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Ch. 2 “Scientific Measurement & Problem Solving”. SAVE PAPER AND INK!!! If you print out the notes on PowerPoint, print "Handouts" instead of "Slides“ in the print setup. Also, turn off the backgrounds (Tools>Options>Print>UNcheck "Background Printing")!. - PowerPoint PPT Presentation

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Page 1: Ch. 2 “Scientific Measurement & Problem Solving”

Ch. 2 “Scientific Measurement & Problem Solving”

SAVE PAPER AND INK!!! If you print out the notes

on PowerPoint, print "Handouts" instead

of "Slides“ in the print setup. Also, turn off the backgrounds

(Tools>Options>Print>UNchec

k "Background Printing")!

Page 2: Ch. 2 “Scientific Measurement & Problem Solving”

Types of Observations and Measurements

• We make QUALITATIVE observations of reactions — Describes using wordsEx. Odor, color, texture, and physical state.

• We also make QUANTITATIVE observations, using numbers- measurements

• Ex. 25.3 mL, 4.239 g

Page 3: Ch. 2 “Scientific Measurement & Problem Solving”

Standards of Measurement

When we measure, we use a measuring tool to compare some dimension of an object to a standard. For example, at one time the

standard for length was the king’s foot. What are some

problems with this standard?

Page 4: Ch. 2 “Scientific Measurement & Problem Solving”

Accuracy – how close a measurementcomes to the true value of what is measured

Precision – is concerned with the reproducibility of the measurement

Our measurements must be bothAccurate & precise!

Page 5: Ch. 2 “Scientific Measurement & Problem Solving”

Three targets with three arrows each to shoot.

Can you hit the bull's-eye?

Both accurate and precise

Precise but not accurate

Neither accurate nor precise

How do they compare?

Page 6: Ch. 2 “Scientific Measurement & Problem Solving”

Stating a Measurement

In every measurement there is a

¨Number followed by a

¨ Unit from a measuring device

The number should also be as precise as the

measurement!

Page 7: Ch. 2 “Scientific Measurement & Problem Solving”

SI Measurement• Le Systeme International d’Unites : SI

Metrics• System of measurement agreed on all over the

world in 1960• Contains 7 base units• units are defined in terms of standards of

measurement that are objects or natural occurrence that are of constant value or are easily reproducible

• We still use some non-SI units!

Page 8: Ch. 2 “Scientific Measurement & Problem Solving”

• SI units — based on the metric system

• The only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularly

• Among countries with non-metric usage, the U.S. is the only country significantly holding out. The U.S. officially adopted SI in 1966.

Information from U.S. Metric Association

Le Système international d'unités

Page 9: Ch. 2 “Scientific Measurement & Problem Solving”
Page 10: Ch. 2 “Scientific Measurement & Problem Solving”

The 7 Base Units of SI

Page 11: Ch. 2 “Scientific Measurement & Problem Solving”

S.I. (the ones you’re responsible for knowing!)

Selected S.I. base (or standard) units

Mass kg

Length m

Time sec

Temperature KAmount of Substance mole mol

Page 12: Ch. 2 “Scientific Measurement & Problem Solving”
Page 13: Ch. 2 “Scientific Measurement & Problem Solving”

Derived Unitsmade by combining Base Units!

• Volume length cubed m3 cm3

• Density mass/volume g/mL kg/L g/ cm3

g/L

• Speed length /time mi/hr m/s km/hr

• Area length squared m2 cm2

Page 14: Ch. 2 “Scientific Measurement & Problem Solving”

We use prefixes to expand on the base units!

Page 15: Ch. 2 “Scientific Measurement & Problem Solving”

S.I. prefixes you must memorize!

Prefix Abbreviation Value

kilo k 103

deci d 10-1

centi c 10-2

milli m 10-3

micro m10-6

nano n 10-9

Page 16: Ch. 2 “Scientific Measurement & Problem Solving”

Metric System• These prefixes are based on powers of

10. • From each prefix every “step” is either:

• 10 times larger or

• 10 times smaller• For example

• Centimeters are 10 times larger than millimeters

• 1 centimeter = 10 millimeters kilo hecto deca

Base Unitsmetergramliter

deci centi milli

Page 17: Ch. 2 “Scientific Measurement & Problem Solving”

Metric System

• An easy way to move within the metric system is by moving the decimal point one place for each “step” desiredExample: change meters to centimeters1.00 meter = 10.0 decimeters = 100.

centimeters

kilo hecto decameterlitergram

deci centi milli

Page 18: Ch. 2 “Scientific Measurement & Problem Solving”

mass – measure of the quantity of matter

SI unit of mass is the kilogram (kg)

1 kg = 1000 g = 1 x 103 g

Not to be confused with -

weight – mass + gravity

force that gravity exerts on an object

Mass does not vary from place to place!

A 1 kg bar will weigh

1 kg on earth

0.1 kg on moon

A 1 kg bar has a mass of 1 kgon earth and on the moon

Page 19: Ch. 2 “Scientific Measurement & Problem Solving”

Volume – Amount of space occupied by matter

SI derived unit for volume is cubic meter (m3)

1 L = 1000 mL = 1000 cm3 = 1 dm3

1 mL = 1 cm3

1 dm3 = 1 L

We often use the Liter (L) when working with liquid volumes!

m3 = m x m x m

Page 20: Ch. 2 “Scientific Measurement & Problem Solving”

Temperature Scales• Fahrenheit• Celsius• Kelvin

Anders Celsius1701-1744

Lord Kelvin(William Thomson)1824-1907

Page 21: Ch. 2 “Scientific Measurement & Problem Solving”

TEMPERATURE SCALES

In Chemistry, the terms heat and temperature are often used to describe specific properties of a sample.

HEAT is the most common form of energy in nature and is directly related to the motion of particles of matter.

The faster the motion of particles in a sample the greater its heat content.

Page 22: Ch. 2 “Scientific Measurement & Problem Solving”

A forest fire and a lit match may both be at the same temperature, but there is a large difference in the amount of heat each possess.

TEMPERATURE is associated only with the intensity of heat and is not affected by the size of the sample.

Heat always spontaneously flows from a hotter system (higher temp.) to a colder system (lower temp.).

Page 23: Ch. 2 “Scientific Measurement & Problem Solving”

Temperature Scales

Notice that 1 Kelvin = 1 degree Celsius

Boiling point of water

Freezing point of water

Celsius

100 ˚C

0 ˚C

100˚C

Kelvin

373 K

273 K

100 K

Fahrenheit

32 ˚F

212 ˚F

180˚F

Page 24: Ch. 2 “Scientific Measurement & Problem Solving”
Page 25: Ch. 2 “Scientific Measurement & Problem Solving”

Temperature Scientists do not know of any limit on how high a temperature may be. The temperature at the center of the sun is about 15,000,000 °C. However, nothing can have a temperature lower than –273°C. This temperature is called absolute zero. It forms the basis of the Kelvin scale. Because the Kelvin scale begins at absolute zero, 0 K equals –273°C, and 273 K equals 0 °C.

Page 26: Ch. 2 “Scientific Measurement & Problem Solving”
Page 27: Ch. 2 “Scientific Measurement & Problem Solving”

Calculations Using Temperature

• Many chemistry equations require temp’s to be

in Kelvin

• K = ˚C + 273• Body temp = 37 ˚C + 273 = 310 K

• Liquid nitrogen = 273 -77 K = -196 ˚C

˚C = K - 273

Page 28: Ch. 2 “Scientific Measurement & Problem Solving”

DENSITY –

Density mass (g)volume (cm3)

Mercury

13.6 g/cm3 21.5 g/cm3

Aluminum

2.7 g/cm3

Platinummercuryplatinum

an important and useful physical property (Derived Unit)ratio of mass per unit of volume

Page 29: Ch. 2 “Scientific Measurement & Problem Solving”

DENSITY• Density is an

INTENSIVE property of matter.• Since it is a ratio

of mass to volume -does NOT depend on quantity of matter.

Styrofoam Brick

The density of 1 g of gold =The density of 5 kg of gold!

Page 30: Ch. 2 “Scientific Measurement & Problem Solving”

Problem A piece of copper has a mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.095 cm thick. Calculate density (g/cm3).

Get out those calculators!

Copper orePure copper metal

Page 31: Ch. 2 “Scientific Measurement & Problem Solving”

SOLUTION1. Make sure dimensions are in common

units. (all are in cm’s)2. Calculate volume in cubic centimeters. L x W x H = volume

3. Calculate the density.57.54 g6.4 cm3 = 9.0 g / cm3

(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm3

Page 32: Ch. 2 “Scientific Measurement & Problem Solving”

Learning Check

Which diagram represents the liquid layers in the cylinder?(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)

1) 2) 3)

K

K

W

W

W

V

V

V

K

Page 33: Ch. 2 “Scientific Measurement & Problem Solving”

Solution

(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)

1)

KW

V

Denser materials ‘sink’ inless dense materials!

Most solids sink in their liquid form.Can you think of an exception to this?!

WATER!!

Page 34: Ch. 2 “Scientific Measurement & Problem Solving”
Page 35: Ch. 2 “Scientific Measurement & Problem Solving”
Page 36: Ch. 2 “Scientific Measurement & Problem Solving”

Finding Volume of an IrregularSolid byWater Displacement

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

25 mL33 mL

Volume of solidis 8 mL

Page 37: Ch. 2 “Scientific Measurement & Problem Solving”

Calculator Time! What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? a) 0.2 g/ cm3 b) 6.0 g/cm3 c) 252 g/cm3

33 mL 25 mL

Page 38: Ch. 2 “Scientific Measurement & Problem Solving”

Percent Error• Percent Error:

• Measures the inaccuracy of experimental data

• Can have + or – value• Accepted value : correct value based on reliable

references• Experimental value: value you measured in the lab

%100accepted

alexperimentaccepted

Page 39: Ch. 2 “Scientific Measurement & Problem Solving”

Scientific NotationThe number of atoms in 12 g of carbon:

602,200,000,000,000,000,000,000

6.022 x 1023

The mass of a single carbon atom in grams:

0.0000000000000000000000199

1.99 x 10-23

N x 10n

N is a number between 1 and 10(1 non-zero digit to left of dec. pt.)

n is a positive or negative integer

Page 40: Ch. 2 “Scientific Measurement & Problem Solving”

To change standard form to scientific notation…

• Place the decimal point so that there is one non-zero digit to the left of the decimal point.

• Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

• If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Page 41: Ch. 2 “Scientific Measurement & Problem Solving”

Examples• Given: 289,800,000• Use: 2.898 (moved 8 places)• Answer: 2.898 x 108

• Given: 0.000567• Use: 5.67 (moved 4 places)• Answer: 5.67 x 10-4

Page 42: Ch. 2 “Scientific Measurement & Problem Solving”

To change scientific notation to standard

form…• Simply move the decimal point to

the right for positive exponent 10. • Move the decimal point to the left

for negative exponent 10.

(Use zeros to fill in places.)

Page 43: Ch. 2 “Scientific Measurement & Problem Solving”

Example• Given: 5.093 x 106

• Answer: 5,093,000 (moved 6 places to the right)

• Given: 1.976 x 10-4

• Answer: 0.0001976 (moved 4 places to the left)

Page 44: Ch. 2 “Scientific Measurement & Problem Solving”

Learning Check• Express these numbers in

Scientific Notation:

1) 4057892) 0.0038723) 30000000004) 25) 0.478260

Page 45: Ch. 2 “Scientific Measurement & Problem Solving”

Scientific Notation568.762

n > 0568.762 = 5.68762 x 102

move decimal left0.00000772

n < 00.00000772 = 7.72 x 10-6

move decimal right

Addition or Subtraction

1. Write each quantity with the same exponent n

2. Combine N1 and N2 3. The exponent, n, remains

the same

4.31 x 104 + 3.9 x 103 =

4.31 x 104 + 0.39 x 104 =

4.70 x 104

Page 46: Ch. 2 “Scientific Measurement & Problem Solving”

Scientific NotationCalculations

Multiplication1. Multiply N1 and N2

2. Add exponents n1 and n2

3. Put in proper format, if necessary

(4.0 x 10-5) x (7.0 x 103) =(4.0 x 7.0) x (10-5+3) =

28 x 10-2 =2.8 x 10-1

Division1. Divide N1 and N2

2. Subtract exponents n1 and n2

3. Put in proper format, if necessary

8.5 x 104 ÷ 5.0 x 109 =(8.5 ÷ 5.0) x 104-9 =

1.7 x 10-5

Page 47: Ch. 2 “Scientific Measurement & Problem Solving”

Significant FiguresThe numbers reported in a

measurement are limited by the measuring tool

Significant Figures in a measurement include all certain digits plus one estimated digit

Page 48: Ch. 2 “Scientific Measurement & Problem Solving”
Page 49: Ch. 2 “Scientific Measurement & Problem Solving”

•7.50 cm

Page 50: Ch. 2 “Scientific Measurement & Problem Solving”

•19.5 mL

Page 51: Ch. 2 “Scientific Measurement & Problem Solving”

Significant Figures• All certain digits plus one

estimated digit (used when recording measurements)

Page 52: Ch. 2 “Scientific Measurement & Problem Solving”

Known + Estimated DigitsIn 2.85 cm…

• Known digits 2 and 8 are 100% certain(there are lines on the ruler for these!)

• The third digit, 5, is estimated (uncertain)

• In the reported length, all three digits (2.76 cm) are significant including the estimated one

Page 53: Ch. 2 “Scientific Measurement & Problem Solving”

Figure 5.5: Measuring a pin.There are not really lines on the scale here – just estimates!

Page 54: Ch. 2 “Scientific Measurement & Problem Solving”

Reading a Meterstick. l2. . . . I . . . . I3 . . . .I . . . . I4. . cm

First digit (known) = 2 2.?? cmSecond digit (known)= 0.8 2.8? cmThird digit (estimated) between 0.03- 0.05Length reported = 2.83 cm

or 2.84 cm

or 2.85 cm

Page 55: Ch. 2 “Scientific Measurement & Problem Solving”

Learning Check

. l8. . . . I . . . . I9. . . . I . . . . I10. . cm

What is the length of the line?

1) 9.3 cm

2) 9.40 cm

3) 9.30 cm

How does your answer compare with your neighbor’s answer?

Page 56: Ch. 2 “Scientific Measurement & Problem Solving”

Rules for Counting Significant Figures

RULE 1. All non-zero digits in a measured number are significant.

Number of Significant Figures?

38.15 cm5.6 mL65.6 kg122.55 m

42

35

Page 57: Ch. 2 “Scientific Measurement & Problem Solving”

Sandwiched ZerosRULE 2. Zeros between nonzero numbers are

significant. Number of Significant Figures?

50.8 mm

2001 min

.702 mg

400005 m

34

3

6

Page 58: Ch. 2 “Scientific Measurement & Problem Solving”

Leading Zeros (in front)

RULE 3. Leading zeros in decimal numbers are NOT significant. Number of Significant Figures?

0.008 mm

0.0156 g

0.0042 cm

0.0002602 mL

1

3

2

4

Page 59: Ch. 2 “Scientific Measurement & Problem Solving”

Trailing Zeros (at end)RULE 4. Trailing zeros in numbers

without decimals are NOT significant. They are only serving as place holders.

Number of Significant

Figures?

25,000 m

200 L

48,600 mg

25,005,000 kg

2

1

35

Page 60: Ch. 2 “Scientific Measurement & Problem Solving”

Trailing Zeros, cont.

RULE 5. Trailing zeros in numbers with decimals ARE significant.

Number of Significant

Figures?

35,000.0 m

700. s

48.600 L

25,005.000 g

6

3

5

8

Page 61: Ch. 2 “Scientific Measurement & Problem Solving”
Page 62: Ch. 2 “Scientific Measurement & Problem Solving”

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

24 mL 2 significant figures

3001 g 4 significant figures

0.0320 m3 3 significant figures

6.4 x 104 molecules 2 significant figures

560 kg 2 significant figures

Page 63: Ch. 2 “Scientific Measurement & Problem Solving”

Significant Numbers in Calculations

A calculated answer cannot be more precise than the measuring tool.

A calculated answer must match the least precise measurement.

Significant figures are needed for final answers from 1) adding or subtracting

2) multiplying or dividing

Page 64: Ch. 2 “Scientific Measurement & Problem Solving”

Rounding• Need to use rounding to write a calculation

involving measurements correctly.• Calculator gives you lots of insignificant

numbers so you must round to the correct decimal place

• When rounding, look at the digit after the one you can keep• Greater than or equal to 5, round

up• Less than 5, keep the same

Page 65: Ch. 2 “Scientific Measurement & Problem Solving”

ExamplesRound each of the following measurements

so they have 3 sig figs: 761.50 14.334 10.44 10789 8024.50 203.514

76214.3

10.4108008020204

Page 66: Ch. 2 “Scientific Measurement & Problem Solving”

Series of operations: keep all non-significant digits during the intermediate calculations, and round to the correct number of SF only when reporting an answer.

Ex: (4.5 + 3.50001) x 2.00 =

(8.00001) x 2.00 = 16.0002 → 16

Page 67: Ch. 2 “Scientific Measurement & Problem Solving”

Adding and SubtractingThe answer has the same number of decimal places as the measurement with the fewest decimal places.

25.2 one decimal place (to right of decimal pt.)

+ 1.34 two decimal places (to right of decimal pt.)

26.54Answer: 26.5 (one decimal place)

Page 68: Ch. 2 “Scientific Measurement & Problem Solving”
Page 69: Ch. 2 “Scientific Measurement & Problem Solving”

Using Sig Figs in Calculations• Adding/Subtracting:

• end with the least number of decimal places

Page 70: Ch. 2 “Scientific Measurement & Problem Solving”

Using Sig Figs in Calculations• Adding/Subtracting:

• end with the least number of decimal places

Page 71: Ch. 2 “Scientific Measurement & Problem Solving”

Significant Figures

Addition or Subtraction (con’t,)

89.3321.1+

90.432 round off to 90.4one significant figure after decimal point

3.70-2.91330.7867

two significant figures after decimal point

round off to 0.79

Page 72: Ch. 2 “Scientific Measurement & Problem Solving”

Learning Check

In each calculation, round the answer to the correct number of significant figures.A. 235.05 + 19.6 + 2.1 =

1) 256.75 2) 256.8 3) 257

B. 58.925 - 18.2 =1) 40.725 2) 40.73 3) 40.7

Page 73: Ch. 2 “Scientific Measurement & Problem Solving”

Multiplying and Dividing

Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.(Sometimes you’ll need to put the answer into Sci. Notation to get correct # of sig figs!)

Page 74: Ch. 2 “Scientific Measurement & Problem Solving”
Page 75: Ch. 2 “Scientific Measurement & Problem Solving”

Using Sig Figs in Calculations

• Multiplying/Dividing:• end with the least number of sig figs

(Counting sig figs from left)

Page 76: Ch. 2 “Scientific Measurement & Problem Solving”

Using Sig Figs in Calculations• Multiplying/Dividing:

• end with the least number of sig figs

Page 77: Ch. 2 “Scientific Measurement & Problem Solving”

Significant Figures

Multiplication or DivisionThe number of significant figures in the result is set by the original number that has the smallest number of significant figures

4.51 x 3.6666 = 16.536366 = 16.5

3 sig figs round to3 sig figs

6.8 ÷ 112.04 = 0.0606926

2 sig figs round to2 sig figs

= 0.061

Page 78: Ch. 2 “Scientific Measurement & Problem Solving”

Learning Check A. 2.19 X 4.2 =

1) 9 2) 9.2 3) 9.198

B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60

C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.3 2) 11 3) 0.041

Page 79: Ch. 2 “Scientific Measurement & Problem Solving”

For exact numbers (e.g. 4 beakers) and those used in conversion factors (e.g. 1 inch = 2.54 cm), there is no uncertainty in their measurement. Therefore, IGNORE exact numbers when finalizing your answer with the correct number of significant figures.

(Numbers from definitions or numbers of objects are consideredto have an infinite number of significant figures)

The average of three measured lengths, 6.64, 6.68 and 6.70 is:

6.64 + 6.68 + 6.70

3= 6.67333 = 6.67

Because 3 is an exact number

= 7

Page 80: Ch. 2 “Scientific Measurement & Problem Solving”

Chemistry In ActionOn 9/23/99, $125,000,000 Mars Climate Orbiter entered Mar’s atmosphere 100 km lower than planned and was destroyed by heat.

1 lb = 1 N

1 lb = 4.45 N

“This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”

Page 81: Ch. 2 “Scientific Measurement & Problem Solving”

Conversion Factors• Ratio that comes from a statement of

equality between 2 different units• every conversion factor is equal to 1

dollarquarters 14

Example:

statement of equality

conversion factor 141

quartersdollar 4 quarters

1 dollar=

Page 82: Ch. 2 “Scientific Measurement & Problem Solving”

Conversion Factors (con’t.)

Fractions in which the numerator and denominator are EQUAL quantities expressed in different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

Page 83: Ch. 2 “Scientific Measurement & Problem Solving”

Learning Check

Write conversion factors that relate each of the following pairs of units:1. Liters and mL

2. Hours and minutes

3. Meters and kilometers

1 L. and 1000 mL 1000 mL 1 L

1 hr. and 60 mins. 60 mins. 1 hr

1000 m and 1 km__ 1 km 1000 m .

Page 84: Ch. 2 “Scientific Measurement & Problem Solving”

Conversion Factors

• can be multiplied by other numbers without changing the value of the number (since you are just multiplying by 1)

quartersdollar

quartersdollars 121

43

Page 85: Ch. 2 “Scientific Measurement & Problem Solving”

1.9

Dimensional Analysis Method of Solving Problems

1. Start with the given

2. Determine what unit label is needed on the answer

3. Add conversion factor(s) & cancel units until you are left with the desired unit label!

1 L = 1000 mL

How many mL are in 1.63 L?

1L1000 mL

1.63 L x = 1630 mL

1L1000 mL

1.63 L x = 0.001630 L2

mL

Page 86: Ch. 2 “Scientific Measurement & Problem Solving”
Page 87: Ch. 2 “Scientific Measurement & Problem Solving”
Page 88: Ch. 2 “Scientific Measurement & Problem Solving”

Sample Problem• You have $7.25 in your pocket in

quarters. How many quarters do you have?

7.25 dollars 4 quarters 1 dollar

X = 29 quarters

Page 89: Ch. 2 “Scientific Measurement & Problem Solving”

Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x

Page 90: Ch. 2 “Scientific Measurement & Problem Solving”

Solution

Unit plan: days hr min seconds

1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min

= 1.2 x 105 sec

Page 91: Ch. 2 “Scientific Measurement & Problem Solving”

Example Convert 5.2 cm to mm

• Known: 100 cm = 1 m1000 mm = 1 m

• MUST use m as an intermediate

mmmmm

cmmcm 52

11000

10012.5

Page 92: Ch. 2 “Scientific Measurement & Problem Solving”

Example

Convert 0.020 kg to mg

• Known: 1 kg = 1000 g1000 mg = 1 g

• Must use g as an intermediate

mggmg

kggkg 000,20

11000

11000020.0

Page 93: Ch. 2 “Scientific Measurement & Problem Solving”

Advanced Conversions

• A more difficult type of conversion deals w/units that are fractions themselves

• Be sure convert one unit at a time; don’t try to do both at once

• Setup your work the exact same way

Page 94: Ch. 2 “Scientific Measurement & Problem Solving”

When unit labels are fractions (or ratios), unzip them!

11.3 g/mL can be written as 11.3 g 1 mL

OR 1 mL 11.3 g

Ex. Convert 11.3 g/mL to g/L

11.3 g 1 mL = 1.13 x 104 g/L

1000 mL

1 L

Page 95: Ch. 2 “Scientific Measurement & Problem Solving”

PROBLEM: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 cm3 of Hg in grams?

Solve the problem using DIMENSIONAL ANALYSIS.

95 cm3 • 13.6 gcm3 = 1.3 x 103 g

Page 96: Ch. 2 “Scientific Measurement & Problem Solving”

The speed of sound in air is about 343 m/s. What is this speed in miles per hour?

What is the given? What do you have to convert?

1 mi = 1609 m 1 min = 60 s 1 hour = 60 min

343 ms x 1 mi

1609 m 60 s

1 minx 60 min

1 hourx = 767 mi

hour

meters to miles seconds to hours

1.9

Page 97: Ch. 2 “Scientific Measurement & Problem Solving”

Advanced Conversions

• Another difficult type of conversion deals with squared or cubed units

• Be sure to square or cube the conversion factor you are using to cancel all the units

• If you tend to forget to square or cube the number in the conversion factor, try rewriting the conversion factor instead of just using the exponent

Page 98: Ch. 2 “Scientific Measurement & Problem Solving”

Square and Cubic units• Use the conversion factors you already

know, but when you square or cube the unit, don’t forget to cube the number also!

• Best way: Square or cube the ENTIRE conversion factor

• Example: Convert 4.3 cm3 to mm3

4.3 cm3 10 mm 3 1 cm ( ) =

4.3 cm3 103 mm3

13 cm3

= 4300 mm3

Page 99: Ch. 2 “Scientific Measurement & Problem Solving”

Example

• Convert: 2000 cm3 to m3

• No intermediate needed

OR

Known:100 cm = 1 m cm3 = cm x cm x cmm3 = m x m x m

3002.0100

1100

1100

12000 mcm

mcm

mcm

mcmcmcm

33

3 002.0100

12000 mcm

mcm