1. Science Math

2. OBJECTIVES Precision VS Accuracy Significant Figures
Scientific Notation
Metric Conversions
Factor Label Method
Temperature Conversions

3. DUCK QUESTIONS

4. TIP: Accuracy = Actual What is Accuracy?
DEF: The accuracy of a measurement is how close a result comes to the true measurement.
TIP: Accuracy = Actual

5. In the picture you see 4 darts are all close to the bulls eye but not to each other.
They are ACCURATE because they are close

6. What is Precision?
Precision is how well the values agree with each other in multiple tests.

7. Precision
The 4 darts are not close to the bulls eye BUT they are all very close to each other.

8. ACCURATE AND PRECISE
DARTS ARE ALL ACCURATE – because they are all in the bullseye
DARTS ARE ALL PRECISE –
Because they are all very close to EACH OTHER

9. ACCURATE AND PRECISE
Measurements can most definitely be accurate and precise! This simply means that ALL of your measurements are close to the “correct” or “actual” measurement.

11. Accuracy VS Precision

12. HW
Accuracy and Precision worksheet

14. Accuracy Set up a chart Put trials in TRIAL LENGTH 1 12.54 2 12.57 3
12.52 4
12.53 5
12.55

15. Accuracy Set up a chart Put trials in, find the MEAN (average) TRIAL
LENGTH 1
12.54 2
12.57 3
12.52 4
12.53 5
12.55
MEAN (average)

16. Accuracy Set up a chart Put trials in, find the MEAN (average)
Take the highest value and subtract the MEAN
TRIAL
LENGTH 1
12.54 2
12.57 3
12.52 4
12.53 5
12.55
MEAN (average)
12.57 – = .03

17. Accuracy Set up a chart Put trials in, find the MEAN (average)
Take the lowest value and subtract the MEAN
TRIAL
LENGTH 1
12.54 2
12.57 3
12.52 4
12.53 5
12.55
MEAN (average)
12.52 – = .02

18. Accuracy .03+.02 = .05 .05 +/- Uncertainty Set up a chart
Put trials in, find the MEAN (average)
Take the lowest value and subtract the MEAN
Determine uncertainty interval
= .05
.05 +/- Uncertainty
TRIAL
LENGTH 1
12.54 2
12.57 3
12.52 4
12.53 5
12.55
MEAN (average)

19. Percent Error
Percent Error is a way for scientists to express their uncertainty and error in measurement by giving a percent error.

20. Defined
% error = actual value-measured value X100
Actual value

22. Percent Error

23. OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures
Scientific Notation
Metric Conversions
Factor Label Method
Temperature Conversions

24. 2.6 Rounding Off Numbers
Often when doing arithmetic on a pocket calculator, the answer is displayed with more significant figures than are really justified.
How do you decide how many digits to keep?
Simple rules exist to tell you how.
Chapter Two

25. Once you decide how many digits to retain, the rules for rounding off numbers are straightforward:
RULE 1. If the first digit you remove is 4 or less, drop it and all following digits becomes 2.4 when rounded off to two significant figures because the first dropped digit (a 2) is 4 or less.
RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept is 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater.
If a calculation has several steps, it is best to round off at the end.
Chapter Two

26. Practice Rule #2 Rounding
Make the following into a 3 Sig Fig number
Your Final number must be of the same value as the number you started with,
129,000 and not 129
1.5587
1367
128,522
106
1.56
.00374
1370
129,000
1.67 106

27. Examples of Rounding For example you want a 4 Sig Fig number
0 is dropped, it is <5
8 is dropped, it is >5; Note you must include the 0’s
5 is dropped it is = 5; note you need a 4 Sig Fig
780,582
1999.5
4965
780,600
2000.

28. RULE 1. In carrying out a multiplication or division, the answer cannot have more significant figures than either of the original numbers.
Chapter Two

29. RULE 2. In carrying out an addition or subtraction, the answer cannot have more digits after the decimal point than either of the original numbers.
Chapter Two

30. Multiplication and division
32.27  1.54 =
3.68  =
1.750  =
3.2650106  =  107
6.0221023  1.66110-24 =
49.7
46.4
.05985
1.586 107
1.000

31. Addition/Subtraction ‑

32. Addition and Subtraction
Look for the last important digit
.71
82000 .1
= .713 = =
10 – =
__ ___ __

33. OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures
Scientific Notation
Metric Conversions
Factor Label Method
Temperature Conversions

34. Significant Figures
When using our calculators we must determine the correct answer; our calculators are mindless drones and don’t know the correct answer.
Chapter Two

35. Significant Figures There are 2 different types of numbers Exact
Measured

36. Exact Exact numbers are infinitely important
A. Exact numbers are obtained by:
1. counting
2. definition

37. EXAMPLES: Exact Numbers
Counting objects are always exact 2 soccer balls 4 pizzas
Exact relationships, predefined values, not measured 1 foot = 12 inches 1 meter = 100 cm
For instance is 1 foot = inches? No
1 ft is EXACTLY 12 inches.

38. Measured (Inexact) Measured numbers are obtained by
1. using a measuring tool
Measured number = they are measured with a measuring device so these numbers have ERROR.

39. Example: example: any measurement.
If I quickly measure the width of a piece of notebook paper, I might get 220 mm (2 significant figures). If I am more precise, I might get 216 mm (3 significant figures). An even more precise measurement would be mm (4 significant figures).

40. Remember Exact numbers you get by counting and definition.
Inexact numbers you get by MEASUREMENT

41. QUESTION Check… do in notes
Classify each of the following as an exact or a
measured number.
1 yard = 3 feet
The diameter of a red blood cell is 6 x 10-4 cm.
There are 6 hats on the shelf.
Gold melts at 1064°C.

42. SOLUTION 1 yard = 3 feet : EXACT: This is a defined relationship.
2. The diameter of a red blood cell is 6 x 10-4 cm.
MEASURED: A measuring tool is used to determine length.
3. There are 6 hats on the shelf.
EXACT: The number of hats is obtained by counting.
Gold melts at 1064°C.
MEASURED: A measuring tool is required.

43. QUESTION Check A. Exact numbers are obtained by
1. using a measuring tool
2. counting
3. definition
B. Measured numbers are obtained by

44. Solution 2. counting 3. definition B. Measured numbers are obtained by
A. Exact numbers are obtained by
2. counting
3. definition
B. Measured numbers are obtained by
1. using a measuring tool

45. Measured numbers in an answer that matter for reporting.
Significant Figures
Measured numbers in an answer that matter for reporting.
Meant to make writing answers EASY!
VIDEO

46. RULES

47. ALL NON ZERO’S ARE SIGNIFICANT
Rule #1
ALL NON ZERO’S ARE SIGNIFICANT

48. Zeros in between significant digits are always significant.
RULE 2.
Zeros in between significant digits are always significant.
Thus, g has five significant figures.

49. RULE 2B.
Zeros at the beginning of a number are not significant; they act only to locate the decimal point.
Thus, cm has three significant figures, and mL has four.

50. RULE 3.
Zeros at the end of a number and after the decimal point are significant.
It is assumed that these zeros would not be shown unless they were significant m has six significant figures. If the value were known to only four significant figures, we would write m.

51. VIDEO
Use the rules! Everytime!

52. Practice Rules ; Zeros – in your notebook6 3 5 2 4
All digits count
Leading 0’s don’t
Trailing 0’s do
0’s count in decimal form
0’s don’t count w/o decimal
0’s between digits count as well as trailing in decimal form
48000.
48000
3.982106

53. How many significant figures are in each of the following?1)
4 significant figures 2)
5 significant figures 3)
4 significant figures
4) 210
2 significant figures
5) 200 students
1 significant figures
1 significant figures
6) 3000

54. HOMEWORK : ID SIG FIGS
Practice !
Practice!
Chapter Two

56. ADD AND SUBTRACT SIG FIGS!
Add and subtract accordingly – always use the LEAST AMOUNT OF SIGNIFICANT FIGURES AFTER THE DECIMAL!

57. Using Significant Figures in Calculations
Addition and Subtraction
Line up the decimals.
Add or subtract.
Round off to first full column.
= ?
= 38.4 or three significant fingures

58. EXAMPLE
g g g ______________________ Final Answer

59. HOMEWORK : ADD AND SUBTRACT
Practice !
Practice!
Chapter Two

60. MULTIPLY AND DIVIDE!
YEAH!

61. Using Significant Figures in Calculations
Multiplication and Division
Do the multiplication or division.
Round answer off to the same number of significant figures as the least number in the data.
(23.345)(14.5)(0.523) = ?
= 177 or three significant figures

62. DO HW SHEET! MULTIPLY AND DIVIDE
Practice !
Practice!

64. OBJECTIVES Precision VS Accuracy Significant Figures
Scientific Notation 1
Metric Conversions
Factor Label Method
Temperature Conversions

65. DO NOW!
Put 215 into scientific notation

66. 2.5 Scientific Notation
Scientific notation is a convenient way to write a very small or a very large number.
Numbers are written as a product of a number between 1 and 10, times the number 10 raised to power.
215 is written in scientific notation as:
215 = 2.15 x 100 = 2.15 x (10 x 10) = 2.15 x 102
Chapter Two

67. Scientific Notation
Scientists have developed a shorter method to express very large numbers.
This method is called scientific notation.
Scientific Notation is based on powers of the base number 10.

68. UNDERSTANDING SCIENTIFIC NOTATION

69. Scientific Notation
The number 145,000,000,000 in scientific notation is written as :
1.45 X 1011
The first number 1.45 is called the coefficient. It must be greater than or equal to 1 and less than 10.
The second number is called the base . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.45 x 1011 the number 11 is referred to as the exponent or power of ten.

70. To write a number in scientific notation:
If the number 123,000,000,000
Put the decimal after the first digit and drop the zeroes.
The coefficient will be 1.23
To find the exponent count the number of places from the decimal to the end of the number.
In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as:

71. ANSWER
1.23 X 10 11

72. King Henry Doesn’t Usually Drink Chocolate Milk
Kilo Hecto Deka UNIT Deci Centi Milli 1,
If you move LEFT from the decimal exponent goes UP
IF you move RIGHT from the decimal exponent goes DOWN

73. Scientific Notation
VIDEO
Worksheet
Fix Incorrect

74. Operations w scientific notation

75. Exponent Rules To multiply exponents = add exponent
To Divide exponents = subtract exponent
VIDEO

76. DO WORKSHEET
answers

77. OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures
Scientific Notation
Metric Conversions
Factor Label Method
Temperature Conversions

78. METRIC SYSTEM What everyone else in the world uses.
Based on multiples of 10.
Called the “International System of Units” or SI for short.

79. Who uses it?
Not Metric ; Liberia, Burma and the United States (black)

80. Metric System
The United States is the only industrialized country that does not use the metric system as its official system of measurement, although the metric system has been officially sanctioned for use here since 1866.

81. Measurement in Chemistry
Length Mass Volume Time
meter gram Liter second
Km=1000m Kg=1000g KL=1000L 1min=60sec
100cm=1m 1000mg=1 g 1000mL=1L 60min=1hr
1000mm=1m
SI System
Foot pound gallon second
British
12in=1ft 16oz=1 lb 4qt=1gal (same)
3ft=1yd 2000 lb=1 ton 2pts=1qt
5280ft=1mile

82. Metric to Metric Conversion
VIDEO

83. King Henry Doesn’t Usually Drink Chocolate Milk
1,000 Kilo
Hecto
Deka
UNIT
Deci
Centi
Milli

84. Do Practice Problems http://sciencespot.net/Media/metriccnvsn2.pdf
Wksht / answers

86. OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures
Scientific Notation
Metric Conversions
Factor Label Method
Temperature Conversions

87. SI Prefixes Multiple Prefix Symbol 106 mega M 103 kilo k 10-1 deci D
10-2
centi C
10-3
milli m
10-6
micro
10-9
nano n
10-12
pico p 2

88. Relationships of Some U.S. and Metric Units
Length
Mass
Volume
1 in = 2.54 cm
1 lb = kg
1 qt = L
1 yd = m
1 lb = 16 oz
4 qt = 1 gal
1 mi = km
1 oz = g
1 mi = 5280 ft
1 L = 1.06 qt
1 lb = 454 g 2

89. One Step Conversions

90. Feet to Inches So using that set up how many inches in 3 feet?
Hours in a day?
Feet in a mile?

91. Multiple Step Conversions

92. Factor Label Method
How many Years have you been alive? Days? Seconds?

93. Units: Dimensional Analysis
The ratio (3 feet/1 yard) is called a conversion factor. 2

94. TIPS
1. Start simple. 2. Write units with your numbers ALWAYS! 3. Go step by step. 4. Check your conversion factors. 5. Pinpoint what the question is asking 6. Is your answer logical? 7. Practice, practice, practice.

95. Worksheet
VIDEO
Video

97. OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures
Scientific Notation
Metric Conversions
Factor Label Method
Temperature Conversions

98. Temperature
The Fahrenheit scale is at present the common temperature scale in the United States.
The conversion of Fahrenheit to Celsius, and vice versa, can be accomplished with the following formulas:
C to F : C 9/5 +32 = F
F to C : (F-32) 5/9 = C 2

100. Figure 1.23: Comparison of Temperature Scales

101. Temperature
The Celsius scale (formerly the Centigrade scale) is the temperature scale in general scientific use.
However, the SI base unit of temperature is the kelvin (K), a unit based on the absolute temperature scale.
The conversion from Celsius to Kelvin is simple since the two scales are simply offset by o. 2