i. using measurements measurement in science. a. accuracy vs. precision accuracy - how close a...

I. Using MeasurementsI. Using Measurements

MEASUREMENTIN

SCIENCE

MEASUREMENTIN

SCIENCE

A. Accuracy vs. 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

• Accuracy - how close a measurement is to the accepted value

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

ACCURATE = CORRECT

PRECISE = REPEATABLE

B. Percent ErrorB. Percent Error

• Indicates accuracy of a measurement

• Indicates accuracy of a measurement

100literature

literaturealexperimenterror %

your value

accepted value

B. Percent ErrorB. 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.

• 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 FiguresC. Significant Figures

• Indicate precision of a measurement.

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

• 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 FiguresC. Significant Figures• Counting Sig Figs

• Count all digits (1-9)

• Zero Rules:• Trapped zeros -- 101

are always significant

• Preceding zeros -- 0.0025

are never significant

• Trailing zeros -- 2500

only with a decimal point

• Counting Sig Figs

• Count all digits (1-9)

• Zero Rules:• Trapped zeros -- 101

are always significant

• Preceding zeros -- 0.0025

are never significant

• Trailing zeros -- 2500

only with a decimal point

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.

• 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 FiguresC. 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.

• 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


• 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

• 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)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 NotationD. Scientific Notation

• Converting into Sci. Notation:

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

• Large # (>1) Þ positive exponent (left) Small # (<1) Þ negative exponent (right)

• Only include sig figs.

• Converting into Sci. Notation:

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

• Large # (>1) Þ positive exponent (left) Small # (<1) Þ negative exponent (right)

• Only include sig figs.

65,000 kg 6.5 × 104 kg

D. Scientific NotationD. Scientific Notation

7. 2,400,000 g

8. 0.00256 kg

9. 7 10-5 km

10. 6.2 104 mm

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 NotationD. Scientific Notation• Calculating with Sci. 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:

II. Units of MeasurementII. Units of Measurement

MEASUREMENTMEASUREMENT

A. Number vs. QuantityA. Number vs. Quantity• Quantity - number + unit• Quantity - number + unit

UNITS MATTER!!

B. SI UnitsB. SI Units

Quantity Base Unit Unit Abbrev.

Length

Mass

Time

Temp

meter

kilogram

second

kelvin

m

kg

s

K

Amount mole mol

Variable Symbol

l

m

t

T

n

B. SI UnitsB. 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

C. Derived UnitsC. Derived Units

• Combination of base units.• Volume (m3 or cm3) • length x length x length

• Combination of base units.• Volume (m3 or cm3) • length x length x length

1 cm3 = 1 mL1 dm3 = 1 L

Problem-Solving StepsProblem-Solving Steps

1. Analyze

2. Plan

3. Compute

4. Evaluate

1. Analyze

2. Plan

3. Compute

4. Evaluate

III. Unit Conversions

(Dimensional Analysis)

III. Unit Conversions

(Dimensional Analysis)

MEASUREMENTMEASUREMENT

A. SI Prefix Conversions


1. Find the difference between the exponents of the two prefixes.

2. Move the decimal that many places.

1. Find the difference between the exponents of the two prefixes.

2. Move the decimal that many places.

To the leftor right?

=



NUMBERUNIT

NUMBER

UNIT

532 m = _______ km

0.532



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

move left

move right BASE UNIT --- 100



1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ______________ nm

4) 805 dm = ______________ km

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

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

g



• 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.

• 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.



• Lining up conversion factors:• Lining up conversion factors:

1 in = 2.54 cm2.54 cm 2.54 cm

1 in = 2.54 cm 1 in 1 in

= 1

1 =



• How many milliliters are in 1.00 quart of milk?• How many milliliters are in 1.00 quart of milk?

1.00 qt 1 L1.057

qt

= 946 mL

qt mL

1000 mL

1 L



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

• 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 lb1 kg

2.2 lb= 35 cm3

1000 g

1 kg

1 cm3

19.3 g



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

• 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 L

1000 cm3



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

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 in

2.54 cm= 3.2 in

cm in



6) WF football needs 550 cm for a 1st down. How many yards is this?6) WF 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



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

7) 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 cm

1 m= 86 pieces

cm pieces

1 piece

1.5 cm

i. using measurements measurement in science. a. accuracy vs. precision accuracy - how close a...

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