131 1-31-2011
DESCRIPTION
significant figuresTRANSCRIPT
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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 = _____________
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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
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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
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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
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• 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??
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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!!
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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
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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
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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
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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
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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 = _____________
![Page 12: 131 1-31-2011](https://reader036.vdocuments.mx/reader036/viewer/2022062418/555e97ffd8b42a6d068b4d53/html5/thumbnails/12.jpg)
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
![Page 13: 131 1-31-2011](https://reader036.vdocuments.mx/reader036/viewer/2022062418/555e97ffd8b42a6d068b4d53/html5/thumbnails/13.jpg)
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
![Page 14: 131 1-31-2011](https://reader036.vdocuments.mx/reader036/viewer/2022062418/555e97ffd8b42a6d068b4d53/html5/thumbnails/14.jpg)
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
![Page 15: 131 1-31-2011](https://reader036.vdocuments.mx/reader036/viewer/2022062418/555e97ffd8b42a6d068b4d53/html5/thumbnails/15.jpg)
• 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??
![Page 16: 131 1-31-2011](https://reader036.vdocuments.mx/reader036/viewer/2022062418/555e97ffd8b42a6d068b4d53/html5/thumbnails/16.jpg)
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!!
![Page 17: 131 1-31-2011](https://reader036.vdocuments.mx/reader036/viewer/2022062418/555e97ffd8b42a6d068b4d53/html5/thumbnails/17.jpg)
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
![Page 18: 131 1-31-2011](https://reader036.vdocuments.mx/reader036/viewer/2022062418/555e97ffd8b42a6d068b4d53/html5/thumbnails/18.jpg)
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
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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
![Page 20: 131 1-31-2011](https://reader036.vdocuments.mx/reader036/viewer/2022062418/555e97ffd8b42a6d068b4d53/html5/thumbnails/20.jpg)
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
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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!!
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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
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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
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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
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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
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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
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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)
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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
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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