Unit 2. Measurement

Do Now In your own words, what do you think is the

difference between:

Accuracy and Precision?

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 = CORRECTPRECISE = CONSISTENT

ACCURATE = CORRECTPRECISE = 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 = 2.90 %

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

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 (Table 2-5, p.47)

Count all numbers EXCEPT:

Leading zeros -- 0.0025 (not significant)

Trailing zeros without a decimal point -- 2,500 (not Significant)

Zeros between numbers are significant

4. 0.080

3. 5,280

2. 402

1. 23.50

C. Significant FiguresCounting Sig Fig Examples

1. 23.50

2. 402

3. 5,280

4. 0.080

4. 0.080

3. 5,280

2. 402

1. 23.50

C. 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

C. Significant Figures Calculating with Sig Figs

Multiply/Divide –

The # with the fewest sig figs determines the # of sig figs in the answer.

Multiplication and Division Rules Do the sum Round the answer to the least

significant figure in the problem

13.91g/cm3)(23.3cm3) = 324.103g 4SF 3SF 3SF

324g

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.

Addition and Subtraction Rules Stack the numbers so that the decimal

point is aligned Do the sum Figure out which number has least

decimal place (least precise/decimal area least far out)

Draw a line after the last number with the least decimal place

Round the digit by looking at the number that follows

Example

3.75 mL + 4.1 mL 7.85 mL 7.9 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 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

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 exponent

Small # (<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

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 g2.56 10-3 kg

0.00007 km62,000 mm

D. Scientific Notation Calculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44EXPEE

÷EXPEE ENTER

EXE7 8.1 4

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

Type on your calculator:

E. Proportions Direct Proportion

Inverse Proportion

xy

xy 1

y

x

y

x

Units of Measurement

A. Number vs. Quantity Quantity - number + unit

UNITS MATTER!!

B. SI UnitsQuantity Base Unit Abbrev.

Length

Mass

TimeTemp

meter

kilogram

secondkelvin

m

kg

sK

Amount mole mol

Symbol

l

m

tTn

B. SI Unitsmega- 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

C. 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/mL or g/cm3)

mass per volume

D. Density

Mas

s (g

)

Volume (cm3)

ΔxΔyslope D

VM

Problem-Solving Steps

1. Analyze

2. Plan

3. Compute

4. Evaluate

D. 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:

VMD

D. 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 gVMD

D. 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/mLV = ?M = 25 g

WORK:

VMD

D. 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/mLV = ?M = 25 g

WORK:V = M D

V = 25 g 0.87 g/mLV = 29 mLV

MD

III. Unit Conversions

A. SI Prefix Conversions1. Find the difference between the exponents of the

two prefixes.

2. Move the decimal that many places.

To the leftor right?

A. SI Prefix Conversionsmega- 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

mov

e le

ftm

ove

right

BASE UNIT --- 100

A. SI Prefix Conversions1) 20 cm = ______________ m

2) 0.032 L = _____________ mL

3) 45 m = ______________ nm

4) 805 dm = ______________ km

C. Johannesson

A. 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

33

cmgcm

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

bottom number.4. Check units & answer.

B. Dimensional Analysis Lining up conversion factors:

ARE THESE THE SAME?1 in = 2.54 cm

2.54 cm 2.54 cm

1 in = 2.54 cm 1 in 1 in

= 1

1 =

B. Dimensional Analysis

How many milliliters are in 1.00 quart of milk?

1.00 qt 1 L1.057 qt

= 946 mL

qt mL

1000 mL1 L

B. Dimensional Analysis You 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 kg2.2 lb

= 35 cm31000 g

1 kg1 cm3

19.3 g

B. Dimensional Analysis How many liters of water would fill a container that

measures 75.0 in3?

75.0 in3 (2.54 cm)3

(1 in)3= 1.23 L

in3 L

1 L1000 cm3

B. Dimensional Analysis

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

8.0 cm 1 in2.54 cm

= 3.2 in

cm in

B. Dimensional Analysis6) Taft football needs 550 cm for a 1st down. How

many yards is this?

550 cm 1 in2.54 cm

= 6.0 yd

cm yd

1 ft12 in

1 yd3 ft

B. Dimensional Analysis7) A piece of wire is 1.3 m long. How many 1.5-cm

pieces can be cut from this wire?

1.3 m 100 cm1 m

= 86 pieces

cm pieces

1 piece1.5 cm