2 What makes a measurement useful? It must include a number and a unit.A standard must be usedAn exact quantity that people agree to use for comparison.
3 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
4 SI Standard Units Quantity Standard Unit Symbol Length meter m Mass kilogramkgTemperatureKelvinKTimesecondsAmount of substancemolemolElectric Currentampere (amp)ALuminous IntensitycandelacdThe SI system is built on these 7 units, each of which have a standard. All other SI units can be derived from these.
5 Derived SI units Any combination of SI units such as g/cm3 m/s2 Newton (N)
6 Common SI derived units QuantityUnitsymbolAreaSquare meterm2VolumeCubic meterm3DensityKilograms per cubic meterkg/m3PressurePascal (kilogram per meter second squared)Pa (kg/m•s2)EnergyJouleJ (kg•m2/s2 )ForceNewtonN (kg•m/s2)FrequencyHertz (cycles per second, reciprocal second))Hz (1/s or s-1)Electric chargeCoulomb (ampere second)C (A•s)
7 Non SI units commonly used in science QuantityUnitUseful relationshipsExampleVolumeLiter (L)1L=1000cm31mL=1cm31L approximately equals a quart1mL≈ 20 drops H2OEnergycalorie (cal)1cal=4.184J1J=0.2390calAmount of heat that raises the temperature of 1g of H2O by 1◦CTemperatureCelsius, CFahrenheit, FK=◦C + 273◦C=5/9 (◦F - 32)◦F=9/5◦C +32Water freezes at 273K, 0◦C, and 32◦FWater boils at 373K, 100◦C, and 212◦F
8 Prefixes Base units are not always convenient For very large or very small valuesRepresent measurements in a more compact way with the use of prefixes
9 ExampleThe 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
10 SI Prefixes Prefix Symbol Meaning giga- G Billion (109) mega- M Million (106)kilo-KThousand (103)hecto-HHundred (102)deka-daTen (101)deci-dTenth (10-1)centi-cHundredth (10-2)milli-mThousandth (10-3)micro-μMillionth (10-6)nano-nBillionth (10-9)pico-pTrillionth (10-12)femto-f(10-15)
11 Examples to remember: length UnitExampleKilometer (km)Length of about 5 city blocksMeterHeight of doorknob from floorDecimeterDiameter of a large orangeCentimeterWidth of a shirt buttonMillimeterThickness of a dimeMicrometerDiameter of a bacterial cellNanometerThickness of an RNA molecule
12 Examples to remember: volume UnitExampleLiter (L)Quart of milkMilliliter (mL)About 20 drops of waterCubic centimeter (cm3)Cube of sugarMicroliter (μL)Crystal of table salt
13 Examples to remember: mass UnitExampleKilogram (kg)Small textbookGram (g)Dollar bill or paper clipMilligram (mg)Ten grains of saltMicrogram (μg)Particle of baking powder
14 Converting SI units The SI system is based on powers of 10 units can be converted by simply moving the decimal
15 King Henry’s Daughter Barbara Drinks Chocolate Milk kilo hecto deka Base deci centi milli(No prefix)
16 To convert a unit by moving the decimal… Find the prefix of the given measurement on the chartCount over to the right or left to reach the desired unitMove the decimal the same direction and same number of placesExample:Convert 360 g to mgStart at the base unit gramsCount over 3 steps to the right to reach milli-Move the decimal 3 places to the rightso 360,000mg
17 Example45.2cg = _____kgStart at the prefix centi-Count over 5 steps to the left to reach kilo-Move the decimal 5 places to the leftso kg
18 TemperatureRelated to the average kinetic energy of the particles in a sample of mattera physical property that determines the direction of heat flowHeat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature
19 Temperature Conversions Three temperature scalesFahrenheit (⁰F)U.S. commonly uses (weather, oven temperatures, etc)Celsius (⁰C)Most other countries commonly useThis is the scale we use in labKelvin (K)“absolute” temperature scaleO Kelvin is called absolute zero- the lowest possible temperature when molecular motion ceases, particles have no kinetic energy
20 Temperature ScaleWater Freezes atWater Boils atBody TemperatureAbsolute ZeroFahrenheit32◦F212◦F98.6◦F-460◦FCelsius0◦C100◦C37◦C-273◦CKelvin273 K373 K310 KO KNote 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”.
21 Temperature conversions Use the following equations to convert from one temperature scale to another.ConversionFormulaCelsius to KelvinK = C + 273Kelvin to CelsiusC= K - 273Fahrenheit to CelsiusC = (F – 32) x 5/9Celsius 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.
22 English UnitsMost 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.
23 Dimensional AnalysisEquality 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
24 Keeping track of units can help you convert one measured quantity into its equivalent quantity of a different unitSet up a calculation without the need for a formula
25 To set up a conversion problem… write down all “=“ statements you know that will help you get from the given unit to the new unitLook for equalities given in the problemExampleHow many inches are in 1.25 miles? (There are 5,280ft in 1mile.)“=“ statements:Given: 5,280ft=1mileOther: 12in=1ft
26 2. Make fractions out of your “=“ statements 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”Example5,280ft=1mile 5,280ft or 1mile1mile ,280ft12in.=1ft in or 1ft1ft in
27 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
28 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=
29 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
30 exampleSuppose 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¢ = 1LFrom a reference table, 1L=1.06qt4qt=1gal
31 More complex problems… Measurements may containMore than one unit, such as miles/hrfractional or exponential units such as cm3treat each unit independentlyStructure your conversion factors to ensure the given units cancel with a numerator or denominator as appropriate and the answer ends with the appropriate unitRemember information given in the problem can be an equality
32 A car is traveling down the interstate at a speed of 70 miles per hour (70miles/1hr). Convert this speed to m/s.
33 Squared and cubed units Squared and cubed units are potentially trickyFor example, remember that a cm3 is really a cm x cm x cmIf we were going to convert cm3 to mm3We need to use the conversion factor 1cm=10mm three times (or cube it) so that all three centimeter units cancel out
34 One liter is exactly 1000cm3. How many cubic inches are there in 1.0L? 1000cm3=1L1in=2.54cm