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SI System and Unit Conversions

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What makes a measurement useful? It must include a number and a unit. A standard must be used – An exact quantity that people agree to use for comparison. 2

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SI System Scientists use SI system – International System of Units – SI comes from the French “Systeme International d’Unites” – revised version of the metric system 3

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SI Standard Units QuantityStandard UnitSymbol Lengthmeterm Masskilogramkg TemperatureKelvinK Timeseconds Amount of substancemolemol Electric Currentampere (amp)A Luminous Intensitycandelacd The SI system is built on these 7 units, each of which have a standard. All other SI units can be derived from these. 4

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Derived SI units Any combination of SI units such as – g/cm 3 – m/s 2 – Newton (N) 5

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Common SI derived units QuantityUnitsymbol AreaSquare meterm2m2 VolumeCubic meterm3m3 DensityKilograms per cubic meterkg/m 3 PressurePascal (kilogram per meter second squared) Pa (kg/ms 2 ) EnergyJoule J (kgm 2 /s 2 ) ForceNewtonN (kgm/s 2 ) FrequencyHertz (cycles per second, reciprocal second)) Hz (1/s or s -1 ) Electric chargeCoulomb (ampere second)C (As) 6

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Non SI units commonly used in science QuantityUnitUseful relationships Example VolumeLiter (L)1L=1000cm 3 1mL=1cm 3 1L approximately equals a quart 1mL≈ 20 drops H 2 O Energycalorie (cal)1cal=4.184J 1J=0.2390cal Amount of heat that raises the temperature of 1g of H 2 O by 1 ◦ C TemperatureCelsius, C Fahrenheit, F K= ◦ C ◦ C=5/9 ( ◦ F - 32) ◦ F=9/5 ◦ C +32 Water freezes at 273K, 0 ◦ C, and 32 ◦ F Water boils at 373K, 100 ◦ C, and 212 ◦ F 7

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Prefixes Base units are not always convenient – For very large or very small values Represent measurements in a more compact way with the use of prefixes 8

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Example – The time it takes for a computer hard drive to read or write data might be seconds. – We can more conveniently represent this time as 9 milliseconds, where the prefix “milli” means “thousandth” So 9 milliseconds means 9 thousandths of a second, or seconds 9

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SI Prefixes PrefixSymbolMeaning giga-GBillion (10 9 ) mega-MMillion (10 6 ) kilo-KThousand (10 3 ) hecto-HHundred (10 2 ) deka-daTen (10 1 ) deci-dTenth (10 -1 ) centi-cHundredth (10 -2 ) milli-mThousandth (10 -3 ) micro-μMillionth (10 -6 ) nano-nBillionth (10 -9 ) pico-pTrillionth ( ) femto-f( ) 10

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Examples to remember: length UnitExample Kilometer (km)Length of about 5 city blocks MeterHeight of doorknob from floor DecimeterDiameter of a large orange CentimeterWidth of a shirt button MillimeterThickness of a dime MicrometerDiameter of a bacterial cell NanometerThickness of an RNA molecule 11

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Examples to remember: volume UnitExample Liter (L)Quart of milk Milliliter (mL)About 20 drops of water Cubic centimeter (cm 3 )Cube of sugar Microliter (μL)Crystal of table salt 12

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Examples to remember: mass UnitExample Kilogram (kg)Small textbook Gram (g)Dollar bill or paper clip Milligram (mg)Ten grains of salt Microgram (μg)Particle of baking powder 13

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Converting SI units The SI system is based on powers of 10 – units can be converted by simply moving the decimal 14

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King Henry’s Daughter Barbara Drinks Chocolate Milk kilo hecto deka Base deci centi milli (No prefix) 15

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To convert a unit by moving the decimal… 1.Find the prefix of the given measurement on the chart 2.Count over to the right or left to reach the desired unit 3.Move the decimal the same direction and same number of places Example: Convert 360 g to mg 1.Start at the base unit grams 2.Count over 3 steps to the right to reach milli- 3.Move the decimal 3 places to the right so 360,000mg 16

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Example 45.2cg = _____kg 1.Start at the prefix centi- 2.Count over 5 steps to the left to reach kilo- 3.Move the decimal 5 places to the left so kg 17

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Temperature Related to the average kinetic energy of the particles in a sample of matter a physical property that determines the direction of heat flow Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature 18

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Temperature Conversions Three temperature scales – Fahrenheit (⁰F) U.S. commonly uses (weather, oven temperatures, etc) – Celsius (⁰C) Most other countries commonly use This is the scale we use in lab – Kelvin (K) “absolute” temperature scale O Kelvin is called absolute zero- the lowest possible temperature when molecular motion ceases, particles have no kinetic energy 19

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Temperature Scale Water Freezes at Water Boils atBody Temperature Absolute Zero Fahrenheit32 ◦ F 212 ◦ F 98.6 ◦ F -460 ◦ F Celsius0◦C0◦C 100 ◦ C 37 ◦ C -273 ◦ C Kelvin273 K373 K310 K O K Note that the degree symbol is not used with the Kelvin scale. When reading a Kelvin temperature, the correct way is to say “273 Kelvin” instead of “273 degrees Kelvin”. 20

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Temperature conversions Use the following equations to convert from one temperature scale to another. ConversionFormula Celsius to KelvinK = C Kelvin to CelsiusC= K Fahrenheit to CelsiusC = (F – 32) x 5/9 Celsius to FahrenheitF = (C x 9/5) + 32 *To convert between Kelvin and Fahrenheit is a two step process. Convert to Celsius first, then to Kelvin or Fahrenheit. 21

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English Units Most of us in the U.S. grow up using English units such as pounds and inches. To convert between English units or between English and metric units, you must use a method called dimensional analysis. 22

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Dimensional Analysis Equality statements such as 1ft=12in. are made into fractions and then strung together in such a way that all units except the desired one are canceled out of the problem 23

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Keeping track of units can help you – convert one measured quantity into its equivalent quantity of a different unit – Set up a calculation without the need for a formula 24

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To set up a conversion problem… 1.write down all “=“ statements you know that will help you get from the given unit to the new unit – Look for equalities given in the problem Example How many inches are in 1.25 miles? (There are 5,280ft in 1mile.) “=“ statements: Given: 5,280ft=1mile Other: 12in=1ft 25

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2. Make fractions out of your “=“ statements. There are 2 fractions for each “=“ that are reciprocals of each other. These fractions are called “conversion factors” Example 5,280ft=1mile 5,280ft or 1mile 1mile 5,280ft 12in.=1ft 12in or 1ft 1ft 12in 26

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3. Begin solving the problem by writing the given amount with units on the left side of your paper then choose the fractions that will let a numerator unit be canceled with a denominator unit and vice versa until all units are canceled except the desired unit Example 1.25miles x 5,280ft x 12in =_______in 1mile 1ft 27

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4. Using your calculator, read from left to right and enter the numerator and denominator numbers in order. Precede each numerator with a multiplication sign and each denominator with a division sign. Example 1.25miles x 5,280ft x 12in =_______in 1mile 1ft On your calculator: 1.25x5280/1x12/1= 28

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5. Round your calculated answer to the same number of significant digits your original given number had. (conversion factors are exact numbers and so don’t affect the number of sig. digits) Example 1.25miles x 5,280ft x 12in = 79,200 in 1mile 1ft 29

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example Suppose your automobile tank holds 23 gallons and the price of gasoline is 33.5 ¢ per liter. How many dollars will it cost you to fill your tank? From the problem, 33.5 ¢ = 1L From a reference table, 1L=1.06qt 4qt=1gal 30

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More complex problems… Measurements may contain – More than one unit, such as miles/hr – fractional or exponential units such as cm 3 treat each unit independently Structure your conversion factors to ensure the given units cancel with a numerator or denominator as appropriate and the answer ends with the appropriate unit Remember information given in the problem can be an equality 31

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A car is traveling down the interstate at a speed of 70 miles per hour (70miles/1hr). Convert this speed to m/s. 32

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Squared and cubed units Squared and cubed units are potentially tricky For example, remember that a cm 3 is really a cm x cm x cm If we were going to convert cm 3 to mm 3 – We need to use the conversion factor 1cm=10mm three times (or cube it) so that all three centimeter units cancel out 33

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One liter is exactly 1000cm 3. How many cubic inches are there in 1.0L? 1000cm 3 =1L 1in=2.54cm 34

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