Scientific Notation



Foundations ChemistryLearning Objectives FoundationsEssential knowledge and skills:Understand Material Safety Data Sheet (MSDS) warnings, including handling chemicals, lethal dose (LD), hazards, disposal, and chemical spill cleanup.Identify the following basic lab equipment: beaker, Erlenmeyer flask, graduated cylinder, test tube, test tube rack, test tube holder, ring stand, wire gauze, clay triangle, crucible with lid, evaporating dish, watch glass, wash bottle, and dropping pipette.Make the following measurements, using the specified equipment: volume: graduated cylinder, volumetric flask, buret mass: triple beam and electronic balancestemperature: thermometer and/or temperature probepressure: barometer and/or pressure probe.Identify, locate, and know how to use laboratory safety equipment including aprons, goggles, gloves, fire extinguishers, fire blanket, safety shower, eye wash, broken glass container, and fume hood.design and perform controlled experiments to test predictions, including the following key components: hypotheses, independent and dependent variables, constants, controls, and repeated trials.Identify variables.Predict outcome(s) when a variable is changed.Record data using the significant digits of the measuring equipment.Demonstrate precision (reproducibility) in measurement.Recognize accuracy in terms of closeness to the true value of a measurement.Know most frequently used SI prefixes and their values (milli-, centi-, micro-, kilo-).Demonstrate the use of scientific notation, using the correct number of significant digits with powers of ten notation for the decimal place.Correctly utilize the following when graphing data: Dependent variable (vertical axis)Independent variable (horizontal axis)Scale and units of a graph Regression line (best fit curve).Use the rules for performing operations with significant digits.Utilise dimensional analysis to convert measurements.Read measurements and record data, reporting the significant digits of the measuring equipment.Use data collected to calculate percent error.Determine the mean of a set of measurements.Discover and eliminate procedural errors.Essential understandings:The nature of science refers to the foundational concepts that govern the way scientists formulate explanations about the natural world. The nature of science includes the following conceptsa) the natural world is understandable;b) science is based on evidence - both observational and experimental;c) science is a blend of logic and innovation;d) scientific ideas are durable yet subject to change as new data are collected;e) science is a complex social endeavor; andf) scientists try to remain objective and engage in peer review to help avoid bias.Techniques for experimentation involve the identification and the proper use of chemicals, the description of equipment, and the recommended statewide framework for high school laboratory safety.Measurements are useful in gathering data about chemicals and how they behave.Repeated trials during experimentation ensure verifiable data.Data tables are used to record and organize measurements.Mathematical procedures are used to validate data, including percent error to evaluate accuracy.Measurements of quantity include length, volume, mass, temperature, time, and pressure to the correct number of significant digits.Measurements must be expressed in International System of Units (SI) units.Scientific notation is used to write very small and very large numbers.Algebraic equations represent relationships between dependent and independent variables.Graphs are used to summarize the relationship between the independent and dependent variable.Graphed data give a picture of a relationship.Ratios and proportions are used in calculations.Significant digits of a measurement are the number of known digits together with one estimated digit.The last digit of any valid measurement must be estimated and is therefore uncertain.Dimensional analysis is a way of translating a measurement from one unit to another unit.Graphing calculators can be used to manage the mathematics of chemistry.Scientific questions drive new technologies that allow discovery of additional data and generate better questions. New tools and instruments provide an increased understanding of matter at the atomic, nano, and molecular scale.Constant reevaluation in the light of new data is essential to keeping scientific knowledge current. In this fashion, all forms of scientific knowledge remain flexible and may be revised as new data and new ways of looking at existing data become available.Material Safety Data Sheet (MSDS) ActivityPurpose: To become familiar with a MSDS sheet.My chemical is: ___________________________Are there any common names for your substance? What does your substance look like? (These are examples of physical properties.)What may happen if you inhale your substance?What substances are incompatible with your chemical? What chemicals should not be stored with your chemical?How would you clean up a spill of your chemical?Physical Data:Melting Point: __________________ Water Solubility: _______________________Boiling Point: _________________ Appearance & Odour:____________________Specific Gravity: ________________Fire and Explosion Hazards:Flash Point:Health Hazard Data:Carcinogenicity:Acute (Short term) effects:Chronic (long term) effects:Routes of Entry into the body:Scientific Method Experimental Design worksheet IV, DV, controls, and control groupsDIRECTIONS: Use each description and/or data table to help you identify or describe: 1) any independent variable(s), 2) the best dependent variable, 3) at least 3 variables that should be controlled or held constant, and 4) any control group(s) in the experiment. Make sure your answers are specific. Keep in mind that not all experiments have a control group.FISH EGGS: A scientist knows that the percent of fish eggs that hatch is affected by the temperature of the water in an aquarium. She is attempting to identify which water temperature will cause the highest percentage of fish eggs to hatch. The scientist sets up 5 aquariums at the following temperatures: 10°C, 20°C, 30°C, 40°C, and 50°C. She adds 50 fish eggs to each aquarium and records the number of eggs that hatch in each aquarium.independent variable(s): dependent variablelist 3 variables that should be controlled (held constant): describe any control group(s) in the experiment (if one doesn’t exist, leave this section blank): mouthwashusedtime mouthwashwas in mouth# of bacteria inmouth (average)none135A60 sec.23B60 sec.170C60 sec.84D60 sec.39E60 sec.81MOUTHWASH: The makers of brand A mouthwash want to prove that their mouthwash kills more bacteria than theother 4 leading brands of mouthwash.They organize 60 test subjects into 6 groups of 10 test subjects. The data for the experiment is shown to the right.independent variable(s): dependent variable: list 3 variables that should be controlled (held constant): describe any control group(s) in the experiment (if one doesn’t exist, leave this section blank): GAS MILEAGE: A car magazine is trying to write an article that rates the top 5 most fuel efficient SUVs (the SUVs that can drive the most miles for each gallon of gasoline). They make sure each model of SUV has exactly 10 gallons of gasoline in its fuel tank and reset the odometer (instrument that measures the distance a vehicle has traveled) to zero. The SUVs are then driven until they run out of gasoline. The distance on the odometer is recorded.independent variable(s): dependent variable: list 3 variables that should be controlled (held constant): describe any control group(s) in the experiment (if one doesn’t exist, leave this section blank): FIRE EXTINGUISHERS: A firefighter is trying to figure out which type of fire extinguisher (CO2, water, or dry chemical) will put out fires the fastest. Think about the issue being tested and imagine an appropriate experiment to determine which type of fire extinguisher can extinguish fires the fastest. Then, identify the key elements of the experimental design listed below.independent variable(s): dependent variable: list 3 variables that should be controlled (held constant): describe any control group(s) in the experiment (if one doesn’t exist, leave this section blank): Rules for Graphing:All graphs should be done by hand in pencil on graph paper. Unless instructed to do otherwise, draw only one graph per page. The independent variable should be on the horizontal axis and the dependent variable on the vertical axis, unless otherwise stated. When instructions are given in a lab, such as "graph voltage vs. current", they are always given as vertical axis vs. horizontal axis (so the first variable listed is on the vertical axis). The graph should use as much of the graph paper as possible. Carefully choosing the best scale is necessary to achieve this. The axes should extend beyond the first and last data points in both directions. All graphs should have a short, descriptive title at the top of each graph, detailing what is being measured. Each axis should be clearly labeled with titles and units.The axes should be linear unless otherwise mentioned. Also, the axes should begin at zero and continue beyond the highest value for that variable, unless otherwise stated. Never connect the dots on a graph, but rather give a best-fit line or curve. The best-fit line should be drawn with a ruler or similar straight edge, and should closely approximate the trend of all the data, not any single point or group of points. A best-fit line should extend beyond the data points. The slope should be calculated from two points on the best-fit line. The two points should be spaced reasonably far apart. Data points should not be used to calculate the slope. On a linear graph, draw the rise, ?y, and run, ?x, to form a triangle with the best-fit line. Be sure to label these values and include units. The calculation of the slope, ?y/?x, should be clearly shown on the graph itself. Units should be included, and value of the slope should be easily visible. See the sample graph below which incorporates the above requirements. See the Example graph below: INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET Scientific NotationSometimes, you may come up with a very long number. It might be a big number, like 4,895,000,000 or it might be a small number, like 0.0000073.Scientific Notation is a used to make these numbers easier to work with. Scientific Notation for a number is expressed as M x 10n. In this expression “n” is an integer, and “M” is a number greater than or equal to 1 and less than 10. M is expressed in decimal notation.Example 1: Convert 4,895,000,000 to Scientific Notation. Steps to conversion Remember that any whole number can be written with a decimal point. For example: 4,895,000,000 = 4,895,000,000.0The decimal place is moved to the left until you have a number between 1 and 10. In this example the decimal point was moved nine places to the left to achieve 4.895.The fact that the decimal was moved 9 places to the left is balanced by applying a multiple of 109. 4.895 x 109 = 4.895 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 4,895,000,000 Scientific Notation can also be used to turn 0.0000073 into 7.3 x 10-6.Example 2: Convert 0.0000073 to Scientific notation. Steps to conversion First, move the decimal place until you have a number between 1 and 10. If you keep moving the decimal point to the right in 0.0000073 you will get 7.3. Next, count how many places you moved the decimal point. You had to move it 6 places to the right to change 0.0000073 to 7.3. You can show that you moved it 6 places to the right by noting that the number should be multiplied by 10-6.7.3 x 10-6 = 0.0000073Remember: In a power of ten, the exponent — the small number above and to the right of the 10 tells which way you moved the decimal point.A power of ten with a positive exponent, such as 105, means the decimal was moved to the left. A power of ten with a negative exponent, such as 10-5, means the decimal was moved to the right.Practice ProblemsExpress the following in scientific notation:1) 0.00012 2) 1000 3) 0.01 4) 12 5) 0.987 Express the following as whole numbers or as decimals.1) 4.9 x 1022) 3.75 x 10-23) 5.95 x 10-44) 9.46 x 1035) 3.87 x 101Using Scientific Notation in Multiplication, Division, Addition and SubtractionMULTIPLYING in scientific notationMultiply the mantissas and ADD the exponents.00000055 x 24,000 = (5.5 x 10-7) x (2.4 x 104) = (5.5 x 2.4) x 10-7+4 = 13 x 10-3 = 1.3 x 10-2DIVIDING in scientific notationDivide the mantissas and SUBTRACT the exponents(7.5 x 10-3) / (2.5 x 10-4)= 7.5/2.5 x 10-3-(-4)= 3 x 101 = 30.ADDING or SUBTRACTING in scientific notation1. First make sure that the numbers are written in the same form (have the same exponent)3.2 x 103 + 40. x 102 (change to 4.0 x 103)Add (or subtract) first part of exponent (mantissas)3.2 + 4.0 = 7.2The rest of the exponent remains the sameAnswer: 7.2 x 103How do you make the exponents the same?Let’s say you are adding 2.3 x 103 and 2.1 x 105. You can either make the 103 into the 105 or vise versa. If you make the 103 into 105, you are moving up the exponent two places. You will need to move your decimal place in the mantissa down two places to the left.2.3 x 103 = .023 x 105Take 2.3 and move the decimal three places to the right. It equals 2300.Take .023 and move it five places to the right…it is still 2300Now add the two mantissas (2.1 + .023) = 2.123Add the exponent ending: 2.123 x 105In conclusion*if you increase (↑) the exponent, you must move the decimal in the mantissa to the left (←) the same number of places. *If you decrease (↓) the exponent, you must move your decimal point to the right (→) in the mantissa that number of places.Significant FiguresSuppose a ruler is used to measure the length of an object as shown in the figure below. Some of you may say its length is 6.75 cm. Some may say it is 6.74 cm or 6.76 cm. We are quite certain that the length is somewhere between 6.7 cm and 6.8 cm. The third (last) digit is a reasonable guess. In other words, we can only estimate to the nearest hundredth of a centimeter. There is an uncertainty of at least 0.01cm. It is unreasonable to report a value like 6.75342183 cm since we are not even sure about the third digit. The last six digits are meaningless. Suppose we take the value 6.75 cm. In this reported measurement, the first two digits are definitely significant. The third digit is also significant but has some uncertainty associate with it. It is our best estimate of where it is between 6.7 and 6.8 cm. Therefore, there are three significant figures in the measured quantity reported above. Similarly, all measured quantities are generally reported in such a way that the last digit is uncertain. All digits in a measurement including the uncertain one are called significant figures. Exact Numbers – Many times calculations involve numbers that were not obtained using measuring devices, but were determined by counting: 10 fingers, 4 sheets of paper, 20 desks, etc. Such numbers are called exact numbers. They can be assumed to have an infinite number of significant figures. Other examples of exact numbers are the 2 in 2r. Exact numbers can also arise from definitions. For example, one inch is defined as exactly 2.54 centimeters. Thus in the statement, 1 in=2.54cm, neither the 2.54 nor the 1 limits the number of significant figures when used in a calculation.Counting sig figs in reported numbers:1.All non-zero numerals are ALWAYS significant.(1, 2, 3, 4, 5, 6, 7, 8, 9)2.Zeros are frequently significant.a.In number's with explicit decimal places: left, not; trapped & right, yes.dot0 . 0 0 5 0 0 4 0 left zerostrappedright zero NOT zerosYES YESdot 3 0 0 . 8 0 trappedright zero zerosYES YESdot 5 1 , 0 0 0, 0 0 0 . 0 0 right zeros YESb.In number's WITHOUT explicit decimal places:no dot 3 0 , 1 0 0trappedright zeros zero NOT YESno dot 5 0 , 1 0 0 , 0 0 0 trappedright zeros zero NOT YESVideo tutorials HYPERLINK "" Significant figures tutorialSignificant figures againSignificant Figures WorksheetHow many significant figures are in each of the following numbers?1)5.406)1.2 x 1032)2107)0.00120 3)801.58)0.01024)1,0009)9.010 x 10-65)101.010010)2,370.0Round these numbers to 3 significant digits.1,566,311 2.7651 X 10 -3 84,592 0.0011672 0.07799 Rules for calculations with significant figures.1.Multiplication and divisionResult has the same number of sig figs as the lowest number of sig figs in the input.5.0 2.00 = 10. 2 sig figs 3 sig figs2 sig figs10. / 2.00 = 5.0 2 sig figs 3 sig figs 2 sig figs2.Addition and subtractionResult has the shortest number of decimal places as the lowest number of decimal places in the input.5.00 + 6.0 = 11.0 2 dec place 1 dec place 1 dec place10. - 2.00 = 80 dec place 2 dec place0 dec place3.Sig figs in logs.Result has the same number of decimal places in the input has sig figs.Log (1.00 10–5) = - 5.000 3 sig figs 3 dec place4.Sig figs in antilogs.Result has the same number of sig figs as the number of decimal places in the input.10–6.00 = 1.0 10–6 2 dec place2 sig binations of addition and subtraction. Follow order of operations: [(parenthesis), x and /, + and -]x (5 + 7.00) = 3.00 (12) 0 dec place 2 dec place 0 dec place3.00 (12) = 36 3 sig figs 2 sig figs 2 sig figsAddition and SubtractionLook at the measurements you are using in the calculation. Identify the measurement that has the LEAST number of decimal places. Your final answer cannot have more decimal places or fewer decimal places than that measurement.Add or subtract as usual. Then ROUND YOUR ANSWER TO THE APPROPRIATE NUMBER OF DECIMAL PLACES. 9.0 m18.005 L 9.1 m 9.1 L+ 9 m 8.905 L = 8.9 Lm = 27 mThe addition answer is rounded to 27 m with no decimal places because 9 m has no decimal place.The subtraction answer is rounded to 8.9 L because 9.1 L has only 1 decimal place.Multiplication and DivisionLook at the measurements you are using in the calculation. Identify the measurement having the LEAST number of significant figures. Your final answer cannot have more sig. figs. or fewer sig. figs. than that measurement.Multiply or divide as usual. Then ROUND YOUR ANSWER TO THE APPROPRIATE NUMBER OF SIGNIFICANT FIGURES.m300.45 m2 5 m = 60.09 m = 60 m x 2.5 mm2 = 54 m2The multiplication answer is rounded to 54 m2 because 2.5 m has only 2 sig. figs.The division answer is rounded to 60 m because 5 m has only 1 sig. fig.Video tutorialstutorial on using sig figs in calculationsmultiple step calculationsPerform the following calculations. Report your answer to the correct number of significant figures.16) 144.3854 + 8.04 – 165.32 + 30.0 = 17) 1 x 0.074 ÷ 2.014 = 18) 73.8967 x 9.03 ÷ 875.34 = 19) (410 x 63.91) ÷ (17.9 ÷ 0.002) = 20) 50.31 + 70.408 = 13.38 x 0.018 _______Review WorksheetDetermine the number of significant figures in each measurement.508.0 L ______________________820400.0 L______________________1.0200 x 105______________________807000 kg______________________0.049450 s______________________0.000482 mL______________________3.1587 x 10-8______________________0.0084 mL______________________Round all numbers to four significant figures. Write the answers to e-h in scientific notation.84791 kg ______________________38.5421 g______________________256.75 cm______________________4.9356 m______________________0.00054818 g______________________136758 kg______________________308659000 mm______________________20.145 mL______________________Complete the following addition and subtraction problems. Round off the answers when necessary43.2 + 51.0 + 48.7 = ______________________258.3 + 257.11 + 253 =______________________0.0587 + 0.05834 + 0.00483 =______________________93.26 – 81.14 = ______________________5.236 - 3.15 = ______________________4.32 x 103 – 1.6 x 103 = ______________________Complete the following calculations. Round off the answers to the correct number of significant figures.24 x 3.25 = ______________________120 x .010 = ______________________53.0 x 1.53 = ______________________4.84 / 2.5 =______________________60.2 / 20.1 = ______________________102.4 / 51.2 = ______________________Metric ConversionConversion within the metric system is simple. You either divide or multiply by 10. Anyone who can read a number line can be successful at conversions. Step1: Identify the location of the prefix of your measurement. Step 2: Identify the location of the prefix of the unit to which you want to convert. Step 3: Are you converting to a larger unit or a smaller unit? Step 4: Count the number of increments you must move to get there. Step 5: If moving to a larger unit, move the decimal point in the original measurement to the left. If you are going to a smaller unit, move the decimal point to the right. Mnemonicprefixsymbolnumberpower of 10Kingkilok1 000103Henryhectoh100102dieddekada10101bybase unitb1100drinkingdecid0.110-1chocolatecentic0.0110-2milkmillim0.00110-3yotta Y 1,000,000,000,000,000,000,000,000 1024 zetta Z 1,000,000,000,000,000,000,000 1021 exa E 1,000,000,000,000,000,000 1018 peta P 1,000,000,000,000,000 1015 tera T 1,000,000,000,000 1012 giga G 1,000,000,000 109 mega M 1,000,000 106 kilo k 1,000 103 hecto h 100 102 deca da 10 101 no prefix means: 1 100 deci d 0.1 10?1 centi c 0.01 10?2 milli m 0.001 10?3 micro μ 0.000001 10?6 nano n 0.000000001 10?9 pico p 0.000000000001 10?12 femto f 0.000000000000001 10?15 atto a 0.000000000000000001 10?18 zepto z 0.000000000000000000001 10?21 yocto y 0.000000000000000000000001 10?24 Video Tutorialsmetric conversionsKing Henry methodMetric PracticeHow many megabytes in 25 gigabytes?What is the speed of an 866 MHz computer in Hertz?The distance from the sun to Pluto is 5.9 gigametres. How many km is this?What is the power of a 120 W light bulb in kilowatts?How many grams in 0.50 kilogram? (write as a decimal, not a fraction)A thin piece of metal is 2500 micrometers. How much is this in centimeters?Convert 2.3456 x 10-5 m to nmHow many litres of pop in nine 350 mL cans?0.0032 m = ___________ mmConvert the following:1. 36.52 mg = ___________________g2. 14.72 kg = ___________________mg3. 0.0035 hm = ___________________dm4.0 .134 m = ___________________ km5. 25 mm = ___________________ cm6. 2.5 cm3 = ___________________ mL7. 243 daL = ___________________ L8. 45.23 L = ___________________ mLDimensional Analysis1. Read the entire problem.2. Find what you need to convert (start with) and what it needs to be converted to (end with).3. Find any conversion factors given in the problem. (and have your reference sheet ready)4. Write what you need to convert with units. (1st written thing)5. Find a conversion factor that has the same unit and orient so cancellation is possible.6. Continue until desired units are reached. (Like a puzzle - don’t stop trying!)7. Multiply the top numbers and divide by the bottom numbers.8. Double-check you did everything that was asked.Video TutorialsDimensional analysis explainedMultiple step dimensional analysisConversion TablesCapacity (volume)1 gallon = 1gal = 4 quarts = 4 qts1 quart = 1 qt = 2 pints = 2 pt1 pint = 1 pt = 2 cups = 2 c = 16 fluid ounces = 16 fl oz1 cup = 1c = 8 fluid ounces = 8 fl. oz (Note: a fluid ounce is not the same as the weight measure ounce.)1 fluid ounce = 1 fl oz = 2 tablespoons = 2 tbsp1 tablespoon = 1 tbsp = 3 teaspoons = 3 tsp1 fluid ounce = 1 fl oz = 480 minims ( A minim is an apothecaries’ measure.)TemperatureTemperature is measured in degrees Fahrenheit (°F)(At sea level, water freezes at 32 °F and boils at 212 °F.)Remember: the metric system measurement for temperature are Celsius (°C) and Kelvin (°K).The formulas used for temperature conversions are?F = C + 32?C = (F – 32)K = C + 273.15?C = K – 273.15Length 1 foot = 1 ft = 12 inches = 12 in1 yard = 1 yd = 3 feet = 3 ft = 36 in1 rod = 5.5 yd = 16.5 ft = 198 in1 furlong = 220 yd1 mile = 1 mi = 5280 feet = 5280 ft = 1760 yd = 8 furlongsTime1 minute = 1 min = 60 seconds = 60 s1 hour = 1 hr = 60 min1 day = 24 hrMass437.5 grains = 1 ounce = 1 oz1 pound = 1 lb = 16 ounces = 16 oz1 ton = 2000 pounds = 2000 lb(This is sometimes called a short ton or ton(US). A long ton or ton(UK) is equal to 2240 pounds.)Conversions to metric1 inch = 0.0254 meters = 2.54 centimeters1 yard = 0.9144 meters1 mile = 1609.344 meters = 1.609344 kilometers1 pound = 453.59237 grams1 ounce 28.35 grams1 grain 0.065 grams = 65 milligrams1 gallon 3.784 liters1 quart 0.9464 liters1 fluid ounce 0.02957 liters = 29.57 milliliters1 teaspoon 0.00493 liters = 4.93 milliliters 1 minim = 0.062 milliliters1 tsp = 4.93 mL1 tbsp = 14.8 mL1 grain (a small unit of weight) = 65 mg = 0.065 g?C = (?F – 32)K = (?F – 32) + 273.15Conversions to American1 meter = 1.0936 yards = 3.2808 feet = 39.37 inches1 kilometer = 0.62137 miles1 gram = 0.03527 ounces1 kilogram = 35.27 ounces = 2.205 pounds1 liter = 0.26417 gallons = 1.0567 quarts?F = C + 32?F= (K – 273.15) + 32Milliliters are used extensively in the sciences and medicine. The abbreviation “cc” is often used instead of mL. The relation of mL to volume is given by1 mL = 1 cc = 1 cm3Areas and volumesRecall that area is measured in squares. One square foot or 1 ft2 represents the area covered by a square 1 foot by 1 foot. 123456789101112Example: 12 square feet = 12 ft2 means 12 squares 1 foot by 1 foot. The measure of the area of a rectangle 3 ft by 4 ft is 12 ft2 since it can be covered (tiled) with 12 squares each 1 foot by 1 foot.374713529972000Volume is measured in cubes. One cubic centimeter or 1 cm3 represents the volume that can be covered by a cube 1 cm by 1 cm by 1 cm.Example: Find the volume of a box 3 cm by 3 cm by 4 cm. The question is, how many cubes 1 cm on a side can be put into this box. 3 cm × 3 cm × 4 cm = 36 cm3.That is, the box will hold 36 cubes 1cm by 1 cm by 1 cm.Making metric conversions on both the top and the bottom and when the unit is raised to a powerDetermine the relationships needed to make the top conversion and the bottom conversionDo the conversions in stepsCancel the units raised to a power Example Convert 45 m/s2 to km/min2 (notice the m to km is one conversion and s2 to min2 is another conversion)Relationships 1000 m = 1 km 60 s = 1 min1003935302260002089785146050001470660174625008039101651000045 m 1 km 60 s 60 s = 162 km only 2 sig figs allowed2280285184150016421101841500737235247015003943351841500 s2 1000 m 1 min 1 min min2160 km/min2 final answer place the units properly, convert the top unit, then the bottom unit. Practiceconvert 4.56 g/cm3 to kg/m3b. convert 78.4 g/mL to kg/LApplying dimensional analysis to word problemsRead the problem carefully to determine the starting and ending units. Look for the actual question. Determine if the starting and ending units are for the same dimension. (Is it asking to change from mass to volume, or from money to mass?) If they are not, look for a relationship between those dimensions in the problem.Find a pathway from the starting units to the final unitsDetermine all of the relationshipsWrite the starting value with the units and cancel the unitsEvaluate how many significant figures are allowed and round answerExample:Gold sells for $815/ounce. Considering that there are 16 ounces in a pound and 454 g in a pound, how many milligrams of gold could you buy for 10 cents? The underlined section is the question. Convert 10 cents to mg of gold.The price of the gold gives a relationship between $ and ounces (cents can be converted to $ and ounces can be converted to mg)Pathways cents to $ to ounces to grams to mgRelationships$1 = 100 cents 16 oz = 1 lb = 454 g 1 g = 1000 mg $815 = 1 oz gold3213735431800013658852413000105156043180004324355270500279463552705002223135527050017659355270500-628651670050010 cent $1 1 oz gold 1 lb 454 g 1000 mg = 3.4815 mg rounded to 3 sig fig 100 cents $815 16 oz 1 lb 1 g 3.4814230354508500 3 sig figsPracticea. The density of aluminum is 2.70 g/cm3. What is the mass in kg of a block of aluminum that measures 5.00 cm x 8.00 cm x 3.0 cmb. A large river flows at the rate of 6.5 x 10 5 cm3/s into a rectangular shaped boat lock 25 m long, 45 m wide and 20 m high. How many minutes before the lock would be filled to the top with water? (Start with the volume of the lock)Multiple-Step Dimensional AnalysisHow many inches are there in a football field (100 yards)? How many walking paces are there approximately as you walk down Main Street (0.25 miles)? 22 inches = 1 walking paceHow many feet are between the first and second story of a building (1 story)? 1 story = 3.33 meters; How many hours are in a fortnight (2 weeks)? How many decades are equal to 1.7 x 1025 minutes?On average, there are 3 pages in every chapter of a James Patterson novel. Each book has approximately 79 chapters. James Patterson has published 58 books. Approximately how many pages has James Patterson written?Houston has approximately 2,210,000 million people. Each person has 2 hands and each hand has 5 fingers. How many fingers are in Houston? Answer in scientific notation.There are 2850.5 miles between Houston, TX and Vancouver, Canada, site of the 2010 Olympic Games. How many meters is that equal to if 1 mile is equal to 1.6 km? Express your answer in scientific notation.A newborn baby eats 8 times a day. At each feeding, he eats 2.5 ounces of formula. How many days would it take for the baby to eat 1000 ounces?Jonathan raised 60 goats, then entered into a series of business transactions. He traded all the goats for sheep at an exchange rate of 5 goats for 7 sheep. Next, he exchanged all the sheep for hogs at a rate of 4 sheep for 2 hogs. How many hogs did he get?Eggs are shipped from a poultry farm in trucks. Each carton of eggs holds 12 eggs. The cartons of eggs are then placed in a crate that holds 20 cartons. The cartons are packed in trucks that carry 3125 crates of eggs. How many truckloads will it take to carry 3.75 x 106 eggs?A chemistry teacher spends 5 minutes grading 1 student’s lab. She has 150 students who turn in lab papers for each lab. If we do 25 labs in class, how many minutes will I spend grading lab papers?My son drinks 3 cups of milk a day. There are 8 ounces in a cup. How many ounces would he have drunk after 10 weeks?In the average US household, the television is on 6.75 hours a day! How many hours will have passed after 77.7 years (the average life expectancy of an American)?Each dimensional analysis problem has taken you 1.5 minutes to complete. How many dimensional analysis problems could you complete in 6 weeks of chemistry class (242 minutes a week)?Density WorksheetQuote your final answer using the correct number of significant digitsDensity = Mass / Volume units: g/cm3Calculate the density of a material that has a mass of 52.457 g and a volume of 13.5 cm3. A student finds a rock on the way to school.? In the laboratory he determines that the volume of the rock is 22.7 mL, and the mass in 39.943 g. ? What is the density of the rock?The density of silver is 10.49 g/cm3.? If a sample of pure silver has a volume of 12.993 cm3, what is the mass? What is the mass of a 350 cm3 sample of pure silicon with a density of 2.336 g/cm3?Pure gold has a density of 19.32 g/cm3.? How large would a piece of gold be if it had a mass of 318.97 g? Accuracy and PrecisionVideo TutorialsDifference between accuracy and precisionCareful measurements are very important in physics because theories are based on observation and experiment. No measurement is perfect. The imperfection must be described so a measurement’s accuracy and precision must be considered. Accuracy and precision are used interchangeably in everyday life but they have more specific meanings in science. 3248025153034Precision- the degree of exactness of a measurement; how reproducible a measurement is00Precision- the degree of exactness of a measurement; how reproducible a measurement is38862038100Accuracy- describes how close a measurement is to the correct or accepted value of the thing you’re measuring.00Accuracy- describes how close a measurement is to the correct or accepted value of the thing you’re measuring.Random errors: Precision (Errors inherent in apparatus.) ?A random error makes the measured value both smaller and larger than the true value. Chance alone determines if it is smaller or larger. Reading the scales of a balance, graduated cylinder, thermometer, etc. produces random errors. In other words, you can weigh a dish on a balance and get a different answer each time simply due to random errors. They cannot be avoided; they are part of the measuring process. Uncertainties are measures of random errors. These are errors incurred as a result of making measurements on imperfect tools which can only have certain degree of accuracy. They are predictable, and the degree of error can be calculated. Generally they can be estimated to be half of the smallest division on a scale. For a digital reading such as an electronic balance the last digit is rounded up or down by the instrument and so will also have a random error of ± half the last digit.?Systematic errors: Accuracy (Errors due to "incorrect" use of equipment or poor experimental design.) ?400050099695Examples of Systemic errors:Leaking gas syringes. Calibration errors in pH meters. Calibration of a balance Changes in external influences such as temperature and atmospheric pressure affect the measurement of gas volumes, etc. Personal errors such as reading scales incorrectly. Unaccounted heat loss. Liquids evaporating. Spattering of chemicals 00Examples of Systemic errors:Leaking gas syringes. Calibration errors in pH meters. Calibration of a balance Changes in external influences such as temperature and atmospheric pressure affect the measurement of gas volumes, etc. Personal errors such as reading scales incorrectly. Unaccounted heat loss. Liquids evaporating. Spattering of chemicals 32950151714500A systematic error makes the measured value always smaller or larger than the true value, but not both. An experiment may involve more than one systematic error and these errors may nullify one another, but each alters the true value in one way only. Accuracy (or validity) is a measure of the systematic error. If an experiment is accurate or valid then the systematic error is very small. Accuracy is a measure of how well an experiment measures what it was trying to measure. These are difficult to evaluate unless you have an idea of the expected value (e.g. a text book value or a calculated value from a data book). Compare your experimental value to the literature value. If it is within the margin of error for the random errors then it is most likely that the systematic errors are smaller than the random errors. If it is larger then you need to determine where the errors have occurred. Assuming that no heat is lost in a calorimetry experiment is a systematic error when a Styrofoam cup is used as a calorimeter. Thus, the measured value for heat gain by water will always be too low. When an accepted value is available for a result determined by experiment, the percent error can be calculated.?Categories of Systematic Errors and how to eliminate them: ???????? a. Personal errors: These errors are the result of ignorance, carelessness, prejudices, or physical limitations on the experimenter. This type of error can be greatly reduced if you are familiar with the experiment you are doing. Be sure to thoroughly read over every lab before you come to class and be familiar with the equipment you are using. Be Prepared!!!???????? b. Instrumental Errors: Instrumental errors are attributed to imperfections in the tools with which the analyst works. For example, volumetric equipment such as burets, pipets, and volumetric flasks frequently deliver or contain volumes slightly different from those indicated by their graduations. Calibration can eliminate this type of error.???????? c. Method Errors: This type of error many times results when you do not consider how to control an experiment. For any experiment, ideally you should have only one manipulated (independent) variable. Many times this is very difficult to accomplish. The more variables you can control in an experiment the fewer method errors you will have.Percent Error Video TutorialPercent error formulaWhen scientists need to compare the results of two different measurements, the absolute difference between the values is of very little use. What is used invariably is the percent error between the two measurements. ???? % error =?? | experimental result - accepted value |?? * 100 ????????????????????????????????????????? accepted value When you do the subtracting that gives you the numerator of the fraction, note how many significant figures remain after the subtraction and express your final answer to no more than that number. If neither of the two values being compared is an "accepted value", then use either number in the denominator to get the fraction. ?If one value is more reliable than the other, choose it for the denominator. Example:? A student measures the volume of a 2.50 liter container to be 2.38 liters. What is the percent error in the student's measurement? % error = (2.50 liters - 2.38 liters)? x?? 100 ????????????????????????????????? 2.50 liters ?????????????????????? =? (0.12 liters)???? x??? 100 ??????????????????????????? 2.50 liters ???????????????????????=? 0.048???? x?? 100 ??????????????????????? =? 4.8% (2 sf)% Error WorksheetSolve each of the following problems. Show all your work, watch the significant figures in your final answer and remember to include units!!As the result of experimental work, a student finds the density of a liquid to be 0.1369 g/cm3. The known density of that liquid is 0.1478 g/cm3. What is the percent error of this student’s work?After heating a 10.00 g sample of potassium chlorate, a student obtains an amount of oxygen calculated to be 3.90 g. In theory there should be 3.92 g of oxygen in this amount of potassium chlorate. What is the percent error in this experiment?The melting point of potassium thiocyanate determined by a student in the laboratory turned out to be 174.5 oC. The accepted value of this melting point is 173.2 oC. What is the percent error in this reading?A person attempting to lose weight on a diet weighed 175.0 lb. On a bathroom scale at home. An hour later at the doctor’s office, on a more accurate scale, this person’s weight is recorded as 178.0 lb. Assuming that there was no real weight change in that hour, what is the percent error for these reading?The Handbook of Chemistry and Physics lists the density of a certain liquid to be 0.7988 g/mL.? Taylor experimentally finds this liquid to have a density of 0.7925 g/mL.? The teacher allows up to +/- 0.500% error to make an “A” on the lab.? Did Fred make an “A”?? Prove your answer.An object has a mass of 35.0 grams.? On Anthony’s balance, it weighs 34.85?grams.? What is the percent error of his balance??Shelby measured the volume of a cylinder and determined it to be 54.5 cm3. The teacher told her that she was 4.25% too high in her determination of the volume.? What is the actual volume of the cylinder?Walter gets a paper back in lab with “-2.75% error” written on it.? He had found the mass of an object to be 100.7 grams.? What should he have found as the mass of the object?? After lab, all of Darrel’s friends looked at his data and laughed and laughed. They told him that he was 30.8% too low in the boiling point he had just recorded.? He had recorded a boiling point of 50o C on his data sheet.? What is the correct boiling point of the liquid he was working with in lab?? Video tutorialAccuracy and Precision in measurementsAnalysing dataWhen taking scientific measurements, the goals are to measure accurately and with precision.Accuracy indicates the closeness of the measurements to the true or accepted value.Precision is the closeness of the results to others obtained in exactly the same way.In this image, the bull’s-eye represents the accepted true value. Each cross represents a repeated measurement of the same quantity.In certain situations in the laboratory, you may be measuring a quantity that has an accepted value. The difference between the measured result and the accepted value is the error in the result.error = measured value - accepted value% error = (error in measurement/accepted value) x 100For example, the accepted value for the mass of a new golf ball is 45.93 g. A student weighs a golf ball and finds it to be 46.45 g. The % error is: % error= (error in measurement/accepted value) x 100= [(46.45 – 45.93)/45.93] x 100= [0.52/45.93] x 100= 1.1%Rather than measuring once, it is common practice to take a number of separate measurements. This eliminates any ‘outlier’ results (results that do not fit the expected outcome) and allows for an average value to be taken.For example, a student weighs a golf ball on five separate occasions, and the results are: 45.89 g, 45.91 g, 46.06 g, 36.98 g and 45.94 g. On looking carefully at the results, it is clear that the result ‘36.98 g’ does not fit in with the other results. It is an ‘outlier’ and is discarded. The average mass is calculated as: (45.89 + 45.91 + 46.06 + 45.94)/4 = 45.95 g Coin diameter A gold coin has an ‘accepted’ diameter of 28.054 mm.Two students are asked to measure the diameter of four gold coins. Student A uses a simple plastic ruler. Student B uses a precision measuring tool called a micrometer.Student A – plastic rulerStudent B – micrometer27.9 mm28.0 mm27.8 mm28.1 mm28.246 mm28.244 mm28.246 mm28.248 mmCalculate the average value for each set of measurementsStudent A – plastic rulerStudent B – micrometerCalculate the % error for each set of measurements.Student A – plastic rulerStudent B – micrometerCompare the average value for each set with the accepted value:Which student’s data is more accurate?Which student’s data is more precise?Compare the percentage error for each set:Which student’s data is more accurate?Which student’s data is more precise?Explain any odd findings:Aluminium bar densityTwo students are given a small cylinder of aluminium of known mass and asked to determine its density. (The ‘accepted’ density of aluminium is 2.702 g/cm3.) Since density is mass/volume, the students need to calculate the volume of the cylinder. To do this, the height and diameter of the cylinder need to be measured. Student A is told to use a simple plastic ruler and to make four independent measurements for each dimension. Student B is told to use a precision measuring tool called a micrometer.Student A – plastic rulerStudent B – micrometer2.2 g/cm32.3 g/cm32.7 g/cm32.4 g/cm32.703 g/cm32.701 g/cm3 2.705 g/cm3 5.811 g/cm3 Calculate the average value for each set of density values, making sure that any ‘outliers’ are not included.Student A – plastic rulerStudent B – micrometerCalculate the % error for each set of values.Student A – plastic rulerStudent B – micrometerCompare the average value for each set with the accepted value:Which student’s data is more accurate?Which student’s data is more precise?Compare the percentage error for each set:Which student’s data is more accurate?Which student’s data is more precise?Explain any odd findings: ................
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