1 Introductory Chemistry, 2 nd Edition Nivaldo Tro Chapter 2 Measurement and Problem Solving Part 1:...

Tro's Introductory Chemistry, Chapter 2Tro's Introductory Chemistry, Chapter 2 11

Introductory ChemistryIntroductory Chemistry, 2, 2ndnd Edition EditionNivaldo TroNivaldo Tro

Chapter 2Measurement

andProblem Solving

Part 1: Measurements


What is a Measurement?What is a Measurement?

quantitative observation quantitative observation of a property of a property

comparison to an comparison to an agreed upon standardagreed upon standard

every measurement has every measurement has a a numbernumber and a and a unitunit


Parts of a MeasurementParts of a Measurement

The The unitunit tells you what property of and tells you what property of and standard you are comparing your object standard you are comparing your object to to

The The numbernumber tells you tells you1.1. what multiple of the standard the object what multiple of the standard the object

measuresmeasures

2.2. the uncertainty in the measurementthe uncertainty in the measurement

A number without a unit is meaningless A number without a unit is meaningless because it doesn’t tell what property is because it doesn’t tell what property is being measured.being measured.


Scientists measured the average global Scientists measured the average global temperature rise over the past century to temperature rise over the past century to be be 0.6°C0.6°C

°C °C tells you that the temperature is tells you that the temperature is being compared to the Celsius being compared to the Celsius temperature scaletemperature scale

0.6°C0.6°C tells you that tells you that1.1. the average temperature rise is the average temperature rise is 0.60.6 times times

the standard unitthe standard unit

2.2. the uncertainty in the measurement is the uncertainty in the measurement is such that we know the measurement is such that we know the measurement is between between 0.5 and 0.7°C0.5 and 0.7°C


Scientific NotationScientific Notation

A way of writing very large and A way of writing very large and very small numbersvery small numbers

Writing large numbers of zeros Writing large numbers of zeros is confusingis confusing

– not to mention the 8 digit limit of not to mention the 8 digit limit of your calculator!your calculator!

Very easy to drop or add zeros Very easy to drop or add zeros while writingwhile writing

The sun’sdiameter is

1,392,000,000 m

an atom’s average diameter

is0.000 000 000 3 m


Scientific NotationScientific NotationEach decimal place in our Each decimal place in our number system represents a number system represents a different power of 10different power of 10

Scientific notation writes Scientific notation writes numbers so they are easily numbers so they are easily comparable by looking at comparable by looking at powers of 10powers of 10

Has two parts:Has two parts:

1. 1. coefficientcoefficient = number with values = number with values from 1 to 10.from 1 to 10.

2. 2. exponentexponent = power of 10 = power of 10

the sun’sdiameter is

1.392 x 109 m

an atom’s average diameter is

3 x 10-10 m


ExponentsExponents = Powers of 10 = Powers of 10

When exponent on 10 is When exponent on 10 is positivepositive, it means the number , it means the number is that many powers of 10 is that many powers of 10 largerlarger – sun’s diameter = 1.392 x 10sun’s diameter = 1.392 x 1099 m = m =

1,392,000,000 m1,392,000,000 m

when exponent on 10 is when exponent on 10 is negativenegative, it means the number , it means the number is that many powers of 10 is that many powers of 10 smallersmaller– avg. atom’s diameter = 3 x 10avg. atom’s diameter = 3 x 10-10-10 m m

= 0.0000000003 m= 0.0000000003 m

the sun’s

diameter is

1.392 x 109

m

an atom’s average diameter is

3 x 10-10 m


Scientific NotationScientific Notation

To compare numbers written in To compare numbers written in scientific notationscientific notation– First compare exponents on 10First compare exponents on 10– If exponents equal, then compare decimal If exponents equal, then compare decimal

numbers (coefficient)numbers (coefficient)

1.23 x 10-8

decimal part(coefficient)

exponent part

exponent1.23 x 101.23 x 1055 > 4.56 x 10 > 4.56 x 1022

4.56 x 104.56 x 10-2-2 > 7.89 x 10 > 7.89 x 10-5-5

7.89 x 1010 > 1.23 x 1010


Writing Numbers in Scientific NotationWriting Numbers in Scientific Notation

1.1. Locate the decimal pointLocate the decimal point2.2. Move the decimal point to the Move the decimal point to the rightright of of

the the first non-zero digit from the leftfirst non-zero digit from the left3.3. Multiply the new number by 10Multiply the new number by 10nn

where where nn is the number of places you is the number of places you moved the decimal pointmoved the decimal point

4.4. if the number is if the number is 1, 1, nn is +; if the is +; if the number is < 1, number is < 1, nn is - is -


12340123401 Locate the Decimal PointLocate the Decimal Point

1234012340..2 Move the decimal point to the Move the decimal point to the rightright of the of the first non-first non-

zero digit from the leftzero digit from the left

11..2342343 Multiply the new number by Multiply the new number by 1010nn

– where where nn is the number of places you moved the is the number of places you moved the decimal pt.decimal pt.

11..234 x 10234 x 1044

4 If the number is If the number is 1, 1, nn is is ++; if the number is < 1, ; if the number is < 1, nn is - is -

11..234 x 10234 x 1044

Writing a Number In Scientific NotationWriting a Number In Scientific Notation


Writing a Number In Scientific NotationWriting a Number In Scientific Notation

0.000123400.000123401 Locate the Decimal PointLocate the Decimal Point

00..00012340000123402 Move the decimal point to the Move the decimal point to the right of the first non-right of the first non-

zero digit from the leftzero digit from the left

11..234023403 Multiply the new number by Multiply the new number by 1010nn

– where where nn is the number of places you moved the is the number of places you moved the decimal pt.decimal pt.

11..2340 x 102340 x 1044

4 if the number is if the number is 1, 1, nn is +; if the number is is +; if the number is < 1,< 1, nn isis --

11..2340 x 102340 x 10- 4- 4


Writing a Number in Standard Writing a Number in Standard FormForm

11..234 x 10234 x 10-6-6

• since exponent is -6, make the since exponent is -6, make the number smaller by moving the number smaller by moving the decimal point to the left 6 placesdecimal point to the left 6 places– if you run out of digits, add zerosif you run out of digits, add zeros

000 001000 001..234234

0.000 001 234


Scientific Notation: Example 2.1Scientific Notation: Example 2.1

The U.S. population in 2004 was The U.S. population in 2004 was estimated to be 293,168,000 people. estimated to be 293,168,000 people. Express this number in scientific Express this number in scientific notation.notation.

293,168,000 people = 2.93168 x 10293,168,000 people = 2.93168 x 1088 peoplepeople


Entering Scientific Notation into a CalculatorEntering Scientific Notation into a Calculator

Enter decimal part of Enter decimal part of the numberthe number– if negative press +/- if negative press +/-

keykey((––) on some) on some

Press EXPPress EXP– EE on someEE on some

Enter exponent on 10Enter exponent on 10– press +/- key to press +/- key to

change exponent to change exponent to negativenegative

-1.23 x 10-1.23 x 10-3-3

Enter 1.23Enter 1.23 1.231.23

PressPress EXP -1.23 00-1.23 00

-1.23 -03

Press +/-

Enter 3 -1.23 03-1.23 03

-1.23 PressPress +/-


Entering Scientific Notation into a Entering Scientific Notation into a TI-83 CalculatorTI-83 Calculator

use ( ) liberally!!use ( ) liberally!!

type in decimal part of type in decimal part of the numberthe number– if negative, first press the if negative, first press the

(-) (-)

Enter exponentEnter exponent

Enter exponent numberEnter exponent number– if negative, first press the if negative, first press the

(-) (-)

-1.23 x 10-1.23 x 10-3-3

––PressPress (-)

Enter 1.23Enter 1.23 ––1.231.23

Press (-)(-) -1.23E-

Enter 3Enter 3 -1.23E-3-1.23E-3

Press 2Press 2ndnd, , then EEthen EE -1.23E-1.23E


Exact Numbers vs. MeasurementsExact Numbers vs. Measurements

Exact numbers:Exact numbers: sometimes you sometimes you can determine an exact value can determine an exact value for a quality of an objectfor a quality of an object– often by often by countingcounting

pennies in a pilepennies in a pile

– sometimes by sometimes by definitiondefinition1 in (inch) is exactly = 2.54 cm1 in (inch) is exactly = 2.54 cm

Measured numbersMeasured numbers are inexact are inexact = obtained using a measuring = obtained using a measuring tool, i.e. height, weight, length, tool, i.e. height, weight, length, temperature, volume, etc.temperature, volume, etc.


Uncertainty in MeasurementUncertainty in Measurement

Measurements are subject to error.Measurements are subject to error.Errors reflected in number of Errors reflected in number of significant figures reported.significant figures reported.Significant figuresSignificant figures = all numbers = all numbers measured precisely plus one estimated measured precisely plus one estimated digit.digit.Errors also reflected in observation Errors also reflected in observation that two successive measurements of that two successive measurements of same quantity are different.same quantity are different.


Uncertainty in MeasurementUncertainty in Measurement

Precision and AccuracyPrecision and Accuracy

AccuracyAccuracy = how close measurements = how close measurements are to “correct or true” value.are to “correct or true” value.

PrecisionPrecision = how close several = how close several measurements of same quantity are measurements of same quantity are to each other.to each other.

Prentice HallPrentice Hall 1919

Precision and AccuracyPrecision and Accuracy

Measurements can Measurements can bebea) accurate and a) accurate and

precise precise

b) precise but b) precise but inaccurate inaccurate

c) neither accurate c) neither accurate nor precise.nor precise.

aa bb cc


Reporting MeasurementsReporting Measurements

Measurements are written to indicate Measurements are written to indicate uncertainty in the measurementuncertainty in the measurement

The system of writing measurements we The system of writing measurements we use is called use is called significant figuressignificant figures

When writing measurements, all the digits When writing measurements, all the digits written are known with certainty except the written are known with certainty except the last one, which is an estimatelast one, which is an estimate

45.872

certaincertainestimatedestimated

45.8745.8722


Estimating the Last DigitEstimating the Last Digit

For instruments marked For instruments marked with a scale, you get with a scale, you get the last digit by the last digit by estimating between the estimating between the marksmarks

– if possibleif possible

Mentally divide the Mentally divide the space into 10 equal space into 10 equal spaces, then estimate spaces, then estimate how many spaces over how many spaces over the indicator isthe indicator is

1.2 grams


Skillbuilder 2.3 – Reporting the Right Skillbuilder 2.3 – Reporting the Right Number of DigitsNumber of Digits

A thermometer used to A thermometer used to measure the temperature measure the temperature of a backyard hot tub is of a backyard hot tub is shown to the right. What shown to the right. What is the temperature reading is the temperature reading to the correct number of to the correct number of digits?digits?

103.4103.4°F°F


Significant FiguresSignificant Figures

Significant figures tell us Significant figures tell us the range of values to the range of values to expect for repeated expect for repeated measurementsmeasurements

The more significant The more significant figures there are in a figures there are in a measurement, the smaller measurement, the smaller the range of values is; the the range of values is; the more precise.more precise.

12.3 cm12.3 cmhas has 33 sig. figs. sig. figs. and its range isand its range is12.2 to 12.4 cm12.2 to 12.4 cm

12.30 cm12.30 cmhas has 44 sig. figs. sig. figs. and its range isand its range is

12.29 to 12.31 cm12.29 to 12.31 cm


Counting Significant FiguresCounting Significant Figures

All non-zero digits are significantAll non-zero digits are significant– 1.5 has 2 sig. figs.1.5 has 2 sig. figs.

Interior zeros are significantInterior zeros are significant– 1.05 has 3 sig. figs.1.05 has 3 sig. figs.

Trailing zerosTrailing zeros after a decimal point are after a decimal point are significantsignificant– 1.051.0500 has 4 sig. figs. has 4 sig. figs.


Counting Significant FiguresCounting Significant Figures

4.4. Leading zerosLeading zeros are are NOTNOT significant significant– 00..000010501050 has has 44 sig. figs. sig. figs.

1.050 x 101.050 x 10-3-3

5.5. Zeros at the end of a number without a Zeros at the end of a number without a written decimal point are ambiguous and written decimal point are ambiguous and should be avoided by using scientific should be avoided by using scientific notationnotation

– if 150 has 2 sig. figs. then 1.5 x 10if 150 has 2 sig. figs. then 1.5 x 1022

– but if 150 has 3 sig. figs. then 1.50 x 10but if 150 has 3 sig. figs. then 1.50 x 1022


Significant Figures and Exact NumbersSignificant Figures and Exact Numbers

Exact Numbers have an unlimited Exact Numbers have an unlimited number of significant figures number of significant figures A number whose value is known with A number whose value is known with complete certainty is complete certainty is exactexact– from counting individual objectsfrom counting individual objects– from definitionsfrom definitions

1 cm is exactly equal to 0.01 m1 cm is exactly equal to 0.01 m

– from integer values in equationsfrom integer values in equations in the equation for the radius of a circle, the 2 is in the equation for the radius of a circle, the 2 is exactexact

radius of a circle = diameter of a circle2


Example 2.4 – Determining the Number Example 2.4 – Determining the Number of Significant Figures in a Numberof Significant Figures in a Number

How many significant figures are in each How many significant figures are in each of the following numbers?of the following numbers?

0.00350.0035

1.0801.080

23712371

2.97 2.97 ×× 10 1055

1 dozen = 121 dozen = 12

100,000 100,000


Example 2.4 – Determining the Number Example 2.4 – Determining the Number of Significant Figures in a Numberof Significant Figures in a Number

How many significant figures are in each of the How many significant figures are in each of the following numbers?following numbers?

0.00350.0035 2 sig. figs. – leading zeros not sig.2 sig. figs. – leading zeros not sig.

1.0801.080 4 sig. figs. – trailing & interior zeros 4 sig. figs. – trailing & interior zeros sig.sig.

23712371 4 sig. figs. – all digits sig.4 sig. figs. – all digits sig.

2.97 2.97 ×× 10 1055 3 sig. figs. – only decimal parts 3 sig. figs. – only decimal parts count count sig.sig.

1 dozen = 121 dozen = 12 unlimited sig. figs. – definitionunlimited sig. figs. – definition

100,000 100,000 ambiguousambiguous


Multiplication and Division with Multiplication and Division with Significant FiguresSignificant Figures

When multiplying or dividing measurements When multiplying or dividing measurements with significant figures, the with significant figures, the result has the result has the same number of significant figures as the same number of significant figures as the measurement with the fewest number of measurement with the fewest number of significant figuressignificant figures; round final answer:; round final answer:

5.02 5.02 ×× 89,665 89,665 ×× 0.100.10 == 45.0118 45.0118 = = 4545 3 sig. figs.3 sig. figs. 5 sig. figs. 5 sig. figs. 2 sig. figs. 2 sig. figs.

2 sig. figs.2 sig. figs.

5.892 5.892 ÷÷ 6.106.10 = = 0.965900.96590 = = 0.9660.966 4 sig. figs. 3 sig. figs. 4 sig. figs. 3 sig. figs. 3 sig. figs. 3 sig. figs.


Rules for RoundingRules for RoundingWhen rounding to the correct number of When rounding to the correct number of significant figures, if the number after the significant figures, if the number after the place of the last significant figure is place of the last significant figure is

1.1. 0 to 4, round down0 to 4, round down– drop all digits after the last sig. fig. and leave drop all digits after the last sig. fig. and leave

the last sig. fig. alonethe last sig. fig. alone– add insignificant zeros to keep the value if add insignificant zeros to keep the value if

necessarynecessary

2.2. 5 to 9, round up5 to 9, round up– drop all digits after the last sig. fig. and drop all digits after the last sig. fig. and

increase the last sig. fig. by oneincrease the last sig. fig. by one– add insignificant zeros to keep the value if add insignificant zeros to keep the value if

necessarynecessary


RoundingRounding

Rounding to Rounding to 22 significant figures significant figures

2.34 rounds to 2.34 rounds to 2.32.3– because the 3 is where the last sig. fig. will be because the 3 is where the last sig. fig. will be

and the number after it is 4 or lessand the number after it is 4 or less


and the number after it is 5 or greaterand the number after it is 5 or greater


and the number after it is 4 or lessand the number after it is 4 or less


Rounding & Writing in Scientific Rounding & Writing in Scientific NotationNotation

Rounding to Rounding to 22 significant figures significant figures0.0234 rounds to 0.0234 rounds to 0.023 or 2.3 0.023 or 2.3 ×× 10 10-2-2

– because the 3 is where the last sig. fig. will because the 3 is where the last sig. fig. will be and the number after it is 4 or lessbe and the number after it is 4 or less

0.0237 rounds to 0.0237 rounds to 0.024 or 2.4 0.024 or 2.4 ×× 10 10-2-2

– because the 3 is where the last sig. fig. will because the 3 is where the last sig. fig. will be and the number after it is 5 or greaterbe and the number after it is 5 or greater

0.02349865 rounds to 0.02349865 rounds to 0.023 or 2.3 0.023 or 2.3 ×× 10 10-2-2

– because the 3 is where the last sig. fig. will because the 3 is where the last sig. fig. will be and the number after it is 4 or lessbe and the number after it is 4 or less


RoundingRoundingrounding to 2 significant figuresrounding to 2 significant figures

234 rounds to 230 or 2.3 234 rounds to 230 or 2.3 ×× 10 1022

– because the 3 is where the last sig. fig. will be because the 3 is where the last sig. fig. will be and the number after it is 4 or lessand the number after it is 4 or less

237 rounds to 240 or 2.4 237 rounds to 240 or 2.4 ×× 10 1022

– because the 3 is where the last sig. fig. will be because the 3 is where the last sig. fig. will be and the number after it is 5 or greaterand the number after it is 5 or greater

234.9865 rounds to 230 or 2.3 234.9865 rounds to 230 or 2.3 ×× 10 1022

– because the 3 is where the last sig. fig. will be because the 3 is where the last sig. fig. will be and the number after it is 4 or lessand the number after it is 4 or less


Determine the Correct Number of Determine the Correct Number of Significant Figures for each Calculation and Significant Figures for each Calculation and

Round and Report the ResultRound and Report the Result

1.1. 1.01 1.01 ×× 0.12 0.12 ×× 53.51 53.51 ÷ 96 = 0.067556÷ 96 = 0.067556

2.2. 56.55 × 0.920 ÷ 34.2585 = 1.5186356.55 × 0.920 ÷ 34.2585 = 1.51863




1.1. 1.01 1.01 ×× 0.12 0.12 ×× 53.51 53.51 ÷ 96 = 0.06÷ 96 = 0.0677556 = 556 = 0.0680.068

2.2. 56.55 × 0.920 ÷ 34.2585 = 1.556.55 × 0.920 ÷ 34.2585 = 1.511863 = 863 = 1.521.52

3 sf3 sf 2 sf2 sf 4 sf4 sf 2 sf2 sf result should result should have 2 sfhave 2 sf

7 is in place 7 is in place of last sig. fig., of last sig. fig., number after number after

is 5 or greater, is 5 or greater, so round upso round up

4 sf4 sf 3 sf3 sf 6 sf6 sf result should result should have 3 sfhave 3 sf


is 5 or greater, is 5 or greater, so round upso round up


Addition and Subtraction with Addition and Subtraction with Significant FiguresSignificant Figures

When adding or subtracting measurements When adding or subtracting measurements with significant figures, the result has the with significant figures, the result has the same number ofsame number of decimal placesdecimal places as the as the measurement with the measurement with the fewest number of fewest number of decimal placesdecimal places

5.74 + 0.823 +5.74 + 0.823 + 2.6512.651= = 9.2149.214 = 9.21= 9.21 2 dec. pl.2 dec. pl. 3 dec. pl. 3 dec. pl. 3 dec. pl. 3 dec. pl. 2 dec. pl.2 dec. pl.

4.8 4.8 -- 3.965 3.965 = = 0.8350.835 = = 0.80.8 1 dec. pl 3 dec. pl. 1 dec. pl 3 dec. pl. 1 dec. pl. 1 dec. pl.




1.1. 0.987 + 125.1 – 1.220.987 + 125.1 – 1.22 = 124.867 = 124.867

2.2. 0.764 – 3.449 – 5.98 = -8.6640.764 – 3.449 – 5.98 = -8.664




1.1. 0.987 + 125.1 – 1.220.987 + 125.1 – 1.22 = 124. = 124.8867 = 67 = 124.9124.9

2.2. 0.764 – 3.449 – 5.98 = -8.60.764 – 3.449 – 5.98 = -8.6664 = 4 = -8.66-8.66

3 dp3 dp 1 dp1 dp 2 dp2 dp result should result should have 1 dphave 1 dp

8 is in place of last 8 is in place of last sig. fig., number sig. fig., number after is 5 or greater, after is 5 or greater, so round upso round up

3 dp3 dp 3 dp3 dp 2 dp2 dp result should result should have 2 dphave 2 dp


is 4 or less, is 4 or less, so round downso round down


Both Multiplication/Division and Both Multiplication/Division and Addition/Subtraction with Significant Addition/Subtraction with Significant

FiguresFigures

When doing different kinds of operations When doing different kinds of operations with measurements with significant figures, with measurements with significant figures, do whatever is in parentheses first, find the do whatever is in parentheses first, find the number of significant figures in the number of significant figures in the intermediate answer, then do the remaining intermediate answer, then do the remaining stepssteps

3.489 3.489 ×× (5.67 – 2.3) = (5.67 – 2.3) = 2 dp 1 dp2 dp 1 dp

3.489 3.489 × 3.4 =× 3.4 = 12 12 4 sf 1 dp & 2 sf4 sf 1 dp & 2 sf 2 sf 2 sf


Basic Units of MeasureBasic Units of Measure

The Standard Units: Scientists agreed on a The Standard Units: Scientists agreed on a set of international standard units called the set of international standard units called the SI unitsSI units– SystSystèème International = me International = International SystemInternational System

QuantityQuantity UnitUnit SymbolSymbol

lengthlength metermeter mm

massmass kilogramkilogram kgkg

timetime secondsecond ss

temperaturetemperature KelvinKelvin KK


Some Standard Units in the Some Standard Units in the Metric SystemMetric System

Quantity Quantity MeasuredMeasured

Name of Name of UnitUnit AbbreviationAbbreviation

MassMass gramgram gg

LengthLength metermeter mm

VolumeVolume literliter LL

TimeTime secondsseconds ss

TemperatureTemperature KelvinKelvin KK


LengthLength

Measure of a single linear Measure of a single linear dimension of an object, dimension of an object, usually the longest usually the longest dimension dimension SI unit = meterSI unit = meter– About 3About 3½ inches longer ½ inches longer

than a yardthan a yardCommonly use centimeters Commonly use centimeters (cm)(cm)– 1 m = 100 cm1 m = 100 cm– 1 cm = 0.01 m = 10 mm1 cm = 0.01 m = 10 mm– 1 inch = 2.54 cm (exactly)1 inch = 2.54 cm (exactly)


MassMass

Measure of the amount of matter Measure of the amount of matter present in an objectpresent in an objectSI unit = kilogram (kg)SI unit = kilogram (kg)– about 2 lbs. 3 oz.about 2 lbs. 3 oz.

Commonly measure mass in Commonly measure mass in grams (g) or milligrams (mg)grams (g) or milligrams (mg)– 1 kg = 2.2046 pounds, 1 lb. = 453.59 g1 kg = 2.2046 pounds, 1 lb. = 453.59 g– 1 kg = 1000 g = 101 kg = 1000 g = 1033 g, g, – 1 g = 1000 mg = 101 g = 1000 mg = 1033 mg mg– 1 g = 0.001 kg = 101 g = 0.001 kg = 10-3-3 kg, kg, – 1 mg = 0.001 g = 101 mg = 0.001 g = 10-3 -3 gg


Related Units (Prefixes) in the Related Units (Prefixes) in the SI SystemSI System

All units in the SI system are related to All units in the SI system are related to the standard unit by a power of 10the standard unit by a power of 10The power of 10 is indicated by a The power of 10 is indicated by a prefixprefixPrefixesPrefixes are used for convenience in are used for convenience in expressing very large or very small expressing very large or very small numbersnumbersThe prefixes are always the same, The prefixes are always the same, regardless of the standard unitregardless of the standard unit


Common Prefixes in the Common Prefixes in the SI SystemSI System

PrefixPrefix SymbolSymbolDecimalDecimal

EquivalentEquivalentPower of 10Power of 10

mega-mega- MM 1,000,0001,000,000 Base x 10Base x 1066

kilo-kilo- kk 1,0001,000 Base x 10Base x 1033

deci-deci- dd 0.10.1 Base x 10Base x 10-1-1

centi-centi- cc 0.010.01 Base x 10Base x 10-2-2

milli-milli- mm 0.0010.001 Base x 10Base x 10-3-3

micro-micro- or mcor mc 0.000 0010.000 001 Base x 10Base x 10-6-6

nano-nano- nn 0.000 000 0010.000 000 001 Base x 10Base x 10-9-9


Prefixes Used to Modify Standard UnitPrefixes Used to Modify Standard Unitkilo = kilo = 1000 times base unit = 101000 times base unit = 1033

– 1 kg = 1000 g = 101 kg = 1000 g = 1033 g g

deci = deci = 0.1 times the base unit = 100.1 times the base unit = 10-1-1

– 1 dL = 0.1 L = 101 dL = 0.1 L = 10-1-1 L; 1 L = 10 dL L; 1 L = 10 dL

centi = centi = 0.01 times the base unit = 100.01 times the base unit = 10-2-2

– 1 cm = 0.01 m = 101 cm = 0.01 m = 10-2-2 m; 1 m = 100 cm m; 1 m = 100 cm

milli = milli = 0.001 times the base unit = 100.001 times the base unit = 10-3-3

– 1 mg = 0.001 g = 101 mg = 0.001 g = 10-3 -3 g; 1 g = 1000 mgg; 1 g = 1000 mg

micro = micro = 1010-6-6 times the base unittimes the base unit– 1 1 m = 10m = 10-6-6 m; 10 m; 1066 m = 1 mm = 1 m

nano = nano = 1010-9-9 times the base unit times the base unit– 1 nL = 101 nL = 10-9-9L; 10L; 1099 nL = 1 L nL = 1 L


VolumeVolumeMeasure of the amount of three-dimensional space Measure of the amount of three-dimensional space occupiedoccupied

SI unit = cubic meter (mSI unit = cubic meter (m33))– a Derived Unita Derived Unit

Solid volume usually measured in cubic Solid volume usually measured in cubic

centimeters (cmcentimeters (cm33))– 1 m1 m33 = 10 = 1066 cm cm33 – 1 cm1 cm33 = 10 = 10-6-6 m m3 3 = 0.000001 m = 0.000001 m33

Liquid or gas volume, in milliliters (mL)Liquid or gas volume, in milliliters (mL)– 1 L = 1 dL1 L = 1 dL33 = 1000 mL = 10 = 1000 mL = 1033 mL mL – 1 mL = 0.001 L = 101 mL = 0.001 L = 10-3-3 L L– 1 mL = 1 cm1 mL = 1 cm33


Common Units and Their Common Units and Their EquivalentsEquivalents

LengthLength1 kilometer (km)1 kilometer (km) == 0.6214 mile (mi)0.6214 mile (mi)

1 meter (m)1 meter (m) == 39.37 inches (in.)39.37 inches (in.)

1 meter (m)1 meter (m) == 1.094 yards (yd)1.094 yards (yd)

1 foot (ft)1 foot (ft) == 30.48 centimeters (cm)30.48 centimeters (cm)

1 inch (in.)1 inch (in.) == 2.54 centimeters (cm) 2.54 centimeters (cm) exactlyexactly


Common Units and Their EquivalentsCommon Units and Their Equivalents

VolumeVolume

1 liter (L)1 liter (L) == 1000 milliliters (mL)1000 milliliters (mL)

1 liter (L)1 liter (L) == 1000 cubic centimeters 1000 cubic centimeters (cm(cm33))

1 liter (L)1 liter (L) == 1.057 quarts (qt)1.057 quarts (qt)

1 U.S. gallon (gal)1 U.S. gallon (gal) == 3.785 liters (L)3.785 liters (L)

MassMass

1 kilogram (km)1 kilogram (km) == 2.205 pounds (lb)2.205 pounds (lb)

1 pound (lb)1 pound (lb) == 453.59 grams (g)453.59 grams (g)

1 ounce (oz)1 ounce (oz) == 28.35 (g)28.35 (g)


Use Table of Equivalent Units to Determine Use Table of Equivalent Units to Determine Which is LargerWhich is Larger

1 yard or 1 meter?1 yard or 1 meter?1 mile or 1 km?1 mile or 1 km?1 cm or 1 inch?1 cm or 1 inch?1 kg or 1 lb?1 kg or 1 lb?1 mg or 1 1 mg or 1 g?g?1 qt or 1 L?1 qt or 1 L?1 L or 1 gal?1 L or 1 gal?1 gal or 1000 cm1 gal or 1000 cm33??


Use Table of Equivalent Units to Determine Use Table of Equivalent Units to Determine Which is LargerWhich is Larger

1 yard or 1 yard or 1 meter1 meter??1 mile1 mile or 1 km? or 1 km?1 cm or 1 cm or 1 inch1 inch??1 kg1 kg or 1 lb? or 1 lb?1 mg1 mg or 1 or 1 g?g?1 qt or 1 qt or 1 L1 L??1 L or 1 L or 1 gal1 gal??1 gal1 gal or 1000 cm or 1000 cm33??

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1 Introductory Chemistry, 2 nd Edition Nivaldo Tro Chapter 2 Measurement and Problem Solving Part 1:...

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