2 Steps in the Scientific Method 1. Observations- quantitative- qualitative2. Formulating hypotheses- possible explanation for the observation3. Performing experiments- gathering new information to decidewhether the hypothesis is valid
3 Outcomes Over the Long-Term Theory (Model)- A set of tested hypotheses that give an overall explanation of some natural phenomenon.Natural Law- The same observation applies to many different systems
4 A law summarizes what happens Law vs. TheoryA law summarizes what happensA theory (model) is an attempt to explain why it happens.Einstein's theory of gravity describes gravitational forces in terms of the curvature of spacetime caused by the presence of mass
5 Nature of Measurement Part 2 - scale (unit) A measurement is a quantitative observation consisting of 2 parts:Part 1 - numberPart 2 - scale (unit)Examples:20 grams6.63 x Joule·seconds
6 The Fundamental SI Units (le Système International, SI)
9 SI Prefixes Common to Chemistry Unit Abbr.ExponentMegaM106Kilok103Decid10-1Centic10-2Millim10-3Micro10-6Nanon10-9Picop10-12
10 Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.Measurements are performed withinstrumentsNo instrument can read to an infinite number of decimal places
11 Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value.Precision refers to the degree of agreement among several measurements made in the same manner.Neither accurate nor precisePrecise but not accuratePrecise AND accurate
12 Types of ErrorRandom Error (Indeterminate Error) - measurement has an equal probability of being high or low.Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration. This can result in measurements that are precise, but not accurate.
13 Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures.3456 has4 sig figs.
14 Rules for Counting Significant Figures - Details Zeros- Leading zeros do not count as significant figures.has3 sig figs.
15 Rules for Counting Significant Figures - Details Zeros- Captive zeros always count as significant figures.16.07 has4 sig figs.
16 Rules for Counting Significant Figures - Details ZerosTrailing zeros are significant only if the number contains a decimal point.9.300 has4 sig figs.
17 Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures.1 inch = cm, exactly
18 Sig Fig Practice #1 1.0070 m 5 sig figs 17.10 kg 4 sig figs How many significant figures in each of the following?m 5 sig figs17.10 kg 4 sig figs100,890 L 5 sig figs3.29 x 103 s 3 sig figscm 2 sig figs3,200,000 2 sig figs
19 Rules for Significant Figures in Mathematical Operations Multiplication and Division:# sig figs in the result equals the number in the least precise measurement used in the calculation.6.38 x 2.0 =12.76 13 (2 sig figs)
20 Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 100.0 g ÷ 23.7 cm3g/cm34.22 g/cm30.02 cm x cmcm20.05 cm2710 m ÷ 3.0 sm/s240 m/slb x 3.23 ftlb·ft5870 lb·ft1.030 g ÷ 2.87 mLg/mL2.96 g/mL
21 Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement.= 18.7 (3 sig figs)
22 Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 100.0 g g76.27 g76.3 g0.02 cm cm2.391 cm2.39 cm713.1 L LL709.2 Llb lblblb2.030 mL mL0.16 mL0.160 mL
23 Metric Prefixes 1 kilometer (km) = 1000 meters (m) Kilo- means 1000 of that unit1 kilometer (km) = meters (m)Centi- means 1/100 of that unit1 meter (m) = 100 centimeters (cm)1 dollar = 100 centsMilli- means 1/1000 of that unit1 Liter (L) = milliliters (mL)
26 Learning Check 1. 1000 m = 1 ___ a) mm b) km c) dm g = 1 ___ a) mg b) kg c) dgL = 1 ___ a) mL b) cL c) dLm = 1 ___ a) mm b) cm c) dm
27 Units of Length ? kilometer (km) = 500 meters (m) 2.5 meter (m) = ? centimeters (cm)1 centimeter (cm) = ? millimeter (mm)1 nanometer (nm) = 1.0 x 10-9 meterO—H distance =9.4 x m9.4 x 10-9 cm0.094 nm
28 Learning Check Select the unit you would use to measure 1. Your height a) millimeters b) meters c) kilometers2. Your massa) milligrams b) grams c) kilograms3. The distance between two citiesa) millimeters b) meters c) kilometers4. The width of an artery
29 Conversion FactorsFractions in which the numerator and denominator are EQUAL quantities expressed in different unitsExample: in. = 2.54 cmFactors: 1 in and cm2.54 cm in.
30 Learning Check 1. Liters and mL 2. Hours and minutes Write conversion factors that relate each of the following pairs of units:1. Liters and mL2. Hours and minutes3. Meters and kilometers
31 How many minutes are in 2.5 hours? Conversion factor2.5 hr x min = min1 hrcancelBy using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!
32 Steps to Problem Solving Write down the given amount. Don’t forget the units!Multiply by a fraction.Use the fraction as a conversion factor. Determine if the top or the bottom should be the same unit as the given so that it will cancel.Put a unit on the opposite side that will be the new unit. If you don’t know a conversion between those units directly, use one that you do know that is a step toward the one you want at the end.Insert the numbers on the conversion so that the top and the bottom amounts are EQUAL, but in different units.Multiply and divide the units (Cancel).If the units are not the ones you want for your answer, make more conversions until you reach that point.Multiply and divide the numbers. Don’t forget “Please Excuse My Dear Aunt Sally”! (order of operations)
33 Sample Problem = 29 quarters X You have $7.25 in your pocket in quarters. How many quarters do you have?7.25 dollars quarters1 dollar= 29 quartersX
34 You Try This One!If Jacob stands on Spencer’s shoulders, they are two and a half yards high. How many feet is that?
36 Learning CheckA rattlesnake is 2.44 m long. How long is the snake in cm?a) cmb) 244 cmc) 24.4 cm
37 Solution A rattlesnake is 2.44 m long. How long is the snake in cm? b) 244 cm2.44 m x cm = 244 cm1 m
38 Learning Check How many seconds are in 1.4 days? Unit plan: days hr min seconds1.4 days x 24 hr x ??1 day
39 Wait a minute! What is wrong with the following setup? 1.4 day x 1 day x min x 60 sec24 hr hr min
40 English and Metric Conversions If you know ONE conversion for each type of measurement, you can convert anything!Mass: 454 grams = 1 poundLength: cm = 1 inchVolume: L = 1 quart
41 Learning CheckAn adult human has 4.65 L of blood. How many gallons of blood is that?Unit plan: L qt gallonEqualities: 1 quart = L1 gallon = 4 quartsYour Setup:
42 Equalities length 10.0 in. 25.4 cm State the same measurement in two different unitslength10.0 in.25.4 cm
43 Steps to Problem Solving Read problemIdentify dataMake a unit plan from the initial unit to the desired unitSelect conversion factorsChange initial unit to desired unitCancel units and checkDo math on calculatorGive an answer using significant figures
44 Dealing with Two UnitsIf your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of feet?
45 What about Square and Cubic units? – Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!Best way: Square or cube the ENITRE conversion factorExample: Convert 4.3 cm3 to mm3( )4.3 cm mm 31 cm4.3 cm mm313 cm3== 4300 mm3
46 Learning CheckA Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?
47 So, a dm3 is the same as a Liter ! A cm3 is the same as a milliliter. Solution( )1000 cm dm 310 cm= 1 dm3So, a dm3 is the same as a Liter !A cm3 is the same as a milliliter.