unit 1: basics // metrics & matter essential question: how do scientists express the degree of...
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Unit 1: Basics // Metrics & MatterEssential Question: How do scientists express the degree of uncertainty in their measurements?
Thursday, September 11, 2014
Because nothing in science is ever certain…
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Do Now
•Use the ruler you have been given to measure the short side of the bill to the best of your ability
•Record your measurement in the given section in your notes
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Quantitative Observation
=measurements; must consist of two parts: a number and a unit
Ms. Ngo is 5’2”
What would happen if we did not have units??
Ms. Ngo is 52
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Uncertainty
•Any measurement involves an estimate and thus is uncertain to some extent
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Person Measurement1 2.85 cm2 2.84 cm3 2.86 cm4 2.85 cm5 2.86 cm
If 5 different people took a measurement of a pin, we could have 5 different measurements:
We saw this during the Do Now activity!
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Person Measurement1 2.85 cm2 2.84 cm3 2.86 cm4 2.85 cm5 2.86 cm
If 5 different people took a measurement of a pin, we could have 5 different measurements:
The first two digits are the same regardless of who made the measurement (these are
called certain numbers))
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Person Measurement1 2.85 cm2 2.84 cm3 2.86 cm4 2.85 cm5 2.86 cm
If 5 different people took a measurement of a pin, we could have 5 different measurements:
The last digit varies; it is called the uncertain number
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Accuracy•Measure of how close a
measurement comes to the actual/accepted value
•Accepted Value = 24 cm
•Measured Values(Experimental Values)
Measurements
24.1 cm
24.0 cm
23.9 cm
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Precision
•Measure of how close a series of measurements are to one another
Measurements
88.7 in
88.8 in
88.9 in
88.7 in
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Group Discussion
* *The more numbers the more precise the tool
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Series of Measurements Can Be…
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Think-Pair-Share…
• Six students used this ruler to measure the metal strip shown. Their measurements are listed in the table.
• In terms of accuracy and precision, how would you classify their measurements?
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Review
•Compare the precision of a 100 mL graduated cylinder with 1 mL increments with a 50 mL graduated cylinder with 0.5 mL increments.
▫A 50 mL graduated cylinder with 0.5 mL increments is more precise because the increments are smaller
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Review• The chart below shows the volume of a solution
measured by four different groups. The actual (correct) volume of the solution is 44.5 mL.
▫What group has both accurate and precise data? Group 1
▫What group has data that is imprecise and inaccurate? Group 2
▫Comment on the accuracy and precision of Group 3’s data? Their data is precise and inaccurate.
Volume (mL) Group 1 Group 2 Group 3
Trial 1 44.5 mL 42.3 mL 49.0 mLTrial 2 44.6 mL 47.2 mL 49.1 mLTrial 3 44.5 mL 48.0 mL 49.0 mL
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Review
•To determine the length of a running shoe, a cross-country runner measured the shoe several times using a metric ruler. If the true length of the shoe is 88.74cm, give an example of:▫imprecise and inaccurate data ▫precise but inaccurate data ▫precise and accurate data
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Measuring Volume in the Lab
•Volume is measured from the bottom of the meniscus
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•Take the Volume!
(Always take a measurement to the first uncertain number.)
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•Correct Answer:
56.0 mL
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•Take the Volume!
(Always take a measurement to the first uncertain number.)
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•To be correct, your answer must be in the following range:
8.40-8.49mL
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Percent Error
•Used to gage how close an measurement taken via experiment is to the accepted value
% Error =|Experimental-Accepted|
Accepted Value
Do not have to memorize formula; It’s located on last page of Reference Table
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Significant Figures in MeasurementThe numbers reported in a measurement are limited by the measuring tool
Significant figures in a measurement include the known digits plus one estimated digit
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Counting Significant Figures
Number of Significant Figures
38.15 cm 45.6 ft 265.6 lb ___122.55 m ___
Complete this sentence: All non-zero digits in a measured number are
(significant or not significant).
5
3
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Leading Zeros
Number of Significant Figures
0.008 mm 1
0.0156 oz 3
0.0042 lb ____
0.000262 mL ____
Complete this sentence : Leading zeros in
decimal numbers are
(significant or not significant).
3
2
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Sandwiched Zeros
Number of Significant Figures
50.8 mm 3
2001 min 4
0.702 lb ____
0.00405 m ____
Complete: Zeros between nonzero numbers are (significant or not significant).
3
3
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Trailing Zeros
Number of Significant
Figures
25,000 in. 2
200 yr 1
48,600 gal 3
25,005,000 g ____ Complete: Trailing zeros in numbers without decimals are
(significant or not significant) if they are serving as place holders.
5
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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
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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
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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) 2.050 x 103 2) 25.300 3) 0.00307
C. 534,675 rounded to 3 significant figures is
1) 535 2) 535,000 3) 5.35 x 105
4 33
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Independent Practice
•Worksheet
•Work alone or with a partner
•Perfect time for questions
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Significant Figures in Calculations & RoundingUnit 1: Measurement & Matter
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1. COMPUTE answer first!!!!
2. CHOOSE whether to round based on sig figs or decimal places
Rounding w/ Sig Figs
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CALCULATION RULES
• For Multiplication & Division
limiting term = one w/ the SMALLEST # of sig figs
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CALCULATION RULES
• Multiplication & Division
Round answer to the same number of sig figs as the answer with the fewest sig figs
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Example
4.56 x 1.4 = Round to 6.4 3 sig
figs2 sig figs
2 sig figs
6.384
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Example
1.234 x 3 = Round to 4 4 sig figs
1 sig fig
1 sig fig
3.702
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• For Addition & Subtraction
limiting term = one w/ the smallest number of DECIMAL PLACES
CALCULATION RULES
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• Addition & Subtraction
Round answer to the same number of decimal places as the measurement with the fewest decimal places
CALCULATION RULES
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12.161 + 3.12 =
Significant Figures in Calculations
Round to 15.283 decimal
places2 decimal
places 2 decimal places
15.281
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6.8 + 3 =
Significant Figures in Calculations
Round to 101 decimal
place0 decimal
places 0 decimal places
9.8
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Summary•Only as precise as your “weakest link”
▫The one w/ fewest sigs figs/decimal places
▫Multiplication/ Division-> sigs figs▫Addition/Subtraction -> decimal places
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1. 2.45 x 3.5
2. 8.315 ÷ 298
3. 135 x 246 x 0.000556 x 0.0998 x 155
4. 3.6x10-3 x 8.123
You Try….
8.6
0.0279286
0.029 or 2.9x10-2
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5. 12.11 + 18.0 + 1.013 =
6. 29.63 + 24.798 + 1.263 =
7. 1081 – 7.25 =
8. 8.445 x 105 – 9.44 x 102 =
You Try…
31.1
55.691074
8.44 x 105