StatVignette03_Sig.Figs_v04_07_15_2020.pptx
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This document discusses the concept of significant figures and how to determine the number of significant figures in measurements and calculations. It defines significant figures as the "important digits" that indicate the precision of a measurement. Rules are provided for determining significant figures depending on leading or trailing zeros and whether the number is read from left to right or right to left. Examples demonstrate applying these rules and how to round final answers in calculations like addition, subtraction, multiplication and division based on the least precise measurement used. The key takeaway is that significant figures convey precision and final answers should not be more precise than the least precise input.
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FinalAssignment(22marks)
Eachquestionisworth1mark.Youmustshowallyourworktoobtainfullmarks.
Markswillbedeductedfornoworkshown.
1. Whathappenstothegraphof 1iftheequationischangedto 1?
2. Thegraphofy=√ undergoesthetransformation(x,y) ( 3,2 5)x y .Whatistheresulting
equation?
3. Determinetheequationofthepolynomialinfactoredformoftheleastdegreethatissymmetric
tothey‐axis,touchesbutdoesnotgothroughthex‐axisat(3,0),andhasP(0)=27
4. Determinethemeasureofallanglesthatsatisfythefollowingconditions.Giveexactanswers.
csc =2inthedomain 2 2
Page2of7
5. Solve:3 cos ² 8 cos 4 0,overallrealnumbers
6. Usefactoringtohelptoproveeachidentityforallpermissiblevaluesofx.Muststate
restrictionsoverallrealnumbers.
2sin sin tan
cos sin cos
x x x
x x x
Page3of7
7. Inapopulationofmoths,78mothsincreaseto1000mothsin40weeks.Whatisthe
doublingtimeforthispopulationofmoths?
8. Solvethefollowingequation:log 3 log 5 2
9. Solveforxalgebraically:5 2 3 .Stateyouranswertothenearesthundredth.
10. Aradioactivesubstancehasahalf‐lifeof92hours.If48gwerepresentinitially,howlongwillit
takeforthesubstancetodecayto3g?Showalgebraically.
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11. Giventhefollowingtwofunctions √ 1and 1,evaluate
3 .
12. Asampleof5peopleisselectedfrom3smokersand12non‐smokers.Inhowmanywayscan
the5peoplebeselected?
13. Giventhefunctions 7 and √ ,determineanexplicitequationfor
,thenstateitsdomain.
14. Determinethe4thtermof 3 2 .
15. Solvebyalgebra√13 1 0
Page5of7
16. Determinethedomain,range,andinterceptsof 2√4 2 3.Graphthefunction.
17. Forthegraphof ,determineannon‐permissiblevaluesof ,writethecoordinatesof
anyholeandwritetheequationofanyverticalasymptote.
Page6of7
18. Sketchthegraphof 3 4 5.Statethedomain,range,andequationofthe
horizontalasymptote.
19. Supposeyouplayagameofcardsinwhichonly5cardsaredealtfromastandard52deck.How
manywaysaretheretoobtainatleast3cardsofthesamesuit?Anexampleofahandthat
containsatleast3cardsofthesamesuitis4heartsand1club.
20. Given ,determine ,theinverseof .
Page7of7
21. Considerthedigits0,2,4,5,6,8.Howmany3‐digitevennumberslessthan700canbe
formedifrepetitionofdigitsisnotallowed?Note:thefirstdigitcannotbezero.
22. If and 2 3,determinethevalueof 1 .
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- Extensive properties depend on amount, while intensive properties do not.
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3. Geometry helps describe real-world objects by classifying triangles based on their angles and sides, and using angle relationships and equations to determine measures of angles in triangular objects.
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1. The spatial extent and timing of the 2012-2017 drought across California and how it compares to historical droughts.
2. How precipitation was measured using tools like snow pillows and GPS reflection to track snow levels.
3. The societal impacts of the drought, including mandatory water rationing and transformations to California's landscape and economy.
Presentation: Unit 3 background information
Presentation: Unit 3 background informationSERC at Carleton CollegeThis document discusses using GPS vertical positioning to monitor groundwater storage changes. It begins by explaining that groundwater mining is a global problem, and that extracting groundwater causes the land surface to rise as the total water storage decreases. It then discusses how GPS networks can detect these vertical position changes at the sub-centimeter level on a daily basis, allowing monitoring of seasonal water changes. Finally, it notes that long-term groundwater pumping can lead to both reversible and irreversible subsidence exceeding several meters, and provides examples from California's Central Valley.
Presentation: Unit 2 Measuring Groundwater Background Information
Presentation: Unit 2 Measuring Groundwater Background InformationSERC at Carleton CollegeThis document discusses methods for characterizing groundwater storage, including traditional well measurements and satellite-based GRACE observations. It defines terrestrial water storage as all water on the land surface, and explains that groundwater often dominates variations in storage. Wells measure groundwater levels, with changes indicating replenishment or depletion over time. GRACE satellites detect changes in mass distribution and associated gravity field variations to infer changes in total water storage, including groundwater, at coarse spatial scales. The document provides examples of using both approaches to monitor groundwater in key aquifers.
Introduction to GPS presentation
Introduction to GPS presentationSERC at Carleton CollegeThe document provides an introduction to GPS/GNSS basics, including:
- GPS uses 24-32 satellites in medium Earth orbit that transmit positioning and timing data. Receivers need signals from 4 satellites to calculate a 3D location.
- Ground control stations monitor the satellites and send updates to synchronize their atomic clocks and orbital data.
- GPS determines location by calculating distances to satellites using signal transmission times and triangulating the receiver's position.
- Precise GPS uses permanent stations with stable monuments to collect data over many years, achieving sub-centimeter positioning and millimeter-per-year velocity estimates.
StatVignette04_Distribution_v04_07_15_2020.pptx
StatVignette04_Distribution_v04_07_15_2020.pptxSERC at Carleton CollegeThe document discusses the normal distribution, which is a specific type of probability distribution where the mean, median, and mode are centered around the middle. It depends on the mean and standard deviation. The document describes the key elements needed to construct a normal distribution like the mean and standard deviation. It also provides an example of calculating the percentage of yearly pizza sales that would be less than $90,000 given the normal distribution of annual sales has a mean of $120,000 and standard deviation of $30,000. Approximately 16% of yearly sales would be less than $90,000.
Cretaceous Coatlines and Modern Voting Patterns Presentation
Cretaceous Coatlines and Modern Voting Patterns PresentationSERC at Carleton College
Presentation: Unit 1 Introduction to the hydrological cycle
Presentation: Unit 1 Introduction to the hydrological cycleSERC at Carleton College
KSKL_Chapter 4_ Chem Properties of Soils.pptx
KSKL_Chapter 4_ Chem Properties of Soils.pptxSERC at Carleton College
Presentation: Unit 3 background information
Presentation: Unit 3 background informationSERC at Carleton College
Presentation: Unit 2 Measuring Groundwater Background Information
Presentation: Unit 2 Measuring Groundwater Background InformationSERC at Carleton College
StatVignette04_Distribution_v04_07_15_2020.pptx
StatVignette04_Distribution_v04_07_15_2020.pptxSERC at Carleton College
StatVignette03_Sig.Figs_v04_07_15_2020.pptx
- 2. Learning Objectives After completing this vignette, a student should be able to: • Apply the rules of significant figures for a measurement • Express numerical values with the correct number of significant figures using a mnemonic device (the "Atlantic Pacific Rule") 2 • Determine the number of significant figures from a given value or mathematical operation Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.
- 3. How tall is Emerson the Giraffe?
- 4. What if you use a different ruler to measure Emerson? Does it make a difference?
- 5. What are Significant Figures? 1 • The “important digits” of a number • They tell us about the precision of the underlying measurement • Important in the final answer
- 6. The precision of your measuring device impacts how many significant figures should be reported. Ruler 1: 5.50 m Ruler 2: 5.5 m
- 7. Leading and Trailing Zeros 1 Leading Zeros to the left of the first nonzero digit are not significant Trailing If the 1st digit is > 1, then zeros to the right of the decimal point are significant If a digit is < 1, then only the zeros at the end and the zeros in-between non- zeros are significant 0.000205 3 Sig Figs 60.090 5 Sig Figs 0.04050 4 Sig Figs
- 8. General Rules 1 • All leading non-zero digits are significant, if there are no digits after a decimal point. • Zeros between nonzero digits are significant • Leading zeros are never significant • Trailing zeros in the decimal portion are significant 6500 9004 0.0064 0.03400 Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.
- 9. How many Sig. Figs are present? 6500 = ? 9004 = ? 0.0064 = ? 0.03400 = ?
- 10. Here are the answers! 6500 = 2 9004 = 4 0.0064 = 2 0.03400 = 4
- 11. Atlantic – Pacific Rule 2 Read values from left to right. All numbers from the first non- zero are significant → 1.270 4 Sig. Figs! Read values from right to left All numbers from the first non-zero are significant 12700 ← 3 Sig. Figs! For counting significant figures Pacific Decimal is Present Atlantic Decimal is Absent Stone, Helen M. Atlantic-Pacific sig figs. Journal of Chemical Education 66.10 (1989): 829. https://www.sas.upenn.edu/~dbalmer/eportfolio/sigfig_article.pdf
- 12. Decimal Precision: When to round 1st Rule: Round up the digit that follow if the first digit in front is less than 5. 17.53 rounds off to 17.5 17.5 = 3 Significant Figures 2nd Rule: If the digit is equal or greater than 5, the digit is rounded up by 1. 17.55 rounds up to 17.6 17.6 = 3 significant Figures
- 13. Addition/Subtraction 1 • Wait to round until the end of the calculation • Round final answer to match the number with the fewest decimal significant figures 10. 1 ← 1 decimal place + 7. 43 ← 2 decimal places 17. 53 17.5 ← Final number 3 Sig. Figs (Rounded to 1 decimal place) Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.
- 14. Multiplication/Division 1 • Wait to round until the end of the calculation • Round final answer to match the number with the fewest decimal significant figures 1.5 ← ? Sig. Figs 4.93 ← ? Sig. Figs x 6.027 ← ? Sig. Figs 45 ← ? Sig. Figs Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.
- 15. Multiplication/Division 1 • Wait to round until the end of the calculation • Round final answer to match the number with the fewest decimal significant figures 1.5 ← 2 Sig. Figs 4.93 ← 3 Sig. Figs x 6.027 ← 4 Sig. Figs 44.5697 ← Round 45 ← 2 Sig. Figs Chang, R and Goldsby, K. (2013). Chemistry. 11th ed. McGraw-Hill Education, pp.19-23.
- 20. Take Home Messages! Significant figures are important - they tell us about the precision of the underlying measurement Final answer should not be more precise than the least precise measurement used in the calculation.