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

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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 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 KkKing (kilo, 1,000) HhHector (hecto, 100) DdDied (deka, 10) abbreviation---(da) UUUnexpectedly (Unit (liter, meter, gram, Celsius) DdDrinking (deci 1/10) CcChocolate (centi 1/100) MmMilk (milli, 1/1,000) SI system is based on multiples of 10 and uses prefixes to indicate a specific unit’s magnitude

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

10 Or use,Multiplying/Dividing

11 KiloHectoDeka Gram decicentimilli Practice Problem 1 How many mg are in 3.6 Kg? Starting pointFinal Destination 3,600,000 mg 6 places to the right of the decimal point 3.6 kg36.0 hectogram dekagrams grams centigrams milligrams deci grams

12 KiloHectoDeka Meter decicentimilli Practice Problem 2 How many hm are in mm? Starting pointFinal Destination 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 VolumeL (l) Temperature o C,Celcius Kelvin ( K)

14 Length: 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 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

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

20 1 gram (1 g)

21 or the mass of a paperclip

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

23 1 kilogram (1 kg)

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

30 New Topic: Temperature: The degree of hotness or coldness of something Base unit in the metric system is the Celsius. 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 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 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 35 Temperature Scales Fahrenheit Celsius Kelvin Water boils 212°F 100°C 373 K Water freezes 32°F 0°C 273 K

36 36 Units of Temperature between Boiling and Freezing FahrenheitCelsius Kelvin Water boils 212°F 100°C 373 K 180° 100°C 100K Water freezes 32°F 0°C 273 K

37 Celsius and Kelvin K= o C + 273

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

39 39 Fahrenheit Formula 180°F = 9°F =1.8°F 100°C 5°C 1°C Zero point: 0°C = 32°F °F = 9/5 T°C + 32 or °F = 1.8 T°C + 32

40 40 Celsius Formula Rearrange to find T°C °F = 1.8 T°C + 32 °F - 32 = 1.8T°C ( ) °F - 32 = 1.8 T°C °F - 32 = T°C 1.8

41 41 Temperature Conversions A person with hypothermia has a body temperature of 29.1°C. What is the body temperature in °F? °F = 1.8 (29.1°C) + 32 exact tenth's exact = = 84.4°F tenth’s

42 42 Solution 2) 41.0 °C Solution: °C = (°F - 32) 1.8 =( ) 1.8 =73.8°F 1.8°= 41.0°C

43 43 Learning Check Pizza is baked at 455°F. What is that in °C? 1) 437 °C 2) 235°C 3) 221°C

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

45 45 Learning Check 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 46 Solution 3) 5°F Solution: °F = 1.8(-15°C) + 32 = = 5°F

47 47 Kelvin Scale On the Kelvin Scale 1K = 1°C 0 K is the lowest temperature 0 K = - 273°C K °C K = °C + 273

48 48 Learning Check What is normal body temperature of 37°C in kelvins? 1) 236 K 2) 310 K 3)342 K

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

50 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. Accurate Not Precise Not Accurate Precise Accurate Precise

56 Introduction to Significant Digits (figures) & Scientific Notation Essential questions: 1.Why is it important to be accurate and / or precise when measuring 2.How can we show large and small numbers Objectives: 1.You will convert, apply, and arrange metric conversion units 2.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? _______________________________________

65 Rule #2 All zeros between significant digits are ALWAYS significant How many significant digits are in the following numbers? _______________________________________

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

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 1) )6.02 x ) ) )800 1)_____________ 2)_____________ 3)_____________ 4)_____________ 5)_____________ How many significant digits are in the following numbers?

73 1) ) )2500 4)7.90 x ) ) ) )_____________ 2)_____________ 3)_____________ 4)_____________ 5)_____________ 6)_____________ 7)_____________

74 Sig Figs in Multiplication/Division The answer has the same sig figs as the factor with the least sig figs. Ex: 3.22 cm x 2.0 cm 6.4 cm 2

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

76 Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 and n is an integer 2.0 x 10 5 a = 2.0, 10 n = x 10 3 a = 4.500, 10 n = 10 3

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. 10,000,000,000,000,000,000,0 00. 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 10 23

80 Metric prefix Write the metric prefix with a unit in Scientific Notation. –kilo ex: 1.0 x 10 3 kl –hecto –deka –Unit – liters, meters, grams, sec, 0 C(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. NumberAtlantic-Pacific ruleScientific 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: × 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: × 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 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 x 10 -8

83 Write in scientific notation x x x x 10 5

84 Evaluate (0.0042)(330,000). T he answer is The answer in decimal notation is 1386 The answer in scientific notation is x 10 3

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

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

87 Write x 10 5 in scientific notation x x x x x x x 10 8

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

89 Going to Ordinary Notation Examples 1)3 x )6.26x )5 x )8.45 x )2.25 x )_____________ 2)_____________ 3)_____________ 4)_____________ 5)_____________ Place the following numbers in ordinary notation:

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 × 10 5 ) (9.2 × 10 –13 ) –The short and simple Multiply the bases and add the exponents. 2.6 x 9.2 = = -8 Put it together in the PROPER form x 10 ? ≠ -8 Why? x 10 -7

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

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 1 st version of a thing (number plus unit) to a 2 nd 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 2.45cs to s 2.45cs x 1 s = s 100cs

97 Derived Metric Units Convert km/h to m/s km x 1000 m x 1 h___ = 15.28m/s h 1 km 3600 s Convert 20 g/ml to cg/ml 20 g x 100 cg = 2000 cg/ml ml 1 g

98 The End Have Fun Measuring and Happy Calculating!


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