Measurement

Measurement• Accuracy vs Precision• Percent Error• Significant Figures• Scientific Notation• Temperature Conversions• Dimensional Analysis• Conversion Factors• SI Conversions

Number vs. Quantity• Quantity = number + unit

UNITS MATTER!!

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

http://www.brainpop.com/science/scientificinquiry/precisionandaccuracy/

A. Accuracy vs. Precision

B. Percent Error

• Indicates accuracy of a measurement

100accepted

acceptedalexperimenterror %

your value

given 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 = 2.94 %

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

2.31 cm

C. Significant Figures• Counting Sig Figs

– Digits from 1-9 are always significant– Zeros between two other sig figs are always

significant– One or more additional zeros to the right of both

the decimal place and another sig digit are significant

– Count all numbers EXCEPT:• Leading zeros -- 0.0025• Trailing zeros without

a decimal point -- 2,500

5085

2.60

739

4. 0.080

3. 5,280

2. 402

1. 23.50


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


• 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


• 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


• 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

• A way to express any number as a number between 1 and 10 (coefficient) multiplied by 10 raised to a power (exponent)

• Number of carbon atoms in the Hope diamond

• 460,000,000,000,000,000,000,000 atoms

• 4.6 x 1023 atoms

coefficient exponent


• 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 – all of them!

65,000 kg 6.5 × 104 kg


7. 2,400,000 g

8. 0.00256 kg

9. 7.0 10-5 km

10. 6.2 104 mm

Practice Problems

2.4 106 g

2.56 10-3 kg

0.000070 km

62,000 mm


• 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:


11. (4 x 102 cm) x (1 x 108cm)

12. (2.1 x 10-4kg) x (3.3 x 102 kg)

13. (6.25 x 102) ÷ (5.5 x 108)

14. (8.15 x 104) ÷ (4.39 x 101)

15. (6.02 x 1023) ÷ (1.201 x 101)

Practice Problems

4 1010 cm2

6.9 10-2 kg2

1.1 x 10-6

1.86 x 103

5.01 x 1022

E. Temperature• Temperature

– measure of the average KE of the particles in a sample of matter

273.15Kelvin Co

32Fahrenheit Co 5

9

32Celsius Fo 9

5

E. Temperature

• Convert these temperatures:

1) 25oC = ______________K

2) -15oF = ______________ K

3) 315K = ______________ oC

4) 288K = ______________ oF

298.15

298

41.85

298

F. Dimensional Analysis

• Dimensional Analysis is also called Unit Analysis and is a great way to solve problems in chemistry (or any time).


• Dimensional Analysis– A tool often used in science for converting units

within a measurement system

• Conversion Factor– A numerical factor by which a quantity expressed in

one system of units may be converted to another system

F. Dimensional Analysis Problem-Solving Steps

1. Analyze

2. Plan

3. Compute

4. Evaluate

3

3

cm

gcm


• The “Factor-Label” Method– Units, or “labels” are canceled, or “factored” out

g


• Steps to solving problems: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.

G. Conversion FactorsG. Conversion Factors

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.

How many minutes are in 2.5 hours?

Conversion factor

cancel

2.5 hr2.5 hr

1 1

x x 60 min60 min

1 hr

= 150 min

G. Conversion FactorsWrite conversion factors that relate Write conversion factors that relate each of the following pairs of units:each of the following pairs of units:

1. Liters and mL1. Liters and mL

2. Hours and minutes2. Hours and minutes

3. Meters and kilometers3. Meters and kilometers

1 L1000 mL

1 hr60 min

1000 m1 km

1000 mL1 L

=

H. SI Prefix Conversions

1. Memorize the following chart. (next slide)

2. Find the conversion factor(s).

3. Insert the conversion factor(s) to get to the correct units.

4. When converting to or from a base unit, there will only be one step. To convert to or from any other units, there will be two steps.


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

kilo- k 103

BASE UNIT --- 100

giga- G 109

deka- da 101

hecto- h 102

tera- T 1012

mo

ve le

ft

mo

ve r

igh

t


a. cm to m

b. m to µm

c. ns to s

d. kg to g

1 m100 cm

1 m106 µm

1 s109 ns

1 kg1000 g


4) 805 Tb = ______________ b

805 Tb 1

1012 b

1 Tb

Terabytes bytes

= 805 x 1012 bytes

= 8.05 x 1014 bytes

8.05 x 1014


5) 400. g = ______________ kg

6) 57 Mm = ______________ nm

Dimensional Analysis Practice

1.1. You have $7.25 in your pocket in You have $7.25 in your pocket in quarters. How many quarters do you quarters. How many quarters do you have?have?

2. How many seconds are in 1.4 days?

Plan: days hr min seconds

3. How many milliliters are in 1.00 quart of milk?

4. You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

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

6. Milton football needs 5.5 yards for a 1st down. How many cm is this?

7. A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

8. How many liters of water would fill a container that measures 75.0 in3?

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Measurement