review• 35 mm = _______ dm _____ mm _____ km• 0.25 dm3 = _____ cL = ______ cc• Bromine heptafluoride _____• N2 S3 ________________________

• Na2S• 6500000 = ________• 0.00344 = __________• 3.6 X 10-3 x 6.1 X 10-6 = _____________• 3.6 X 10-3 / 6.1 X 10-6 = _____________

review• 35 mm = 0.35 dm = 35000 mm = 0.000035 km• 0.25 dm3 (L) = 25 cL = 250 cc (mL) • Bromine heptafluoride __BrF7___

• N2 S3 dinitrogen trisulfide

• Na2S sodium sulfide• 6500000 = 6.5 X 106

• 0.00344 = 3.44 X 10-3

• 3.6 X 10-3 x 6.1 X 10-6 = 21.96 X 10-9 = 2.2 X 10-8

• 3.6 X 10-3 / 6.1 X 10-6 = 0.59 X 103 = 5.9 X 102

Measurements are estimates

• Exact numbers – Counted -- I have 3 sons– Defined -- 4 qt in 1 gal

• Measured– “exactness” limited by measuring device, object

and user

Significant figures

• Measured and exact number• Exact:– Counted

• 13,000 people attended the conference• 49 citizens attended the council meeting

– Defined• 12 in = 1 ft, 2.54 cm = 1 in • 1 kg = 2.2 lb NOT defined – remember weight changes!!!

• Measurements– All are estimates – depend on precision of device

• 16 oz = 1 lb, exact -- defined• 2.54 cm = 1 in, exaact -- defined• 454 g = 1 lb, measured• 1.6 km = 1 mi not exact (rounded off for convenience)• Actual exact number:• 1 mi X 5280ft/mi X 12 in/ft X 2.54 cm/in = 160934 cm• or 1.609344 km this would be the EXACT

conversion• • Exact or measured??

Measuring

Estimate anAdditional digitIf possible

If lines are veryClose togetherMay not bePractical!!!

Your reading might be 3.5 cm

Your reading might be 4.55 – but onA real meter stick, you probably cannotRead between the mm lines

Your reading should be 3.0 cmThis means you think the realValue is between 2.9 and 3.1Not between 2 and 4!!

Counting Significant Figures

Number of Significant Figures

38.15 cm

5.6 ft65.6 lb122.55 m

Complete: All non-zero digits in a measured number are (significant or not significant).Answers: 4,2,3,5

Leading Zeros

Number of Significant Figures

0.008 mm

0.0156 oz

0.0042 lb

0.000262 mL

Complete: Leading zeros in decimal numbers are (significant or not

significant).

Answers: 1,3,2,3

Sandwiched Zeros

Number of Significant Figures

50.8 mm

2001 min

0.702 lb

0.00405 m

Complete: Zeros between nonzero numbers are (significant or not significant).

Answers: 3,4,3,3

Trailing Zeros

Number of Significant Figures

25,000 in.

200 yr

48,600 gal

25,005,000 g Complete: Trailing zeros in numbers without

decimals are (significant or not significant) if they are serving as place holders.

Answers: 2,1,3,5

review• 35 mm = _______ dm _____ mm _____ km• 0.25 dm3 = _____ cL = ______ cc• Bromine heptafluoride _____• N2 S3 ________________________

• Na2S• 6500000 = ________• 0.00344 = __________• 3.6 X 10-3 x 6.1 X 10-6 = _____________• 3.6 X 10-3 / 6.1 X 10-6 = _____________

review• 35 mm = 0.35 dm = 35000 mm = 0.000035 km• 0.25 dm3 (L) = 25 cL = 250 cc (mL) • Bromine heptafluoride __BrF7___

• N2 S3 dinitrogen trisulfide

• Na2S sodium sulfide• 6500000 = 6.5 X 106

• 0.00344 = 3.44 X 10-3

• 3.6 X 10-3 x 6.1 X 10-6 = 21.96 X 10-9 = 2.2 X 10-8

• 3.6 X 10-3 / 6.1 X 10-6 = 0.59 X 103 = 5.9 X 102

Measurements are estimates

• Exact numbers – Counted -- I have 3 sons– Defined -- 4 qt in 1 gal

• Measured– “exactness” limited by measuring device, object

and user

Significant figures

• Measured and exact number• Exact:– Counted

• 13,000 people attended the conference• 49 citizens attended the council meeting

– Defined• 12 in = 1 ft, 2.54 cm = 1 in • 1 kg = 2.2 lb NOT defined – remember weight changes!!!

• Measurements– All are estimates – depend on precision of device

• 16 oz = 1 lb, exact -- defined• 2.54 cm = 1 in, exaact -- defined• 454 g = 1 lb, measured• 1.6 km = 1 mi not exact (rounded off for convenience)• Actual exact number:• 1 mi X 5280ft/mi X 12 in/ft X 2.54 cm/in = 160934 cm• or 1.609344 km this would be the EXACT

conversion• • Exact or measured??

Measuring

Estimate anAdditional digitIf possible

If lines are veryClose togetherMay not bePractical!!!

Your reading might be 3.5 cm

Your reading might be 4.55 – but onA real meter stick, you probably cannotRead between the mm lines

Your reading should be 3.0 cmThis means you think the realValue is between 2.9 and 3.1Not between 2 and 4!!

Counting Significant Figures

Number of Significant Figures

38.15 cm

5.6 ft65.6 lb122.55 m

Complete: All non-zero digits in a measured number are (significant or not significant).Answers: 4,2,3,5

Leading Zeros

Number of Significant Figures

0.008 mm

0.0156 oz

0.0042 lb

0.000262 mL

Complete: Leading zeros in decimal numbers are (significant or not

significant).

Answers: 1,3,2,3

Sandwiched Zeros

Number of Significant Figures

50.8 mm

2001 min

0.702 lb

0.00405 m

Complete: Zeros between nonzero numbers are (significant or not significant).

Answers: 3,4,3,3

Trailing Zeros

Number of Significant Figures

25,000 in.

200 yr

48,600 gal

25,005,000 g Complete: Trailing zeros in numbers without

decimals are (significant or not significant) if they are serving as place holders.

Answers: 2,1,3,5

HW

• Quiz Wed: metrics, sci not, naming• HW problems: CH 1: 9-16-24, 61, 62• 53 a,c (c volume displacement), 54 (density)

• Next class: classification of matter, chem and physical properties, (Ch3 sec 1 and Ch 5 sec 3) start conversion factors (Ch 1: sec 6,7,8)

• Check out mastering chemistry for problems!!

Learning Check

A. Which answers contain 3 significant figures?1) 0.4760 2) 0.00476 3) 4760

B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 103

C. 534,675 rounded to 3 significant figures is

1) 535 2) 535,000 3) 5.35 x 105

Answers: a: 2/3; b: 2/3; c: 2/3

Learning Check

In which set(s) do both numbers contain the same number of significant figures?

1) 22.0 and 22.00

2) 400.0 and 40

3) 0.000015 and 150,000

Answer: #3

Learning Check

State the number of significant figures in each of the following:

A. 0.030 m 1 2 3

B. 4.050 L 2 3 4

C. 0.0008 g 1 2 4

D. 3.00 m 1 2 3

E. 2,080,000 bees 3 5 7

29 people attended the conference ??? EXACT

Answers: a 2 b 4 c 1 d 3 e 3

Significant Numbers in Calculations

Help you decide where to round a number from your calculator

A calculated answer cannot be more precise than the measuring tool.

A calculated answer must match the least precise measurement.

Significant figures are needed for final answers from 1) adding or subtracting

2) multiplying or dividing

Adding and Subtracting

The answer has the same number of decimal places as the measurement with the fewest decimal places.

25.2 g one decimal place

+ 1.34 g two decimal places 26.54 answer 26.5 one decimal place

Learning Check

In each calculation, round the answer to the correct number of significant figures.

A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.8 3) 257

B. 58.925 - 18.2 =1) 40.725 2) 40.73 3) 40.7

Answers: a 2, b 3

Write vertically – calculators do not determine sig fig (84+ apps)

Multiplying and Dividing

Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

Or report in sci notation

Learning Check ? # sig fig?

A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198

B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60

C. 2.54 X 0.0028 = 0.0105 X 0.060

1) 11.3 2) 11 3) 0.041Answers: a 2, b 3, c 2