1. Chapter 2 Data Analysis p24-51

2. What is the Mass of the Sun? g
So how can we write this in a simpler way??

3. Purpose of Scientific Notation
Scientific notation was developed to solve the problem of writing very large and small numbers.
Numbers written in scientific notation have two parts: a stem, which is a number between 1 & 10, and a power of 10.
93,000,000 = 9.3 x 107
Stem
Power of 10

4. Purpose of Scientific Notation
Let’s take a closer look at the parts of a number written in scientific notation to see how it works.
93,000,000 = 9.3 x 107
Stem
The stem is always a number between 1 and 10. In this example, 9.3 is the stem and it is between 1 and 10.

5. Purpose of Scientific Notation
The power of ten has two parts. There is a base and there is an exponent
Exponent = 7
93,000,000 = 9.3 x 107
Base = 10
The base will always be 10.
The exponent in this example is 7.

6. Convert Standard Form to Scientific Notation
Write 8,760,000,000 in scientific notation.
Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. . .
8.76 is the Stem

7. Convert Standard Form to Scientific Notation
Write 8,760,000,000 in scientific notation.
Step 2: The number of places you moved the decimal will be the exponent on the power of 10 . .
9 places
8.76 is the Stem
10 9 is the Power of 10

8. Convert Standard Form to Scientific Notation
Write 8,760,000,000 in scientific notation.
Step 3: Write the number so it is the stem times the power of ten. . .
9 places
8.76 is the Stem
10 9 is the Power of 10
8.76 x = 8,760,000,000

9. Convert Standard Form to Scientific Notation
Write the following numbers in scientific notation.
660,000,000 = =
397 =
6.6 x 108
9.03 x 104
3.97 x 102

10. Convert Standard Form to Scientific Notation
Write in scientific notation.
Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. . .
4.82 is the Stem

11. Convert Standard Form to Scientific Notation
Write in scientific notation.
Step 2: The number of places you moved the decimal will be the exponent on the power of 10. The exponent will be negative because you started with a number less than 1. . .
9 places
4.82 is the Stem
10 -9 is the Power of 10

12. Convert Standard Form to Scientific Notation
Write in scientific notation.
Step 3: Write the number so it is the stem times the power of ten. . .
9 places
4.82 is the Stem
10 -9 is the Power of 10
4.82 x =

13. Convert Standard Form to Scientific Notation
Write the following numbers in scientific notation. = = =
5.43 x
7.4 x x

14. Convert Scientific Notation to Standard Form
Write x 109 in standard form.
The exponent tells us to move the decimal 9 places.
A positive exponent means the number is bigger than the stem. To make 1.98 bigger, we must move the decimal to the right.
x 10 9 . .
9 places
1.98 x 109 = 1,980,000,000

15. Convert Scientific Notation to Standard Form
Write the following numbers in standard form.
2.9 x 104 =
6.87 x 106 =
1.008 x 109 =
29,000
6,870,000
1,008,000,000

16. Convert Scientific Notation to Standard Form
Write x in standard form.
The exponent tells us to move the decimal 9 places.
A negative exponent means the number is smaller than the stem. To make 5.37 smaller, we must move the decimal to the left. . x .
9 places
5.37 x =

17. Convert Scientific Notation to Standard Form
Write the following numbers in standard form.
2.9 x 10-4 =
6.87 x 10-6 =
1.008 x 10-9 =

18. Why are measurement standards important?
What is a standard?
It is an exact quantity that people agree to use for comparison.
Why are measurement standards important?
A meter in the U.S. is the same as a meter in France.

19. Units for Measurement Used in Science
Length
Metric ruler:
Measured in meters (m)
Volume
Graduated cylinder:
Measured in liters (L)
Mass
Balance:
Measured in grams (g)
Temperature
Thermometer:
Measured in degrees Celsius (OC)

20. International Standard Prefixes (SI)
MUST KNOW:
Kilo = 1,000 or 103
Centi = .01 or 10-2
Milli = .001 or 10-3

21. Conversions WITHIN the Metric System
You can simply move the decimal point…
But you have to know how to move it.

22. METRIC UNIT CONVERSIONS
Move decimal 1 place to the right for each step.
BASE
Move decimal 1 place to the left for each step.

23. METRIC UNIT CONVERSIONS
Use this to remember the metric prefixes:
“King Henry Died Drinking Chocolate Milk”
The first letters represent the prefixes (kilo, hecto, deka, deci, centi, milli)

24. EXAMPLE
It is common for runners to do a “10K” run. This means they are running 10 kilometers. How many millimeters is that???
A lot!!!!!

25. Answer Look at the staircase graphic… Start on the prefix “kilo”
Move down the staircase 6 steps (don’t count the step you start on) to get to the prefix “milli”
This means you move the decimal point 6 places to the RIGHT
10 Kilometers is converted to 10,000,000 mm

26. Making Metric Conversions
Home
Make the following metric conversions.
1,000 grams = kg
500 mg = g
2.25 liters = ml
0.07 g = kg
1 kilometer = m
650 cm = m
0.30 kg = mg 1
0.5
2250
1000
6.5
300,000
Table

27. Making Metric Measurements - Length
Choose the most appropriate measure.
Length of a football field
1 km, m, 1,000 um, 10 cm, 100 mm
Length of a newborn baby
0.5 m, km, um, 5,000mm, 50 cm
Thickness of a sheet of paper
0.1 mm, cm, m, 1 km, 10 um

28. Making Metric Measurements - Mass
The following are approximations to help you get a feel for metric units of mass. We will deal only with the most common units.
1 kilogram  Just over 2 pounds
1 gram  Mass of a raisin
1 milligram  Mass of a grain of sand

29. Making Metric Measurements - Mass
Choose the most appropriate measure.
Mass of a nickel
50 g, 5 mg, kg, 5 g, 500 mg
Mass of an aspirin
500 mg, mg, g, 50 kg, 50 g
Mass of an average adult
700 kg, g, mg, 7,000 g, 70 kg
Mass of a baseball
400 mg, g, 4 kg, g, g

30. Making Metric Measurements - Volume
The following are approximations to help you get a feel for metric units of volume. We will deal only with the most common units.
1 liter  Just over 1 quart
1 milliliter  About 20 drops

31. Making Metric Measurements - Volume
Choose the most appropriate measure.
Volume of a car’s gas tank
50 l, 5 l, ml, 50 ml, 500 l
Volume of a teaspoon
0.5 l, ml, 5 l, 5 ml, ml
Volume of a can of soda
500 l, l, ml, ml, ml
Volume of a syringe
0.02 ml, ml, l, 2 l, 2 ml

32. Putting It All Together
prefix
symbol
unit
centi- c m
meter
(0.01)
hundredth of a meter
milli- L m
liter
(.001)
thousandth of a liter
kilo- k g
gram
(1000)
thousand grams

33. VII. The Temperature Scales
Kelvin Scale (K) SI Absolute temperature. Same units as Celsius but the freezing point of water is 273K, and the boiling point is 373K.
Celsius Scale ( ˚C) SI common temperature the freezing point of water is 0O C and the boiling point is 100O C.
Fahrenheit Scale (˚F) Used only in the U.S. Water freezing point 32˚F, and boiling point 212˚F.

34. Converting from Kelvin to Celsius
TC = TK – 273
ex. ? C = 52K
____˚C = 52K – 273
TK = TC
ex.?K = 70˚C
_____K = 70˚C + 273

35. Converting from Celsius to Fahrenheit
TF = 1.80(TC) + 32
Ex. 41˚C = ? ˚F
TF = 1.80 (41˚C) + 32
TF = __________ ˚F

36. Making Metric Measurements
Home
Name at least three benefits of the Metric System.
There is a consistent relationship between units - Prefixes stay the same, It’s easy to convert.
The whole world uses it.
The base units are used to “derive” all other units in the System International (SI)

37. Derived units are defined by a combination of base units.
Density = g/cm3

38. VII.
Density can be defined as the amount of matter present in a given volume of substance.
Density = mass/ volume

39. Practice
Mercury has a density of 13.6g/mL. What volume of mercury must be taken to obtain 225g of the metal?

40. IV. Accuracy and Precision
Compare and contrast accuracy /precision.
Accuracy- refers to how close a measured value is to an accepted value.
Precision – Refers to how close a series of measurements are to one another.

41. Accuracy vs Precision
Is the soda filling machine below accurate and/or precise?
This machine is precise.
It delivers the same amount of soda each time.
This machine is not accurate.
It is not putting 12 oz in each can.

42. Accuracy vs Precision
Is the soda filling machine below accurate and/or precise?
This machine is precise.
It delivers the same amount of soda each time.
This machine is accurate.
It is putting 12 oz in each can.

43. Accuracy and Precision cont…
The difference between an accepted value and an experimental value is the error.
The ratio of an error to the correct value, is percent error.

44. Formula for Percent Error
= Value accepted – Value experimental x 100%
Value accepted

45. Dimensional Analysis
A technique for converting from one unit to another

46. Beyond the metric System
If you need to convert to or from units that are NOT metric units, we use a unit conversion technique called “dimensional analysis”

47. Conversion Factors
In dimensional analysis, we make conversion factors into fractions that we will multiply by.
For example, one conversion factor is:
1 inch=2.54 cm
We can make (2) fractions out of this…
1 inch OR cm
2.54 cm inch

48. Which number goes on top and bottom in the conversion factor?
Usually…
The unit you WANT goes on TOP
The unit you want to CANCEL goes on BOTTOM

49. Dimensional Analysis EXAMPLE
A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES?
Start with the “given”
17.8 cm

50. Dimensional Analysis
A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES?
Multiply by the “conversion factor”
17.8 cm x inch =
2.54 cm

51. Dimensional Analysis
A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES?
Cross cancel “like” units
17.8 cm x inch
2.54 cm

52. Dimensional Analysis
A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES?
Do the math using the correct number of significant figures (based on given information)
17.8 cm x inch = inches
2.54 cm

53. Dimensional Analysis Example
A pencil is 8.1 inches, how many cm is it?
8.1 inches x cm = cm
1 inch
The unit we WANT is cm so we put 2.54 cm on
TOP of the conversion factor

54. Multi-Step Example
Sometimes, we must “string” several conversion factors together to get from one unit to another.
Ex.- Mr. Gray’s class is 55 minutes long. How many days long is this??!!

55. Multi-Step Example Need to go from min hrs days
55 min x 1 hr x day = days
60 min hrs
Note how “like” units can be
cross-canceled (canceled out)

56. Practice
Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case.
55min to hours
6.25km to miles
Apples cost $0.79 per pound. How much does 5.3 lb of apples cost?

57. Significant Figures
Significant figures include the number of all known digits reported in measurement plus one estimated digit.
Non-zero numbers are always significant
Zeros between non-zero #s are always significant
All final zeros to the right of the decimal place are significant

58. Significant rules cont.
4. Zeros that act as placeholders to the left of the decimal are not significant. Positive exponents in scientific notation are not significant.
5. Zeros that are to the right of the decimal are always significant. Negative exponents!
6. Counting numbers and defined constants have an infinite number of significant figures.