cm

= 100 cm100 cm

= 1

A A conversion factorconversion factor is a ratio of equivalent measurements is a ratio of equivalent measurements.

conversion factors



Conversion FactorsConversion Factors

1 meter 100 centimeters

Larger unit

Smaller unit1001 m

cm

Smaller number

Larger number

Conversion factors are useful in solving problems in which a given measurement must be expressed in some other unit of measure.

Conversion factors do not affect the number of Conversion factors do not affect the number of significant figure and rounding of a calculated answer.significant figure and rounding of a calculated answer.



Dimensional AnalysisDimensional Analysis

Dimensional analysisDimensional analysis is a way to analyze is a way to analyze and solve problems using the unitsand solve problems using the units, or dimensions, of the measurements.




Sample Problem 3.9Sample Problem 3.9

Using Dimensional Analysis ExamplesUsing Dimensional Analysis Examples

Follow along with your practice worksheet.

1. How many seconds are in a workday that lasts exactly eight hours? Analyze List the knowns and the unknown.1

UNKNOWNseconds worked = ? sseconds worked = ? s

KNOWNTime worked = 8 hTime worked = 8 h1 hour = 60 min1 hour = 60 min1 min = 60 s1 min = 60 s


10


Calculate Solve for the unknown.2

60 s60 s1 min1 min

60 min60 min

1 h1 h

8 h8 h=

28,800 s28,800 s

11= 2.8800 x 102.8800 x 1044 s s

A. Draw a T table.B. Start with the given measurement in the top left box.C. Determine the first conversion factor. Place the unwanted unit in

the next bottom box (denominator) to cancel the unit. Place the desired unit in the next top box.

D. Determine next conversion factor until units cancel each other out, leaving the desired unit.

E. Multiply the top numbers (numerator) together. Multiply the bottom numbers (denominator) together. Then divide. Write answer in correct # SigFigs & Scientific Notation.



Converting Between Metric Units

(Number 2 on your worksheet)

2. Express 750 dg in grams.

(Refer to your quick references on p.6 of your notebook if you need to refresh your memory of metric prefixes.)




Analyze List the knowns and the unknown.1


UNKNOWNMass = ? gMass = ? g

KNOWNMass = 750 dgMass = 750 dg1 g = 10 dg1 g = 10 dg


750 dg750 dg 750 g750 g

1010

1 g1 g10 dg10 dg

= 75 g75 g=



Using Density as a Conversion Using Density as a Conversion FactorFactor

(Number 3 on your worksheet)

What is the volume of a pure silver coin that has a mass of14 g? The density of silver (Ag) is 10.5 g/cm3.


Density can be used to write two conversion factors. To figure out which one you need, consider the units of your given quantity and the units needed in your answer.





UNKNOWNVolume = ? cmVolume = ? cm33

KNOWNMass = 14 gMass = 14 gDensity of silver = 10.5 g/cmDensity of silver = 10.5 g/cm33

10.5 g = 1 cm10.5 g = 1 cm33


14 g Ag 14 g Ag 14 cm14 cm33 Ag Ag

10.510.51 cm1 cm33 Ag Ag10.5 g Ag10.5 g Ag

= 1.3 cm1.3 cm33 Ag Ag=



• Many complex tasks in your life are best handled by breaking them down into smaller, manageable parts.

• Similarly, many complex word problems are more easily solved by breaking the solution down into steps.

• When converting between units, it is When converting between units, it is often necessary to use more than one often necessary to use more than one conversion factor.conversion factor.


Multistep ProblemsMultistep Problems



Converting Between Metric Units

(Number 4 and 5 on your worksheet)

The diameter of a sewing needle is 0.073 cm. What is the diameter in micrometers?

The density of manganese (Mn), a metal, is 7.21 g/cm3. What is the density of manganese expressed in units of kg/m3?






KNOWNSlength length == 0.073 cm = 7.3 x 10 0.073 cm = 7.3 x 10-2-2 cm cm101022 cm = 1 m cm = 1 m1 m = 101 m = 1066 μμmm

UNKNOWNlength = ? length = ? μμmm

7.3 x 107.3 x 10-2-2 cm cm =7.3 x 107.3 x 1044 μμmm1 m1 m

101022 cm cm101066 μμmm

1 m1 m


= 7.3 x 107.3 x 1022 μμmm

101022





KNOWNSdensity of Mn density of Mn == 7.21 g/cm 7.21 g/cm33

101033 g = 1 kg g = 1 kg101066 cm cm3 3 = 1m= 1m33

UNKNOWNdensity of Mn = ? kg/mdensity of Mn = ? kg/m33


7.21 g7.21 g

1 cm1 cm33

1 kg1 kg

10103 3 gg

101066 cm cm33

1 m1 m33=

= 7.21 x 107.21 x 1033 kg/m kg/m33

7.21 x 107.21 x 1066 kg kg

101033 m m33

3.3 solving conversion problems > 1 unit conversion and dimensional analysis notes copyright ©...

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