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 Gimli Glider Mars Climate Orbiter $327.6 million
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?

7. 7 BASE SI Units Unit Name and Symbol Dimension Symbol
What does it measure?
Meter (m) L
Kilogram (kg) M
Second (s) T
Ampere (A) I
Kelvin (K) Θ
Mole (mol) N
Candela (cd) J

8. 7 BASE SI Units Unit Name and Symbol Dimension Symbol
What does it measure?
Meter (m) L
Length
Kilogram (kg) M
Mass
Second (s) T
Time
Ampere (A) I
Electric Current
Kelvin (K) Θ
Temperature
Mole (mol) N
Amount of substance
Candela (cd) J
Luminous Intensity

9. Other units are DERIVED units

10. 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)

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

12. Concept Check
What is the difference between base, derived and special units?

14. Metric Prefixes Metric Madness Metric is SI
yotta- (Y) septillion units
zetta- (Z) sextillion units
exa- (E) quintillion units
peta- (P) quadrillion units
tera- (T) trillion units
giga- (G) billion units
mega- (M) million units
kilo- (k) thousand units
hecto- (h) hundred units
deka- (da) ten units
BASIC UNIT
deci- (d) tenth units
centi- (c) hundredth units
milli- (m) thousandth units
micro- (µ) millionth units
nano- (n) billionth units
pico- (p) trillionth units
femto- (f) quadrillionth
atto- (a) quintillionth
zepto- (z) sextillionth
yocto- (y) septillionth
Metric Madness
Metric is SI
US is only industrialized country not using it.
We use an inferior system.

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

16. Metric System
Handouts metric mania

17. Scientific Notation
How long would it take to count to a million? How do you know?
Big and Small numbers in science.
Mass of Electron
Mass of Earth
Mass of Proton
Mass of Sun
Diameter of Atom
Size of Galaxy
Handout

18. 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
Determined via Avogadro’s number and the periodic table..

19. 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: ,450,000  x 107
7th power means move the decimal place right 7 places.
Example II:  x 10-4
The - 4th power means to move the decimal place to the left 4 places.

20. Exponent Rules
Rule 1
Example

21. Exponent Rules
Rule 2
Example

22. Exponent Rules
Rule 3
Proof from Rule 1:

23. Exponent Rules
Rule 4
Example

24. Why Scientific Notation is Easier
Example:
6,350,000,000 x 424,000,000 = 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

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

26. Two Videos
Scale of the Universe
Yakkos Univese

27. Dimensional Analysis
Rules for Converting Units 1) Units combine when multiplied just as an x 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).

28. 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:

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

30. 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 = Kilometers so we first convert the 10 miles into kilometers:

31. 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

32. 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 = Kilometers so we first convert the 60 miles into kilometers:

33. Handout on Unit Conversions

34. 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
Control: must use same basketball, drop from same height, on same surface.
IV is temp
DV is height of bounce

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

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

38. 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?

39. Percent Error Problems
1) Clyde Clumsy was directed to determine the mass of a 500g piece of metal. After diligently 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.

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

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

42. 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.

43. 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.
Any act of counting or defini

44. 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.

45. Reading a Meter Stick / Ruler

46. 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.

47. 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.

48. How can you check to see if a thermometer is accurate before you use it?
Why would you want to?
Put it in boiling water or ice water or another substance with a known physical property (boiling point).
It needs to be calibrated because if it is inaccurate all your data will be compromised.

49. Significant Figures Rules
All non-zero numbers are always significant (e.g )
All zeroes between non-zero numbers are significant (7007).
All zeroes both simultaneously to 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.

50. Number # of SigFigs Rule(s)
48,923
3.967
900.06
0.0004
8.1000
3,000,000
10.0

51. Number # of SigFigs Rule(s)
48,923 5 1
3.967 4
900.06
1,2,4
0.0004
1,4
8.1000
1,3 6
1,2,3,4
3,000,000
10.0 3
1,3,4

52. Sigfig Products and Quotients
When multiplying or dividing, the answer cannot have more significant figures than the term with the least number of significant figures.
For example 25.2 x = in a calculator.
The answer is 64.1 however.

53. Is this accurate?
× × 5 =

54. Is this accurate?
× × 5 =
There can only be ONE significant digit:
× × 5 = 20

55. Is this accurate?
× 4.6 =

56. Is this accurate?
× 4.6 =
× 4.6 = 0.020
The answer is NOT 0.02 because there must be 2 significant digits.

57. Sigfigs: Addition and Subtraction
In addition and subtraction the number of decimal places is what is important.
The answer cannot have more decimal places than the term with the least number.
= not
= WHY?

58. Is this correct? =

59. Is this correct? =
Round the result to the tens place:
= 1910

60. Sigfigs’s
HANDOUT

61. Statical Analysis > Sigfigs
Standard Deviation is a measure of how spread out numbers are.
Its symbol is σ (the Greek letter sigma)
The formula is easy: it is the square root of the Variance which is the average of the squared differences from the Mean.
In science there is no such thing as a measurement.
ALL MEASUREMENTS HAVE ERROR.
Any result given without a consideration of error is useless!

62. Standard Deviation (sample)
Calculate the mean or average of each data set. To do this, add up all the numbers in a data set and divide by the total number of pieces of data.  
Get the deviance of each piece of data by subtracting the mean from each number.
 Square each of the deviations.  
Add up all of the squared deviations.
Divide this number by one less than the number of items in the data set.
Calculate the square root of the resulting value. This is the sample standard deviation.

63. Standard Deviation Curve

64. The average height for adult men in the United States is about 70 inches, with a standard deviation of around 3 inches.
68% have a height within 3 inches of the mean (67–73 inches)
95% have a height within 6 inches of the mean (64–76 inches

65. Standard Deviation Problem