I. Scientific Method

The Scientific MethodA logical approach to solving problems or answering questions.

Starts with observation- noting and recording information and facts

hypothesis- educated guess or testable statement

Steps in the Scientific Method1. Observations (uses your senses)

a) quantitative involves numbers = 95oF

b) qualitative is word description = hot

2. Formulating hypotheses (ideas)3. Performing experiments (the test)

- gathers new information to help decide whether the hypothesis is valid

Scientific Method Controls- constants Variables- changing conditions

Limit variables We gather data and observations

by doing the experiment Modify hypothesis - repeat the

cycle based on results

Steps in the Scientific MethodTheorize (model)

- explanation of some natural phenomenonMany phenomena- construct a theory

Publish Results- Do other experts agree

II. Units of Measurement

Number vs. QuantityQuantity - number + unit

UNITS MATTER!!

SI Units

Quantity Base Unit Abbrev.

Length

Mass

Time

Temp

meter

kilogram

second

kelvin

m

kg

s

K

Amount mole mol

Symbol

l

m

t

T

n

SI Units

mega- M 106

deci- d 10-1

centi- c 10-2

milli- m 10-3

Prefix Symbol Factor

micro- 10-6

nano- n 10-9

pico- p 10-12

kilo- k 103

BASE UNIT --- 100

Derived UnitsCombination of base units.

Volume (m3 or cm3) length length length

D = MV

1 cm3 = 1 mL1 dm3 = 1 L

Density (kg/m3 or g/cm3)mass per volume

Mas

s (g

)

Volume (cm3)

Δx

Δyslope D

V

M

DensityAn object has a volume of 825 cm3 and a density of

13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

M = ?

WORK:

M = DV

M = (13.6 g/cm3)(825cm3)

M = 11,200 g

V

MD

DensityA liquid has a density of 0.87 g/mL. What volume is

occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

M = 25 g

WORK:

V = M D

V = 25 g

0.87 g/mL

V = 29 mLV

MD

III. Using Measurements

Accuracy vs. PrecisionAccuracy - how close a measurement is to

the accepted value

Precision - how close a series of measurements are to each other

ACCURATE = CORRECT

PRECISE = CONSISTENT

Percent ErrorIndicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value

accepted value

Percent ErrorA student determines the density of a

substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

% error = 2.9 %

Significant FiguresIndicate precision of a measurement.

Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit

2.35 cm

Significant FiguresCounting Sig Figs (Table 2-5, p.47)

Count all numbers EXCEPT:Leading zeros -- 0.0025

Trailing zeros without a decimal point -- 2,500

4. 0.080

3. 5,280

2. 402

1. 23.50

Significant FiguresCounting Sig Fig Examples

1. 23.50

2. 402

3. 5,280

4. 0.080

4 sig figs

3 sig figs

3 sig figs

2 sig figs

Significant FiguresCalculating with Sig Figs

Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

324 g

4 SF 3 SF3 SF

Significant FiguresCalculating with Sig Figs (con’t)

Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g 7.9 mL 350 g

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g

Significant FiguresCalculating with Sig Figs (con’t)

Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm“1” in any conversion: 1 in = 2.54 cm

Significant Figures

5. (15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

18.1 g

6. 18.9 g

- 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF

Scientific Notation

Converting into Sci. Notation:

Move decimal until there’s 1 digit to its left. Places moved = exponent.

Large # (>1) positive exponentSmall # (<1) negative exponent

Only include sig figs.

65,000 kg 6.5 × 104 kg

Scientific Notation

7. 2,400,000 g

8. 0.00256 kg

9. 7 10-5 km

10. 6.2 104

mm

Practice Problems

2.4 106 g

2.56 10-3 kg

0.00007 km

62,000 mm

Scientific NotationCalculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44EXPEXP

EEEE÷÷

EXPEXP

EEEE ENTERENTER7 8.1 4

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your calculator:

ProportionsDirect Proportion

Inverse Proportion

xy

xy

1

y

x

y

x

Unit Conversions

3

3

cm

gcm

Dimensional AnalysisThe “Factor-Label” Method

Units, or “labels” are canceled, or “factored” out

g

Dimensional AnalysisSteps:

1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

3. Multiply all top numbers & divide by each bottom number.

4. Check units & answer.

Dimensional AnalysisLining up conversion factors:

1 in = 2.54 cm

2.54 cm 2.54 cm

1 in = 2.54 cm

1 in 1 in

= 1

1 =

Dimensional AnalysisHow many milliliters are in 1.00 quart of milk?

1.00 qt 1 L

1.057 qt= 946 mL

qt mL

1000 mL

1 L

Dimensional AnalysisYou have 1.5 pounds of gold. Find its volume

in cm3 if the density of gold is 19.3 g/cm3.

lb cm3

1.5 lb 1 kg

2.2 lb= 35 cm3

1000 g

1 kg

1 cm3

19.3 g

Dimensional Analysis Your European hairdresser wants to cut your

hair 8.0 cm shorter. How many inches will he be cutting off?

8.0 cm 1 in

2.54 cm= 3.2 in

cm in

Dimensional Analysis Taft football needs 550 cm for a 1st down. How

many yards is this?

550 cm 1 in

2.54 cm= 6.0 yd

cm yd

1 ft

12 in

1 yd

3 ft

Dimensional AnalysisA piece of wire is 1.3 m long. How many 1.5-cm

pieces can be cut from this wire?

1.3 m 100 cm

1 m= 86 pieces

cm pieces

1 piece

1.5 cm

SI Prefix Conversions1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ______________ nm

4) 805 dm = ______________ km

0.2

0.0805

45,000

32