Presentation on theme: "Metric System of Measurement"— Presentation transcript:
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 unitsYou will use, apply, and evaluate metric prefixes, and base units to labsYou 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 SystemThe 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, andmilliliters 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, andKiloliters 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 Method123KILO 1000 UnitsHECTO 100 UnitsDEKA 10 UnitsDECI 0.1 UnitMeters Liters GramsCENTI 0.01 UnitMILLI UnitHow 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 jump4 km = _________ mStarting PointEnding PointHow many jumps does it take?1__.2__.3__.4.= 4000 m
11 6 places to the right of the decimal point Practice Problem 1How many mg are in 3.6 Kg?grams3.6 kg36.0 hectogrammilligramsdekagramsdecigramscentigramsGramKiloHectoDekadecicentimilliStarting pointFinal Destination3,600,000 mg6 places to the right of the decimal point
12 5 places to the left of the decimal point Practice Problem 2How many hm are in mm?MeterKiloHectoDekadecicentimilliFinal DestinationStarting pointhm5 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 mMass kgTime sVolume 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 theMeter.
15 About the thickness of a dime 1 millimeter (1 mm)About the thickness of a dime
28 1 kiloliter (1kL or 1 kl)About the capacity of 4 bathtubs
29 A derived unitDensity —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 unitVolume
30 New Topic: Temperature: Base unit in the metric system is the Celsius.The degree of hotness or coldness of somethingTemperature 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 degreeAbsolute 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 TemperatureDetermined by using a thermometer that contains a liquid that expands with heat and contracts with cooling.Other instruments use infrared detection, lasers, bimetallic resistance.
47 Kelvin Scale On the Kelvin Scale 1K = 1°C 0 K is the lowest temperature0 K = °CK °CK = °C
48 Learning CheckWhat is normal body temperature of 37°C in kelvins?1) 236 K2) K3) 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 KK = °C + 273= 37 °C= 310. K
50 Accuracy and Precision Revisited Limits of MeasurementAccuracy and Precision RevisitedEssential QuestionWhat 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: AccuracyWho is more accurate when measuring a book that has a true length of 17.0cm?Susan:17.0cm, 16.0cm, 18.0cm, 15.0cmAmy: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: PrecisionWho is more precise when measuring the same 17.0cm book?Susan:17.0cm, 16.0cm, 18.0cm, 15.0cmAmy:15.5cm, 15.0cm, 15.2cm, 15.3cm
55 Example: Evaluate whether the following are precise, accurate or both. Not PreciseNot AccuratePreciseAccuratePrecise
56 Introduction to Significant Digits (figures) & Scientific Notation Essential questions:Why is it important to be accurate and / or precise when measuringHow can we show large and small numbersObjectives:You will convert, apply, and arrange metric conversion unitsYou 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? ALIASAKA 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 involvesPutting 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 PreciselyA BeakerThe 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 PreciselyA BuretThe 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 knowEstimate the final digit if necessary
64 Rules for Significant figures Rule #1 All non zero digits are ALWAYS significantHow many significant digits are in the following numbers?_____________27425.6328.987
65 Rule #2 All zeros between significant digits are ALWAYS significant How many significant digits are in the following numbers?504600029.077_____________
66 Rule #3 All FINAL zeros to the right of the decimal ARE significant How many significant digits are in the following numbers?32.019.000_____________
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 belowWhat 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?_____________0.00026.02 x 1023150000800
73 How many significant digits are in the following numbers? 0.007325007.90 x 10-3670.018.84_____________
74 Sig Figs in Multiplication/Division The answer has the same sig figs as the factor with the least sig figs.Ex: cmx cm6.4 cm2
75 Scientific NotationScientific notation is used to express very large or very small numbersIt consists of a number between 1 and 10 followed by x 10 to a powerThe 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 10nwhere a is between 1 and 10and n is an integer2.0 x 105 a = 2.0, 10n = 1054.500 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 milesWhere 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?23When the original number is more than 1, the exponent is positive.The answer in scientific notation is2.1 x 1023
80 Metric prefixWrite the metric prefix with a unit in Scientific Notation.kilo ex: 1.0 x 103 klhectodekaUnit – liters, meters, grams, sec, 0C(elsus)decicentimilli
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 ruledecimal 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?9.02The decimal was moved how many places?8When the original number is less than 1, the exponent is negative.9.02 x 10-8
83 Write 28750.9 in scientific notation. x 10-5x 10-4x 104x 105
84 Evaluate (0.0042)(330,000). The answer is 1386.The answer in decimal notation is1386The answer in scientific notation is1.386 x 103
85 Evaluate (3,600,000,000)(23). The answer is: The answer in scientific notation is8.28 x 10 10The answer in decimal notation is82,800,000,000
86 Write in PROPER scientific notation Write in PROPER scientific notation. (Notice the number is not between 1 and 10) x 1092.346 x 1011x 1046.42 x 10 2
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 1If 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 1066.26x 1095 x 10-48.45 x 10-72.25 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 simpleMultiply the bases and add the exponents.2.6 x 9.2 = 23.92= -8Put it together in the PROPER form23.92 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 simpleDivide the bases and subtract the exponents.4.8 = = 8 Put it all together: 2.4 x 1082.2
92 Unit Factor Conversion A math communication graphic organizer, and process that uses: reasoning and explanationEssential 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 MethodA 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 unitsNEW UNIT5km x 1,000m =5,000mkmOLD UNIT