1. Metric System of Measurement
Essential Question: Why do scientists use the metric system?

2. Why do we have to learn this?
Standard: You will demonstrate an understanding of technological design and scientific inquiry, including process skills, mathematical thinking, controlled investigative design and analysis, and problem solving.
School Goal, Math: Student’s math communication skills, reasoning, explaining, justifying will be mastered.
Objectives:
You will convert, apply, and arrange metric conversion units
You will use, apply, and evaluate metric prefixes, and base units to labs
You will apply unit factor analysis, scientific notation, and significant figures to metric calculations.
You will apply the ladder method and division and multiplication by 10 to calculate and convert metric units.

3. Metric System
The Metric system of measurement was created about two hundred years ago by a group of French scientists to simplify measurement.
It is a Standard which is the exact quantity that people agree to use for comparison.

4. For the creatures smaller than the king, the Royal Potter designed
deciliters that were 1/10th the size of a liter,
centiliters that were 1/100th the size of a liter, and
milliliters that were 1/1000th the size of a liter.
The milliliters were just right for the Royal Chocolate Beetles found in the kingdom.

5. For the creatures greater than the king, the Royal Potter designed,
Dekaliters that were 10 times the size of a liter,
Hectoliters that were 100 times the size of a liter, and
Kiloliters that were 1000 times the size of a liter.
The kiloliters were just right for the Royal Elephants of the kingdom.

6. The Royal Potter lined the vessels up in his workroom from largest to smallest to show the king.
The king’s vessel was in the center of the line, for the king was the center of the kingdom. The vessels were arranged in the following order:
kiloliter hectoliter dekaliter Liter deciliter centiliter milliliter

7. King Hector loved the new vessels that were designed larger and smaller than his own for all of the living creatures in his kingdom. The Royal Potter explained that the sizes of the original unit of measurement increased and decreased from the king’s liter by multiples of ten. He explained how to convert between the sizes by multiplying by ten or dividing by ten. King Hector wondered how he would ever remember the order of the vessels.

8. Now it is known as the Metric Conversion Mnemonic
King (kilo, 1,000)
Hector (hecto, 100)
Died (deka, 10) abbreviation---(da)
Unexpectedly (Unit (liter, meter, gram, Celsius)
Drinking (deci 1/10)
Chocolate (centi 1/100)
Milk (milli, 1/1,000)
SI system is based on multiples of 10 and uses prefixes to indicate a specific unit’s magnitude

9. How many jumps does it take?
Ladder Method 1 2 3
KILO 1000 Units
HECTO 100 Units
DEKA 10 Units
DECI 0.1 Unit
Meters Liters Grams
CENTI 0.01 Unit
MILLI Unit
How do you use the “ladder” method?
1st – Determine your starting point.
2nd – Count the “jumps” to your ending point.
3rd – Move the decimal the same number of jumps in the same direction and add zeros for each jump
4 km = _________ m
Starting Point
Ending Point
How many jumps does it take? 1
__. 2
__. 3
__. 4.
= 4000 m

10. Or use,Multiplying/Dividing

11. 6 places to the right of the decimal point
Practice Problem 1
How many mg are in 3.6 Kg?
grams
3.6 kg
36.0 hectogram
milligrams
dekagrams
decigrams
centigrams
Gram
Kilo
Hecto
Deka
deci
centi
milli
Starting point
Final Destination
3,600,000 mg
6 places to the right of the decimal point

12. 5 places to the left of the decimal point
Practice Problem 2
How many hm are in mm?
Meter
Kilo
Hecto
Deka
deci
centi
milli
Final Destination
Starting point hm
5 places to the left of the decimal point

13. Math and Units Math- the language of Science
SI Units--an improved version of the metric system used and understood by scientists worldwide.
Meter m
Mass kg
Time s
Volume L (l)
Temperature oC,Celcius Kelvin (K)

14. Length: Base unit in the metric system is the Meter.
Using the appropriate unit, it is the measured distance from one end to the other of an object.
Base unit in the metric system is the
Meter.

15. About the thickness of a dime
1 millimeter (1 mm)
About the thickness of a dime

16. 1 centimeter (1 cm)

17. 1 kilometer (1 km)

18. OR About the length of 10 football fields
1 kilometer (1 km)
OR About the length of 10 football fields

19. Mass: Base unit in the metric system is the Gram.
A measured quantity of matter.
Base unit in the metric system is the
Gram.

20. 1 gram (1 g)

21. 1 gram (1 g)
or the mass of a paperclip

22. About the mass of a grain of sand
1 milligram (1 mg)
About the mass of a grain of sand

23. 1 kilogram (1 kg)

24. Volume Base unit in the metric system is the Liter.
Space included within limits as measured and is an amount of space an object occupies.
Base unit in the metric system is the
Liter.

25. 1 liter (1 L)
1 liter of coke

26. Capacity of an eyedropper
1 milliliter (1 mL or 1 ml)
Capacity of an eyedropper

27. 1 milliliter (1 mL or 1 ml)

28. 1 kiloliter (1kL or 1 kl)
About the capacity of 4 bathtubs

29. A derived unit
Density —mass per unit volume of a material.
The unit for density is g/ml.
A unit obtained by combining different SI units is called a derived unit
Volume

30. New Topic: Temperature:
Base unit in the metric system is the Celsius.
The degree of hotness or coldness of something
Temperature is measured using a thermometer calibrated in o C

31. Temperature A measure of how hot or how cold an object is.
SI unit: Celsius or Centigrade (old term)
SI Unit: the kelvin ( K )
Note: K not a degree
Absolute Zero= 0 K

32. Temperature Particles are always moving.
When you heat water, the water molecules move faster.
When molecules move faster, the substance gets hotter.
When a substance gets hotter, its temperature goes up.

33. Temperature
Determined by using a thermometer that contains a liquid that expands with heat and contracts with cooling.
Other instruments use infrared detection, lasers, bimetallic resistance.

34. degree Celsius (°C)

35. Temperature Scales Fahrenheit Celsius Kelvin
Water boils °F °C K
Water freezes 32°F °C K

36. Units of Temperature between Boiling and Freezing
Fahrenheit Celsius Kelvin
Water boils °F °C K
180° °C K
Water freezes 32°F °C K

37. Celsius and Kelvin
K= oC + 273

38. Convert Temperatures Formulas °F= °C x 9/5 + 32 or
°C = (°F -32)/1.8
°C = (°F  -  32)  x  5/9

39. Fahrenheit Formula 180°F = 9°F = 1.8°F 100°C 5°C 1°C
Zero point: °C = 32°F
°F = 9/5 T°C or
°F = 1.8 T°C

40. Celsius Formula Rearrange to find T°C °F = 1.8 T°C + 32
°F = T°C
1.8

41. Temperature Conversions
A person with hypothermia has a body temperature of 29.1°C. What is the body temperature in °F?
°F = (29.1°C)
exact tenth's exact =
= 84.4°F
tenth’s

42. Solution Solution: °C = (°F - 32) 1.8 = (105.8 - 32) = 73.8°F
= ( )
= 73.8°F
1.8° = °C

43. Learning Check Pizza is baked at 455°F. What is that in °C? 1) 437 °C

44. Solution Pizza is baked at 455°F. What is that in °C? 2) 235°C
1.8

45. Learning Check 1) 19 °F 2) 59°F 3) 5°F
On a cold winter day, the temperature falls to -15°C. What is that temperature in °F?
1) 19 °F
2) 59°F
3) 5°F

46. Solution
3) 5°F
Solution:
°F = 1.8(-15°C) + 32 =
= 5°F

47. Kelvin Scale On the Kelvin Scale 1K = 1°C
0 K is the lowest temperature
0 K = °C
K °C
K = °C

48. Learning Check
What is normal body temperature of 37°C in kelvins?
1) 236 K
2) K
3) 342 K

49. Solution 2) 310 K K = °C + 273 = 37 °C + 273 = 310. K
What is normal body temperature of 37°C in kelvins?
2) 310 K
K = °C + 273
= 37 °C
= 310. K

50. Accuracy and Precision Revisited
Limits of Measurement
Accuracy and Precision Revisited
Essential Question
What is more important, to be accurate and precise, accurate or precise or does it matter?
Objectives:
Students will know the difference between accuracy and precision.
You will identify accurate and precision using examples.
You will provide real life examples of the essential question.

51. Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

52. Example: Accuracy
Who is more accurate when measuring a book that has a true length of 17.0cm?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

53. Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

54. Example: Precision
Who is more precise when measuring the same 17.0cm book?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

55. Example: Evaluate whether the following are precise, accurate or both.
Not Precise
Not Accurate
Precise
Accurate
Precise

56. Introduction to Significant Digits (figures) & Scientific Notation
Essential questions:
Why is it important to be accurate and / or precise when measuring
How can we show large and small numbers
Objectives:
You will convert, apply, and arrange metric conversion units
You will apply unit factor analysis, scientific notation, and significant figures to metric calculations.

57. How many Significant Digits/Figures are there in a given measurement?
ALIAS
AKA sig figs

58. Precisely Sig Figs show how precise the measuring instrument is.
Another purpose of finding the significant figure is so that we know which place to round our answers to.
Ex: A metric ruler can only be as precise as the last full measurement and your estimation.

59. Summarize the next 3 slides
Reminder What is a summary?
Summarizing involves
Putting the main idea(s) into your own words, and include only the main point(s).
Once again, it is necessary to cite summarized ideas to the original source. (Mr. Albro’s class notes)
Summaries are significantly shorter than the original and take a broad overview of the source material.

60. Precisely
A Beaker
The smallest division is 10 mL, so we can read the volume to 1/10 of 10 mL or 1 mL. The volume we read from the beaker has a reading error of ± 1 mL.
The volume in this beaker is 47 ± 1 mL. You might have read 46 mL; your friend might read the volume as 48 mL. All the answers are correct within the reading error of ± 1 mL.
So, How many significant figures does our volume of 47 ± 1 mL have?
Answer - 2! The "4" we know for sure plus the "7" we had to estimate.
Is this precise? We don’t know yet we have to gather more evidence

61. Precisely A Graduated Cylinder
The smallest division of this graduated cylinder is 1 mL. Therefore, our reading error will be ± 1 mL or 1/10 of the smallest division. An appropriate reading of the volume is 36.5 ± 1 mL. An equally precise value would be 36.6 mL or 36.4 mL.
How many significant figures does our answer have? 3! The "3" and the "6" we know for sure and the "5" we had to estimate a little.
Is this precise? We don’t know yet we have to gather more evidence

62. Precisely
A Buret
The smallest division in this buret is 0.1 mL. Therefore, our reading error is 0.01 mL. A good volume reading is ± 0.01 mL. An equally precise answer would be mL or mL.
How many significant figures does our answer have? 4! The "2", "0", and "3" we definitely know and the "8" we had to estimate.
Conclusion: The number of significant figures is directly linked to a measurement.
Is this precise? Yes

63. The same rules apply with all instruments
Read to the last digit that you know
Estimate the final digit if necessary

64. Rules for Significant figures Rule #1
All non zero digits are ALWAYS significant
How many significant digits are in the following numbers?
_____________
274
25.632
8.987

65. Rule #2 All zeros between significant digits are ALWAYS significant
How many significant digits are in the following numbers?
504
60002
9.077
_____________

66. Rule #3 All FINAL zeros to the right of the decimal ARE significant
How many significant digits are in the following numbers?
32.0
19.000
_____________

67. Rule #4 All zeros that act as place holders are NOT significant
Another way to say this is: zeros are only significant if they are between significant digits OR are the very final thing at the end of a decimal

68. For example… Look at the ruler below
What would be the measurement in the correct number of sig figs?
_______________

69. Let’s try this one Look at the ruler below
What would be the measurement in the correct number of sig figs?
_______________

70. Let’s try graduated cylinders
Look at the graduated cylinder below
What would be the measurement in the correct number of sig figs?
_______________

71. One more graduated cylinder
Look at the cylinder below…
What would be the measurement in the correct number of sig figs?
_______________

72. For example _____________ 0.0002 6.02 x 1023 100.000 150000 800
How many significant digits are in the following numbers?
_____________
0.0002
6.02 x 1023
150000
800

73. How many significant digits are in the following numbers?
0.0073
2500
7.90 x 10-3
670.0
18.84
_____________

74. Sig Figs in Multiplication/Division
The answer has the same sig figs as the factor with the least sig figs.
Ex: cm
x cm
6.4 cm2

75. Scientific Notation
Scientific notation is used to express very large or very small numbers
It consists of a number between 1 and 10 followed by x 10 to a power
The power can be determined by the number of places you have to move to get only 1 number in front of the decimal

76. A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer
2.0 x 105 a = 2.0, 10n = 105
4.500 x 103 a = 4.500, 10n = 103

77. How wide is our universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal notation or expanded form.When numbers get this large, it is easier to write them in scientific notation.

78. Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
Between the 2 and the 1

79. 2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal? 23
When the original number is more than 1, the exponent is positive.
The answer in scientific notation is
2.1 x 1023

80. Metric prefix
Write the metric prefix with a unit in Scientific Notation.
kilo ex: 1.0 x 103 kl
hecto
deka
Unit – liters, meters, grams, sec, 0C(elsus)
deci
centi
milli

81. Sig Figs and Scientific Notation
A and P rule: Convert the number into scientific notation. Any leading or trailing zeros the decimal point bumps past in the conversion will vanish. Everything else is significant.
Here are some examples that apply both rules.
The non-significant zeros are colored red.
Number
Atlantic-Pacific rule
Scientific notation rule
decimal point Present: ignore zeros on the Pacific . 4 sig. digits.
In scientific notation: × sig. digits. The decimal point moved past the three leading zeros; they vanished.
decimal point Present: ignore zeros on the Pacific side. 5 sig. digits.
In scientific notation: × sig. digits. The decimal point bumped past the leading zero; it vanished.
decimal point Present: ignore zeros on the Pacific side (none!) 7 sig. digits.
In scientific notation: × 102. The decimal point moved past two zeros, but they aren't trailing zeros; they're in the middle of the number. 7 sig. digits.
decimal point Absent: ignore zeros on the Atlantic side. 5 sig. digits.
In scientific notation: × 107. The decimal point moved past the trailing three zeros; they vanished. It moved past the zero between the threes, too, but that's not a trailing or leading zero; it stays. 5 sig. digits.

82. 1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02
The decimal was moved how many places? 8
When the original number is less than 1, the exponent is negative.
9.02 x 10-8

83. Write 28750.9 in scientific notation.
x 10-5
x 10-4
x 104
x 105

84. Evaluate (0.0042)(330,000). The answer is
1386.
The answer in decimal notation is
1386
The answer in scientific notation is
1.386 x 103

85. Evaluate (3,600,000,000)(23). The answer is:
The answer in scientific notation is
8.28 x 10 10
The answer in decimal notation is
82,800,000,000

86. Write in PROPER scientific notation
Write in PROPER scientific notation. (Notice the number is not between 1 and 10) x 109
2.346 x 1011
x 104
6.42 x 10 2

87. Write 531.42 x 105 in scientific notation.

88. Going from Scientific Notation to Ordinary Notation (expanded form)
You start with the number and move the decimal the same number of spaces as the power .
If the exponent is positive, the number will be greater than 1
If the exponent is negative, the number will be less than 1

89. Going to Ordinary Notation Examples
Place the following numbers in ordinary notation:
_____________
3 x 106
6.26x 109
5 x 10-4
8.45 x 10-7
2.25 x 103

90. Multiply and Divide Exponents
You might be asked to multiply and divide numbers in scientific notation. Here is the process.
Express in scientific notation: (2.6 × 105) (9.2 × 10–13)
The short and simple
Multiply the bases and add the exponents.
2.6 x 9.2 = 23.92
= -8
Put it together in the PROPER form
23.92 x 10? ≠ Why?
2.392 x 10-7

91. Dividing Scientific Notation
Here is the process.
Express in scientific notation: (4.8 × 1020) / (2.2 × 1012)
The short and simple
Divide the bases and subtract the exponents.
4.8 = = 8 Put it all together: 2.4 x 108
2.2

92. Unit Factor Conversion A math communication graphic organizer, and process that uses: reasoning and explanation
Essential question:
How can we collect and analyze data that is in one unit and needs to be analyzed in another unit?
Objective:
You will apply unit factor analysis, scientific notation, and significant figures to metric calculations.

93. Unit Factor Method
A conversion factor changes something to a different version or form.
A factor is something that brings results or a cause,
Conversion is an action of changing the 1st version of a thing (number plus unit) to a 2nd version.
To accomplish this, a ratio (fraction) is established that equals one (1).
Ex: 1 hour is 60 minutes, (1 hr/60 min) and (60 min is 1 hr) 1 kilometers is 1000 meters (1km/1000m) and (1000m/1km)

94. Unit Factor Method Example: Convert 5km to m: Need a conversion factor
Need to have units
NEW UNIT
5km x 1,000m =5,000m km
OLD UNIT

95. Convert 7,000m to km
7,000m x 1 km = 7 km
1,000m

96. Convert cs to s
2.45cs x 1 s = s
100cs

97. Derived Metric Units Convert 55.00 km/h to m/s
km x 1000 m x 1 h___ = 15.28m/s
h km s
Convert 20 g/ml to cg/ml
20 g x cg = 2000 cg/ml
ml g

98. Have Fun Measuring and Happy Calculating!
The End
Have Fun Measuring and Happy Calculating!