1. Science Math

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

3. DO NOW!
Explain the difference between accuracy and precision.

4. DUCK QUESTIONS

5. 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

6. 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

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

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

9. 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

10. 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.

12. Accuracy VS Precision

13. HW
Accuracy and Precision worksheet

15. Use the following words to describe each (2 labels each) Accurate/Inaccurate/Precise/Imprecise

16. HELLO!
WARM UP
Accuracy – how close your measurement is to the CORRECT value.
Precision is how CONSISTENT your measurements are.

17. What is accurate?

18. Degree of Accuracy Example:
Accuracy depends on the instrument we are measuring with. But as a general rule:
The degree of accuracy is half a unit each side of the unit of measure
Example:
                                                                                   
When an instrument measures in "1"s  any value between 6½ and 7½ is measured as "7"

19. Uncertainty – all measurements have uncertainty… +/-
Set up a chart
Put trials in
TRIAL
LENGTH 1
12.54 2
12.57 3
12.52 4
12.53 5
12.55

20. MEAN means AVERAGE 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)

21.  All measurements have a degree of uncertainty regardless of precision and accuracy. 
Set up a chart
Put trials in, find the MEAN (average)
Take the highest value and subtract the lowest value (RANGE) then divide by 2 for Uncertainty in measurement.
TRIAL
LENGTH 1
12.54 2
12.57 3
12.52 4
12.53 5
12.55
MEAN (average)
12.57 – = .05
.05 / 2 = /- uncertainty

22. What is precise?
We will use % Error to identify precision.

23. Percent Error
Percent Error is a way for scientists to express their uncertainty and error in measurement by giving a percent error.
Kind of like the possible percent amount you may be wrong.

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

25. Percent Error
VIDEO
REAL WORLD APPLICATION

26. % ERROR
Actual – Measured Actual
X = % error

27. Percent Error

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

29. 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

30. VIDEO Grab your white boards – we are going to make sure you REMEMBER how to round correctly.

31. Round 286 to the nearest TEN
Circle the tens spot – use the one to the right to determine if the ten spot goes up or down…
It’s a 6 ….. SO it rounds up to
290

32. Try this one :
Round 387,907 to the nearest hundred thousand:
387,907
Now round it to the nearest hundred…

33. 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

34. ROUNDING to SIGNIFICANT FIGURES is a way that scientists keep their numbers in check. It is a way to determine HOW MANY PLACES your answer should be rounded to.
Remember last week….
Was it or 4.16 or 4.2 or 4?
The idea is to round to the LEAST NUMBER OF SIGNIFICANT DIGITS that were given in the problem.

35. NOW>>>> which are significant?
NOT ALL DIGITS ARE SIGNIFICANT…
OF course – there are RULES!

36. 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

37. 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.

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

39. 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

40. 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

41. Addition/Subtraction ‑

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

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

44. 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

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

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

47. 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.

48. 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.

49. 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).

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

51. 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.

52. 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.

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

54. 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

55. 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

56. VIDEO Grab your white boards – we are going to make sure you REMEMBER how to round correctly.

57. Try this one :
Round 387,907 to the nearest hundred thousand:
387,907
Now round it to the nearest hundred…

58. Round 286 to the nearest TEN
Circle the tens spot – use the one to the right to determine if the ten spot goes up or down…
It’s a 6 ….. SO it rounds up to
290

59. Round 2,945,773 to the nearest
million
Hundred thousand
Thousand
Tens

60. Round to the nearest:
Ten
Tenth
Hundredth
Thousandth

61. Round to the nearest
Hundred million
Hundred
One
Thousandth

62. 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

63. ROUNDING to SIGNIFICANT FIGURES is a way that scientists keep their numbers in check. It is a way to determine HOW MANY PLACES your answer should be rounded to.
Remember last week….
Was it or 4.16 or 4.2 or 4?
The idea is to round to the LEAST NUMBER OF SIGNIFICANT DIGITS that were given in the problem.

65. 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

66. RULES

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

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

69. 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.

70. 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.

71. VIDEO
Use the rules! Everytime!

72. 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

73. 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

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

75. FUNctions with sig figs

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

77. 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

78. EXAMPLE
g g g ______________________ Final Answer

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

80. MULTIPLY AND DIVIDE!
YEAH!

81. 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

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

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

84. DO NOW!
Put 215 into scientific notation

85. 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

86. 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.

87. UNDERSTANDING SCIENTIFIC NOTATION

88. 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.

89. 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:

90. ANSWER
1.23 X 10 11

91. 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

92. Scientific Notation
VIDEO
Worksheet
Fix Incorrect

93. Operations w scientific notation

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

96. DO WORKSHEET
answers

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

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

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

100. 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.
VIDEO

101. 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

102. Metric to Metric Conversion
VIDEO

103. King Henry Doesn’t Usually Drink Chocolate Milk
1,000 Kilo
Hecto
Deka
UNIT Meters, Liters and Grams VIDEO
Deci
Centi
Milli

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

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

107. 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

108. 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

110. One Step Conversions

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

112. Multiple Step Conversions

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

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

115. 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.

116. Worksheet
VIDEO
Video

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

119. 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

121. Figure 1.23: Comparison of Temperature Scales

122. 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