Section Section 3.13.1

Chapter 3: Scientific Chapter 3: Scientific MeasurementMeasurement

Scientific NotationScientific Notationor how to deal with large numbers . .or how to deal with large numbers . . . .

Chemistry uses veryChemistry uses very largelarge and veryand very small numberssmall numbers.. Scientific NotationScientific Notation- - coefficient x 10 coefficient x 10 raised to a power- 10> coefficient > 110> coefficient > 1 -

4.32 x 10 2

coefficient exponent

exponent shows how many times exponent shows how many times the coefficient is multiplied by 10.the coefficient is multiplied by 10.

4.6 x 104

= 4.6 x 10 x 10 x 10 x 10 = 46,000

Scientific Notation to Regular Scientific Notation to Regular NotationNotation

If the exponent is positive, move the If the exponent is positive, move the decimal point to the right decimal point to the right

5.3 x 105.3 x 106 6 = = 5,300,0005,300,000

If the exponent is negative, move If the exponent is negative, move the decimal point to the left the decimal point to the left

5.3 x 10 5.3 x 10 - 6 - 6 = = 0.00000530.0000053

Regular Notation to Scientific NotationRegular Notation to Scientific Notation

Use + if you moved the decimal to the left.Use + if you moved the decimal to the left.Use – if you moved the decimal to the rightUse – if you moved the decimal to the right

630,000,000 = 630,000,000 = 6.3 x 10 6.3 x 10 88

0.000000063 = 0.000000063 = 6.3 x 10 6.3 x 10 - 8- 8

If coefficient smaller If coefficient smaller then then exponent bigger; exponent bigger; if coefficient bigger if coefficient bigger thenthen exponent will get smaller.exponent will get smaller.

54256 = 54256 = 5.4256 x 10 5.4256 x 10 44

0.00248 = 0.00248 = 2.48 x 10 2.48 x 10 - 3- 3

Remember! only Remember! only 11 numbernumber in front in front of decimalsof decimals

Let’s Practice . . .Let’s Practice . . .7348000 =7348000 =

7.348 x 10 7.348 x 10 66 0.24854 = 0.24854 =

2.4854 x 10 2.4854 x 10 - - 11

5842000 = 5842000 = 5.842 x 10 5.842 x 10 66

0.0000124 =0.0000124 =1.24 x 10 1.24 x 10 - 5- 5

Do I move the decimal to the right or the left?

Sometimes you may need to Sometimes you may need to convert between notations . .convert between notations . . . .

If you make one side bigger, If you make one side bigger, make the other side smallermake the other side smallerExample: Example:

6.3 x 106.3 x 104 4 = _______ x 10= _______ x 1022

6.3 x 106.3 x 102 2 = _= ___________ x 10__ x 1044

6.3 x 106.3 x 10-4 -4 = _______ x 10= _______ x 10-2-2

6.3 x 106.3 x 10-3 -3 = = _____________ x 10_ x 1022

630.063.063.000063

Scientific Notation: Scientific Notation: MultiplicationMultiplication

Multiply the coefficients Multiply the coefficients Add the exponentsAdd the exponents

(3.0 x 10(3.0 x 1044) x (2.0 x 10) x (2.0 x 1022) = ) = (3.0 x 2.0) x 10(3.0 x 2.0) x 104+2 4+2 = = 6.0 x 106.0 x 1066

make sure make sure final coefficientsfinal coefficients – – between 1 and 10!!!between 1 and 10!!!

Scientific Notation: Scientific Notation: DivisionDivision

Divide the coefficients Divide the coefficients Subtract the exponentsSubtract the exponents

6.0 x 105

2.0 x 103 = (6.0 / 2.0) x 105-3 = 3.0 x 102 why? 10 x 10 x 10 x 10

x 10 10 x 10 x 10

Scientific Notation: Scientific Notation: Addition and SubtractionAddition and Subtraction

1st make exponents the 1st make exponents the same, same,

then align decimal pointsthen align decimal points

5.40 x 10 5.40 x 10 3 3

+ 6.00 x 10 + 6.00 x 10 22 ________________________________

5.40 x

103

+ 0.600 x 103

____________________________________

6.00 x 6.00 x 101033

Significant FiguresSignificant FiguresMeasurements not more Measurements not more

reliable than measuring toolreliable than measuring tool

Significant Figures = Significant Figures = all digits known all digits known preciselyprecisely in a in a

measurement, + 1 measurement, + 1 estimatedestimated digit digit

SIX RULESSIX RULES to determine if measured values are to determine if measured values are significant:significant:

With the ruler, measure the width of your page of notesWhat is its’ width?

How many digits are you sure of?

How many do you interpolate or “guess”?

How many significant digits in total?

TT

Sig. Figs. in Sig. Figs. in CalculationsCalculations

answer rounded to the leastleast number of decimal places in agreement

12.52 349.0

+ 8.24

369.76 = 369.8 =

Adding/Subtracting

= 3.698 x 102

round number w/ the round number w/ the least least sig. figs.sig. figs.

7.55

x 0.34 2.567 = 2.6

2 sig. figs.

Multiplying and Dividing

ExamplesExamples61.2 9.35

+ 8.6

79.15 = 79.2

7.92 x 101

34.61- 17.3

17.311.73 x 101

2.10 x .70 = 1.47 = 1.5

Percent ErrorPercent Error  Used to evaluate accuracy of a measurement in lab.

Two parts:1.Actual Value –‘correct’

value2. Experimental Value -

measured in the lab

The Equation . . .The Equation . . .% Error =

Actual Amt - Experiment Amtx 100Actual Amt.

Will you have negative % errors?

Section Section

3.33.3International SystemInternational System

Of UnitsOf Units

Why is it important to have Why is it important to have one standard for one standard for measurement?measurement?To ensure consistent & repeatable measurements

Why is the metric system preferred over the English system?

• All units multiplies of 10.• Easy to convert

Which countries don’t use Which countries don’t use metrics in everyday life?metrics in everyday life?

Only 3Liberia (West Africa)Myanmar (or Burma S.W. Asia)

United States

1st established in France 1st established in France 1790’s1790’s

•1960, International System of Units(SI) SI•SI - revised version of metric system

Metric System

International System of International System of UnitsUnits

Seven SI Units:Seven SI Units:

Quantity Unit Symbol

length meter m

mass kilogram kg

time second s

electric current ampere A

thermodynamic temperature kelvin K

amount of substance mole mol

luminous intensity candela cd

Common SI-English Equivalent Quantities

English Equivalent

Mass

Length 1 kilometer(km) 1000(103)m 0.62miles(mi)

1 meter(m) 100(102)m 1.094yards(yd)

1000(103)mm 39.37inches(in)

1 centimeter(cm) 0.01(10-2)m 0.3937in

Volume

1 kilometer(km) 1000(103)m 0.62mi

1,000,000(106) cubic centimeters

35.2cubic feet (ft3)1 cubic meter(m3)

1 cubic decimeter(dm3)

1000cm3 0.2642 gallon (gal) 1.057 quarts (qt)

1 cubic centimeter (cm3)

0.001 dm3 0.0338 fluid ounce

1 kilogram (kg) 1000 grams

2,205 pounds (lb)1 gram (g) 1000 milligrams 0.03527 ounce(oz)

Table 1.4

Quantity SI Unit SI EquivalentEnglish to

SI Equivalent

1 mi = 1.61km

1 yd = 0.9144m

1 foot (ft) = 0.3048m

1 in = 2.54cm (exactly!)

1 ft3 = 0.0283m3

1 gal = 3.785 dm3

1 qt = 0.9464 dm3

1 qt = 946.4 cm3

1 fluid ounce = 29.6 cm3

1 (lb) = 0.4536 kg

1 lb = 453.6 g

1 ounce = 28.35 g

yotta Y 1024

zetta Z 1021

exa E 1018

peta P 1015

tera T 1012

giga G 1 000 000 000 109

mega M 1 000 000 106

kilo k 1000 103

hecto h 100 102

deka da 10 101

deci d 0.1 10-1

centi c 0.01 10-2

milli m 0.001 10-3

micro µ 0.000 001 10-6

nano n 0.000 000 001 10-9

pico p 10-12

femto f 10-15

atto a 10-18

zepto z 10-21

yocto y 10-24

There are 20 SI Prefixes:

G 109

M 1 000 000 106

k 1 000 103

100 102

deka 10 101

base … b 1 100

deci d 0.1 10-1

centi c 0.01 10-2

milli m 0.001 10-3

micro µ 0.000 001 10-6

nano n 0.000 000 001 10-9

1 000 000 000giga

megakilo

hecto hda

“Give Me knowledge brother d.c. mun” Giga

Mega kilo

Base- g,m,L (great mr. Lincoln)

deci centi

milli u(=micro)

nano

1000 cm = ______ mm1000 cm = ______ mm3789.23 mm = ______ dm3789.23 mm = ______ dm

10.34 kg = ______ mg10.34 kg = ______ mg10.34 g = ______ kg10.34 g = ______ kg

93 cm = ______ Mm93 cm = ______ Mm

3789.23 mL = ______ nL3789.23 mL = ______ nL

3.78923 Gm = ______ dm3.78923 Gm = ______ dm

Section Section 3.43.4

DensityDensity

Example:Example:Calculate the density of mercury if 1.00 x 102g occupies a volume of 7.36 cm3.

D = m v

13.586

= 1.00 x 102g 7.36 cm3

= 13.6

= 1.36 x 101

g/cm3

11stst Semester Lecture Ends Here Semester Lecture Ends Here

Example:Example:

A plastic ball has a density of .54 g/cm3.

Will the plastic ball sink or float in a container of gasoline, .66 g/cm3.

floatfloat

Specific GravitySpecific Gravity

Specific gravity = Specific gravity = density of substancedensity of substance density of waterdensity of water

density of golddensity of gold = = 19.3 g/cm19.3 g/cm33 = 19.3= 19.3 density of water 1.000g/cmdensity of water 1.000g/cm33

SectionSection3.53.5

TemperatureTemperature

A. Temperature scalesA. Temperature scales

Boiling pt. of water

Freezing pt. of water

Fahrenheit

Celsius

Kelvin

212 F

32 F

100 C

0 C

373 K

273 K

Common Temperature scale in U.S.

Lowest temp possible all particles motion stops is

O K or absolute zero.

http://www.212movie.com/

http://www.212movie.com/

Equations for Equations for Temperature Temperature ConversionsConversions

K = oC + 273

3259

CF oo

Memorize these

equations!

Normal Normal body tempbody temp is is 98.6 F98.6 F.. Convert to Convert to CelsiusCelsius & & Kelvin.Kelvin.

3259

CF

328.16.98 C

C8.1

326.98

C = 37

K = C + 273K = 37 + 273K = 310

No degree sign!o

boiling point of water on Everest isboiling point of water on Everest is 343 K343 K,, what is this in what is this in CelsiusCelsius??

K = C + 273343 = C + 273

343 - 273= CC = 70o

Dimensional Analysis – Dimensional Analysis – Get p. 16-17Get p. 16-17 ready readyuses units to solve problems & check answers.uses units to solve problems & check answers.

1. Use equivalence statement to get conversion factor.1. Use equivalence statement to get conversion factor.2. Pick conversion factor that 2. Pick conversion factor that cancels appropriate unit.cancels appropriate unit.3. Multiply quantity by conversion factor.3. Multiply quantity by conversion factor.4. Check 4. Check Sig Figs.Sig Figs.5. Ask whether your 5. Ask whether your answer makes senseanswer makes sense..

Sample Problem 1.2 Converting Units of Length

PROBLEM: What is the price of a piece of copper wire 325 centimeters (cm) long that sells for $0.15/ft?

2.54 cm = 1 in

= 325 cm x

in2.54 cm = 128 in

Use the Unit cancelation Method.Use the Unit cancelation Method.

It’s easierIt’s easier

= 325 cm x

1 ft12 inch

1 inch2.54 cm

$ 0.15ft

Dimensional Analysis ReviewDimensional Analysis Review1 week John finds 27 boggles on the ground. Realizing 1 week John finds 27 boggles on the ground. Realizing that in Slopoland they are being devalued and that in Slopoland they are being devalued and Discontinued, he traded them in until he gets all Discontinued, he traded them in until he gets all of his currency in slopos. of his currency in slopos.

Fred is willing to exchange 14 boggles for Fred is willing to exchange 14 boggles for each Jangleeach Jangle

John is willing to exchange 7 Dopies for each John is willing to exchange 7 Dopies for each Jangle.Jangle.

And the bank will accept 1/6 of a Dopey for And the bank will accept 1/6 of a Dopey for each Slopoeach Slopo

If John can find 27 boggles per week, how If John can find 27 boggles per week, how many sloposmany slopos

can he earn in 1 Year.can he earn in 1 Year.

ReviewReview A student is given 3.5 grams of Chocolate for A student is given 3.5 grams of Chocolate for

every 2 miles of running.Each run is 4.0 miles. every 2 miles of running.Each run is 4.0 miles. How many pounds would they receive after How many pounds would they receive after running for 2.0 months. Students run twice per running for 2.0 months. Students run twice per day (1 kg = 2.2 pounds)day (1 kg = 2.2 pounds)

ReviewReview A student is given 4.0 grams of Chocolate for A student is given 4.0 grams of Chocolate for

every 3 miles of running. Each run is 2.0 miles. every 3 miles of running. Each run is 2.0 miles. How many pounds would they receive after How many pounds would they receive after running for 3.0 months. Students run twice per running for 3.0 months. Students run twice per day (1 kg = 2.2 pounds)day (1 kg = 2.2 pounds)

Chp 3 QUIZ Chp 3 QUIZ 1. How many sig figs are in: 73002. How many sig figs are in: 7300.0

4. Which above is best? Why?

6. 73 + 27 = _______ _________ __________

Number FROM 1-10. Skip lines & show work, sig figs, sci. not.

5. G M K b (gml) d c mun. Copy & finish the roots and write the exponents – Giga 109

7. 10.0 x 30.00 = _________ _________ _______?8. 1 dm3 = 1 __ = 1000 ___ = 1000 ___ = 1000 ___9. 3700.42 mg = ______ g10. A dice with 2.0 cm sides is 4.00 g. What’s its’ density? (show all steps). Will it float?

3. What’s the difference between accuracy/precision?

Chp 3 QUIZ Chp 3 QUIZ 1. How many sig figs are in: 22. How many sig figs are in: 5

4. Which above is best? Why?

6. 73 + 27 = 110 1.10 x 102

Number FROM 1-10. Skip lines & show work, sig figs, sci. not.

5.G M K b (gml) d c mun. Copy & finish the roots write the exponents – Giga Mega Kilo base deci centi milli micro nano

10 9 6 3 0 -1 -2 -3 -6 -9

7. 10.0 x 30.00 = 3.00 x 1028. 1 dm3 = 1 L = 1000 cm3 = 1000 mL = 1000 c.c.’s9. 3700.42 mg10. A dice with 2.0 cm sides is 4.00 g. What’s its’ density? (show all steps). Will it float?

3. What’s the difference between accuracy/precision?

1 g = 3.70042 g

1000mg

Chp 3 QUIZ Chp 3 QUIZ 1. How many sig figs are in: 22. How many sig figs are in: 5

4. Which above is best? Why?

6. 73 + 27 = 100 1.00 x 102

Number FROM 1-10. Skip lines & show work, sig figs, sci. not.

5.G M K b (gml) d c mun. Copy & finish the roots write the exponents – Giga Mega Kilo base deci centi milli micro nano

10 9 6 3 0 -1 -2 -3 -6 -9

7. 10.0 x 30.00 = 3.00 x 1028. 1 dm3 = 1 L = 1000 cm3 = 1000 mL = 1000 c.c.’s9. 3700.42 mg10. A dice with 2.0 cm sides is 4.00 g. What’s its’ density? (show all steps). Will it float?

3. What’s the difference between accuracy/precision?

1 g = 3.70042 g

1000mg

NameJob +2Yes/NoWhy 3 reasons

Intro sentenceReason WhyExample +2Intro sentenceReason WhyExample +2

Yes/No +2Why 3 reasonsDeclare better off

Intro sentenceReason WhyExample +2

TAKE NOTES

Let’s review . . .Let’s review . . .

Scientific MeasurementsScientific Measurements  

A measurement assigns a numerical A measurement assigns a numerical value for a physical property.value for a physical property.Two parts:Two parts:

A A NumberNumber and a and a UnitUnit Without a unit the # is not Without a unit the # is not

validvalidI have 3 3 grams?

No, 3 pigs

Types of Types of MeasurementMeasurementQuantitative Measurement -

numerical basketball - diameter = 31 cm.basketball - diameter = 31 cm.

Qualitative Measurement – descriptions, non-numerical The The basketball is basketball is brownbrown..

Qualitative or Quantitative?Qualitative or Quantitative?The solution was copper colored.The solution weighed 150g.The compound was very dense.The compound had a density of

1.54g/l

Which type of measurement do scientists prefer? Why?

Section Section 3.23.2

UncertainUncertainty in ty in

MeasureMeasurementsments

Two types of Two types of Quantitative MeasurementsQuantitative Measurements  A. AccuracyHow close a single measurement comes to the actual value

How close severalHow close several measurementsmeasurements measurements measurements

measurementsmeasurementsare to each otherare to each other – how repeatable repeatable repeatable

B. PrecisionB. Precision

A CB

Compare the accuracy and precision of the following:

Rule 1Rule 1

All non-zeronon-zero numbers are significant (counting numbers 1-9)

1234.7

.7432

How many Significant Figures?

Rule 2Rule 2

All “trapped”“trapped” zeros are significant (between #’s 1-9)

7003 40.79

1.5003

How many Significant Figures?

0 000

0

Trapped Zeros

Rule 3Rule 3

““Leading”Leading” zeros NEVER significant

0.007010.4102

0.000099

How many Significant Figures?

00

The Zeros are

leading!

Rule 4Rule 4After a decimal point all After a decimal point all zeroes,zeroes, other other

than leading, are significant.than leading, are significant.

0.0070100

0.410200.000099

0

Rule 5Rule 5

Zeros “placeholders”“placeholders” at end of a # is NOT significant.

3007000

27210

How many Significant Figures?

A zero holding a place

0

Rule 6Rule 6UnlimitedUnlimited number of sig. figs.

•Defined quantities60 minutes = 1 hour100 cm = 1 m

•Involves counted objectsThere are 36 students in the

class.6.5 counselors “that can’t be”

How many sig. figs. are in the How many sig. figs. are in the following measurements?following measurements?

80.41 g71,000,000 m

0.00023 L10 basketballs93.00 inches

3600 sec = 1 hour

Round the following Round the following numbers to numbers to 33 significant significant

figures:figures:1.035 g =

0.00000789 m =

578,000 mL =

1.04 g

7.89 x 10-6 m

5.78 x 105 mL

0.06055 x 10-

2 =6.06 x 10-4

g

1 dm1 dm1 cm1 cm 1 mm1 mm 1 dm1 dm2 1 dm1 dm3 1 cm1 cm2

1ml

1 cm1 cm3

1 dm3 =10cmx10cmx10cm =

1000 cm3 =1000 ml =

1 liter =