I II III I. Using Measurements MEASUREMENT. A. Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how.

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I. Using Measurements

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

B. Percent Error

Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value

accepted value

B. Percent Error

A 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 %

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

2.35 cm

C. Significant Figures

Counting Sig Figs

Count all numbers EXCEPT:

Leading zeros -- 0.0025

Trailing zeros without a decimal point -- 2,500

Captive zeros– 20004

Always count

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

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

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

- 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:

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II. Units of Measurement

MEASUREMENT

A. Number vs. Quantity

Quantity - number + unit

UNITS MATTER!!

B. SI Units

Quantity Base Unit Abbrev.

Length

Mass

Volume

Temp

meter

gram

liter

Kelvin

m

g

l

K

Amount mole mol

Symbol

l

m

v

T

n

B. SI Units

Prefix Symbol FactorGiga G 109

Mega M 106

Kilo k 103

BASE UNIT -- 100

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro 10-6

Nano n 10-9

Pico p 10-12

C. 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

C. 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

C. DensityM

ass

(g)

Volume (cm3)

Δx

Δyslope D

V

M

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III. Unit Conversions

MEASUREMENT

A. SI Prefix Conversions

1. Find the difference between the

exponents of the two prefixes.

2. Move the decimal that many places.

To the leftor right?

=

A. SI Prefix Conversions

NUMBERUNIT

NUMBER

UNIT

532 m = _______ km0.532

A. SI Units Prefixes

Prefix Symbol FactorGiga G 109

Mega M 106

Kilo k 103

BASE UNIT -- 100

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro 10-6

Nano n 10-9

Pico p 10-12

mo

ve le

ft

mo

ve r

igh

t

A. SI Prefix Conversions

1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ______________ nm

4) 805 dm = ______________ km

0.2

0.0805

45,000

32

3

3

cm

gcm

B. Dimensional Analysis

The “Factor-Label” Method Units, or “labels” are canceled, or

“factored” out

g

B. 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.

B. Converting SI Units with Dimensional Analysis

Convert 10 liters to centiliters. Identify starting and ending points Starting point 10 liters, ending point centiliters Draw a T chart, you can add boxes as you go Line up conversion factors Then cancel the unit top and bottom Multiply across, divide top by the bottom.

10 liters

1 liter

100 clEnd Point

= 1000 cl or 1 X 103 cl

How many milligrams are in 50 kilograms? Identify starting and ending points Start at 50 kg; end at mg Draw a T chart, you can add boxes as you go Line up conversion factors Then cancel the unit top and bottom Multiply across, divide top by the bottom

50 kg

1 kg

1000 g

1 g

1000 mg

End Point

= 50,000,000 mg

or 5 X 107 mg

B. Converting SI Units with Dimensional Analysis

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STOP