1 / 67

Scientific Numeracy

Scientific Numeracy. What is the current temperature of the room?. 22 72 295. What is the current temperature of the room?. 22°F = 72°F = 295°K. The temperature is 72 feet in here. Mars Climate Orbiter. Mars Climate Orbiter $327.6 million. Gimli Glider. Space errors handout. Activity.

troy-contreras
Download Presentation

Scientific Numeracy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Scientific Numeracy

  2. What is the current temperature of the room? • 22 • 72 • 295

  3. What is the current temperature of the room? 22°F = 72°F = 295°K

  4. The temperature is 72 feet in here.

  5. Mars Climate Orbiter Mars Climate Orbiter $327.6 million Gimli Glider Space errors handout

  6. Activity • Have a large footed and small footed student measure the length of the room. • How many feet long is the room? • Who tells a ruler how long to be? • http://en.wikipedia.org/wiki/Foot_(unit)

  7. Other units are DERIVED units

  8. Some units get special names! • A NEWTON is the force required to accelerate a one kilogram object at a rate of one meter per second squared. • Instead of writing (kg)(m)/(s2) physicists just use Newton (N) instead. • Thus 1N = 1(kg)(m)/(s2)

  9. Pressure = Force/Area • Force = (kg)(m)/(s2) • Area = m2 • Units for pressure = = A Pascal

  10. Concept Check • What is the difference between base, derived and special units? • http://www.physics.nist.gov/cuu/Units/units.html

  11. Metric Prefixes • Metric Madness • Metric is SI • US is only industrialized country not using it. • We use an inferior system. • yotta- (Y) 1024 1 septillion units • zetta- (Z) 1021 1 sextillion units • exa- (E) 1018 1 quintillion units • peta- (P) 1015 1 quadrillion units • tera- (T) 1012 1 trillion units • giga- (G) 109 1 billion units • mega- (M) 106 1 million units • kilo- (k) 103 1 thousand units • hecto- (h) 102 1 hundred units • deka- (da) 10 1 ten units • BASIC UNIT • deci- (d) 10-1 1 tenth units • centi- (c) 10-2 1 hundredth units • milli- (m) 10-3 1 thousandth units • micro- (µ) 10-6 1 millionth units • nano- (n) 10-9 1 billionth units • pico- (p) 10-12 1 trillionth units • femto- (f) 10-15 1 quadrillionth • atto- (a) 10-18 1 quintillionth • zepto- (z) 10-21 1 sextillionth • yocto- (y) 10-24 1 septillionth

  12. Conversion is Easier Three Yards into Feet Three Meters into Centimeters 3 goes to 300 Decimal moves two places • 3 goes to 36 • We have a new number. Just moves the decimal to the right two places. Much more convenient especially when dealing with the very large and small numbers of science.

  13. Metric System Handouts metric mania

  14. Scientific Notation • How long would it take to count to a million? How do you know? • Big and Small numbers in science. Handout

  15. H2O is a Compound • One glass of water has 8.36 x 1024 molecules of H2O inside it. 8,360,000,000,000,000,000,000,000

  16. Exponential Numbers: Powers of 10 • Any Number written as A x 10B • A is usually between 1 and 10 • B is usually an integer. • Example I: 93,450,000  9.345 x 107 • 7th power means move the decimal place right 7 places. • Example II: 0.0001728  1.728 x 10-4 • The - 4th power means to move the decimal place to the left 4 places.

  17. Exponent Rules • Rule 1 • Example

  18. Exponent Rules • Rule 2 • Example

  19. Exponent Rules • Rule 3 • Proof from Rule 1:

  20. Exponent Rules • Rule 4 • Example

  21. Why Scientific Notation is Easier Example: 6,350,000,000 x 424,000,000 = 6.35 x10^9 x 4.24x10^8. • Using rule one we add the exponents (8+9) and multiply the leading numbers (6.35 x 4.24). This is an easier calculation to perform. • Answer = (6.35 x 4.24) x 10^17

  22. Addition and Subtraction • Convert to same power. • Keep the exponent. • Add the leading numbers

  23. Two Videos • Scale of the Universe • YakkosUnivese

  24. Dimensional Analysis Rules for Converting Units 1) Units combine when multiplied just as anx does. 7cm · 5cm = 35cm2 (7x · 5x = 35x2) 7cm · 2cm · 3cm = 42cm3 (7x ·2x · 3x = 42x3) 2) Units cancel in division just as x or unknown number would. 10cm / 5cm = 2(10x / 5x = 2) 8cm2/ 2cm = 4cm (8x2 / 2x = 4x) 3) Units stay the same in addition and subtraction. 10cm + 5cm = 15(10x + 5x = 15x) 8cm - 2cm = 6cm (8x - 2x = 6x) 4) You cannot subtract or add units with different powers 10cm2+ 5cm =10cm2 + 5cm just as 10x2 + 5x = 10x2 + 5x Unit Conversion Factor: essentially a ratio that is equal to one. • To convert between different units we use a conversion factor like the two above. When you multiple a number by a conversion factor, you are not changing its value as you are essentially multiplying it by 1 and any number times 1 is equal to itself (245 · 1 = 245).

  25. Problem 1 (Level 2) • Problem 1: Convert 442 seconds into minutes. • Solution: First we must find a Conversion Factor and set it up so the units cancel. A conversion factor is essentially equal to One. • Conversion Factor:60 seconds = 1 minute:

  26. The seconds cancel and we are left with 442 x 60 (minutes)

  27. Problem 2 (Level 2) • Problem 1: Convert 10 miles into centimeters. • Solution: First we must find a Conversion Factor and set it up so the units cancel. A conversion factor is essentially equal to One. • Conversion Factor: 1 Mile = 1.609 Kilometers so we first convert the 10 miles into kilometers:

  28. 1.609 kilometers = 1 mile is the conversion factor • The units of miles cancel in division. • Now we convert kilometers to meters and then meters to centimeters

  29. Problem 3 (level II) • Problem 2: Convert 60 milers per hour into meters per second. • Solution: We must convert both miles into meters and hours into seconds. • Conversion Factor: 1 Mile = 1.609 Kilometers so we first convert the 60 miles into kilometers:

  30. Handout on Unit Conversions

  31. How Does Temperature Affect the Height of a Basketball’s bounce? • Importance of Control • Independent vs Dependent Variable • How are they graphed? • IV: X-axis • DV:Y-axis

  32. Accuracy vs Precision Accuracy: how close a set of measurements is to the actual value. Precision: how close a set of measurements are to one another.

  33. Percent Error A percent error tells you how far off an experimental value is from the currently accepted or theoretical value.

  34. Percent Error Samples • The accepted value for the density of gold is 19.3g/cm3. A student working in the lab measured it to be 18.7g/cm3. What was the student’s percent error? • A student measures the acceleration due to gravity on earth to be 9.86m/s2 whereas the currently accepted value is 9.8m/s2. How far off was this student?

  35. Percent Error Problems 1) Clyde Clumsy was directed to determine the mass of a 500g piece of metal. Afterdiligently goofing off for ten minutes, he quickly weighed the object and reported 458g. 2) Willomina Witty was assigned to determine the density of a sample of nickel metal. When she finished, she reported the density of nickel as 5.59 g/ml. However, her textbook reported the density of nickel to be 6.44 g/ml. 3) An experiment to determine the volume of a "mole" of a gas was assigned to Barry Bungleditup. He didn't read the experiment carefully and concluded the volume was 18.7 liters when he should have obtained 22.4 liters. 4) A student should have received a 93 for a grade but Mr. Sapone accidentally (Scouts honor!) put in an 83 instead. Calculate Mr. Sapone’s error.

  36. Correlation ≠ Causation • All we have to do to stop global warming is become pirates!

  37. Measurements & Uncertainty • Suppose I ask you to measure the length of a desk with a meter stick. • You tell me it is 0.756563874 meters. • Should I applaud you for your high level of precision and accuracy?

  38. Yo mama so stupid she tried to climb Mountain Dew • Did you really read the meter stick with your naked eye to a billionth of a meter? • Your naked eye is not that precise and your value is suspect.

  39. Significant Figures • Important because of Measured vs. known numbers. • Measured: the length of a desk. • Known Number: the number of desks in this room. (counting or by definition) • Think of some other examples.

  40. Significant Figures • Sigfigs tell us that the result of any experiment cannot be more accurate than the data used. • Sigfigs let readers know the accuracy you used in an experiment.

  41. Reading a Meter Stick / Ruler

  42. The Significant Figures of a measured value include those numbers directly readable from a measuring device plus one doubtful figure. • Calculators make errors since they assume all numbers are known.

  43. You must stick with what is known and then include ONE doubtful number. • Just because a device works does not mean it is accurate. It must be CALIBRATED. Calibrate: (1) mark an instrument with a standard scale of readings. (2) correlate the readings of an instrument with those of a standard in order to check the instrument's accuracy.

  44. How can you check to see if a thermometer is accurate before you use it? • Why would you want to?

  45. Significant Figures Rules • All non-zero numbers are always significant (e.g. 123456789) • All zeroes between non-zero numbers are significant (7007). • All zeroes both simultaneouslyto the right of a decimal point and at the end of a number are significant. (.007 has 1 sf and 700 = 1 but 7.00 = 3) • All zeroes left of a decimal point in a number > or = to 10 with a decimal point are significant. (700.4 = 4 sf) To check #3 and #4 write the number in scientific notation. If you can get rid of the zeroes they are not significant.

More Related