I

II

III

I. Using Measurements

CH. 2 - MEASUREMENT

A. Accuracy vs. Precision

Accuracy - how close a measurement is to the accepted value

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

ACCURATE = CORRECT

PRECISE = CONSISTENT

C. Significant Figures

Indicate precision of a measurement.

Recording Sig Figs

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

2.32 cm

C. Significant Figures

Counting Sig Figs

Count all numbers EXCEPT:

Leading zeros -- 0.0025

Trailing zeros without a decimal point -- 2,500

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4. 0.080

3. 5,280

2. 402

1. 23.50

C. Significant Figures

Counting 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

C. Significant Figures

Calculating 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

C. Significant Figures

Calculating 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

7.9 mL

3.75 mL

+ 4.1 mL

7.85 mL

C. Significant Figures

Calculating 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

C. Significant Figures

5. (15.30 g) ÷ (6.4 mL)

Practice Problems

= 2.390625 g/mL

18.1 g

6. 18.9 g

7. - 0.84 g18.06 g

4 SF 2 SF

2.4 g/mL2 SF

D. 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

D. 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

D. Scientific Notation

Calculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44EXPEXP

EEEE÷÷

EXPEXP

EEEE ENTERENTER

EXEEXE7 8.1 4

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

Type on your calculator:

E. 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

F. Derived Units

Combination 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

Problem-Solving Steps

1. Analyze

2. Plan

3. Compute

4. Evaluate

Density

An 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

Density

A 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

SI Prefix Conversions

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

mo

ve le

ft

mo

ve r

igh

t BASE UNIT --- 100

SI Unit Conversions

King Henry Died__drinking chocolate milk

K H D __ d C M

=

SI Prefix Conversions

NUMBERUNIT

NUMBER

UNIT

532 m = _______ km0.532

SI Prefix Conversions

1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ____ mm

4) 805 dm = ______________ km

0.2

0.0805

45,000

32

Dimensional Analysis

Steps:

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 Analysis

Lining 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 Analysis

How many milliliters are in 1.00 quart of milk? (1L = 1.057 qt)

1.00 qt 1 L

1.057 qt= 946 mL

qt mL

1000 mL

1 L

Dimensional Analysis

You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. (1 kg = 2.2 lbs)

lb cm3

1.5 lb 1 kg

2.2 lb= 35 cm3

1000 g

1 kg

1 cm3

19.3 g

Dimensional Analysis

5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? (1 in=2.54cm)

8.0 cm 1 in

2.54 cm= 3.2 in

cm in