3 Units of Measure SI units: Systeme Internationale d’ Unites standard units of measurement to be understood by all scientistsBase Units: defined unit of measurement that is based on an object or event in the physical world
4 Table 2.1 – The Base Units Quantity Base Unit Time Second (s) Length Meter (m)MassKilogram (kg)TemperatureKelvin (K)Amount of a substanceMole (mol)Electric currentAmpere (A)Luminous intensityCandela (cd)
5 Timesecond (s)Many chemical reactions take place in less than a second so scientist often add prefixes, based on multiples of ten, to the base units.ex. MillisecondLengthmeter (m)A meter is the distance that light travels though a vacuum in 1/ of a second.What is a vacuum?Close in length to a yard.Prefixes also apply…ex. millimeter
6 Mass mass is a measurement of matter kilogram (kg) about 2.2 pounds Masses measured in most laboratories are much smaller than a kilogram, so scientists use grams (g) or milligrams (mg).How many grams are in a kilogram?1000How many milligrams are in a gram?
7 Derived Units Not all quantities are measured in base units A unit that is defined by a combination of base units is called a derived unit.Volume and Density are measured in derived units.
8 Volume The space occupied by an object Unit = cm3 = mL Liters are used to measure the amount of liquid in a container (about the same volume as a quart)Prefixes also applied…ex. milliliter
9 Density Density= mass/volume The ratio that compares the mass of an object to its volume is called density.Units are g/cm3You can calculate density by the following equation:Density= mass/volumeEx: What is the density of a sample of aluminum that has a mass of 13.5 g and a volume of 5.0 cm3?Density= 13.5g/5.0cm3=2.7g/cm3
10 We also use the Celsius (C) scale TemperatureA measurement of how hot or cold an object is relative to other objectsThe kelvin (K) scalewater freezes at 273Kwater boils at 373KWe also use the Celsius (C) scalewater freezes at 0oCwater boils at 100oC
11 To Convert Celsius to Kelvin… Add 273!!ex: -39oC + 273= 234 KTo Convert Kelvin to Celsius…Subtract 273!!ex: 234K- 273= -39°C
13 Scientific NotationNumbers that are extremely large can be difficult to deal with…soooScientists convert these numbers into scientific notationScientific notation expresses numbers as a multiple of two factors:A number between 1 and 10 (only 1 digit to the left of the decimal!)Ten raised to a power
14 For example:A proton’s mass = kgIf you put it in scientific notation, the mass of a proton is expressed as x kgRemember:When numbers larger than 1 are expressed in scientific notation, the power of ten is positiveWhen numbers smaller than 1 are expressed in scientific notation, the power of ten is negative
15 Try these: Convert 1,392,000 to scientific notation. = 1 Try these: Convert 1,392,000 to scientific notation. = x 106 Convert 0.000,000,028 to scientific notation. = 2.8 x 10-8
16 Adding and Subtracting using Scientific Notation Make sure the exponents are the same!!7.35 x x 102 = 9.78 x 102If the exponents are not the same, you have to make them the same!!Tip: if you increase the exponent, you decrease the decimal if you decrease the exponent, you increase the decimalExample:Tokyo pop: x 107Mexico City pop: x 106 = 1.56 x 107Sao Paolo pop: x 108 = 1.65 x 107NOW you can add them together and carry thru the exponentTotal= 5.91 x 107
17 Multiplying and Dividing using Scientific Notation Multiplication:Multiply decimals and ADD exponentsEx : (1.2 x 106) x (3.0 x 104) = 3.6 x = 10* Ex: (1.2 x 106) x (3.0 x 10-4) = 3.6 x (-4) = 2Division:Divide decimals and SUBTRACT exponentsEx: (5.0 x 108) ÷ (2.5 x 104) = 2.0 x – 4 = 4*Ex: (5.0 x 108) ÷ (2.5 x 10-4) = 2.0 x – (-4) = 12
19 Dimensional Analysis Conversion factor: A numerical factor used to multiply or divide a quantity when converting from one system of units to another.Conversion factors are always equal to 1Dimensional analysis:A fancy way of saying “converting units” by using conversion factors
20 Table 2.2 – SI Prefixes Prefix Symbol Numerical Value in Base Units Power of 10 EquivalentGigaG1,000,000,000109MegaM1,000,000106KiloK1000103--1100Decid0.110-1Centic0.0110-2Millim0.00110-3Micro10-6Nanon10-9Picop10-12
21 Dimensional analysis often uses conversion factors Suppose you want to know how many meters are in 48 km. You have to choose a conversion factor that relates kilometers to meters. You know that for every 1 kilometer there is 1000 meters. What will your conversion factor be? 1000m/1km Now that you know your conversion factor, you can multiply it by your known…BUT you want to make sure you set it up so that kilometers cancels out. How would you do this?
22 48km x 1000m 1km =48,000 m TIP: Put the units you already have on the bottom of the conversion factor and the units you want on top.
23 2.3 - Accuracy vs. Precision Significant Figures
24 Accuracy and Precision Accuracy: How close measurements are to the actual value Precision: How close measurements are to each other
25 Percent ErrorAn error is the difference between an experimental value and an accepted valuePercent error=Percent error = accepted - experimental x 100accepted valueA tolerance is a very narrow range of error
26 Example:The accepted density for copper is 8.96g/mL. Calculate the percent error for each of these measurements.8.86g/mL8.92g/mL9.00g/mL8.98g/mL[(8.96 – 8.86)/8.96] x 100% = 1.12%[(8.96 – 8.92)/8.96] x 100% = 0.45%[(9.00 – 8.96)/8.96] x 100% = 0.45%[( )/8.96] x 100% = 0.22%
27 Significant FiguresSignificant figures include all known digits plus one estimated digitRulesNon-zero numbers are always significantZeros between non-zero numbers are always significant (“trapped zeros”)All final zeros to the right of the decimal place are significant (“trailing zeros”) (but trailing zeros don’t count if there is no decimal in the number)Zeros that act as place holders are not significant (convert to SN to remove placeholder zeros) (“leading zeros”)Counting numbers and defined constants have an infinite number of sig figs
28 Rounding numbersAn answer should have no more significant figures than the data with the fewest significant figuresExample:Density of a given object = m = 22.44g = g/cm3V cm3How should the answer be rounded?1.58 g/cm3
29 Addition & Subtraction How do you add or subtract numbers that contain decimal point?The easiest way (which you learned in third grade) is to line up the decimal points then perform the mathThen round according to the previous rule, rounding to the least numbers after the decimal! (ex: = 15.6)
30 Multiplication & Division When you multiply or divide, your answer must have the same number of significant figures as the measurement with the fewest significant figures…just like adding or subtracting!Ex: 38736km4784km= 8.097
32 Representing DataA goal of many experiments is to discover whether a pattern exists in a certain situation…when data are listed in a table the patterns may not be obviousSoooo, scientists often use graphs, which are visual displays of dataX-axis independent variableY-axis dependent variable
33 Graphing TypesLine Graphs – most graphs you complete will be line graphsTemperature and Elevation RelationshipTemperature (°C)Elevation (m)
34 Graphing TypesCircle Graphs – used for graphing parts of a whole (percentages)
35 Graphing TypesBar Graphs – shows how a quantity varies across categoriesDietary sources of magnesiumMagnesium Content (mg)