# 6. SCIENTIFIC NOTATION - DR. CHIRIE SUMANASEKERA - Home

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Chemistry notes Full Name:__________________________ Period:__ Seat___ Date:________ Unit 2: Analyzing Data1. UNCERTAINTY IN DATAWhen measurements are made, they always have a degree of uncertainty. For example, if you get 1.234 g, 1.236 g and 1.233 g as mass measurements for a pinch of sugar, the certain values are 1.23 as all the measurements have this number but the underlined value varies between the readings. So, in this example, we are certain up to 3 digits but not 4 and the fourth or last digit is the uncertain value. 2. PRECISION vs. ACCURACYWhen scientists look at measurements, they want to know how accurate as well as how precise the measurements are. PRECISION refers to how close a series of measurements are to one another. Precise measurements might not be accurate, and accurate measurements might not be precise. When you make measurements, you want to aim for both precision and accuracy.ACCURACY refers to how close a measured value is to an accepted value. The more decimal places there are to a measurement, the more accurate it becomes. Ex: 2.021 cm is more accurate than 2.02 cm.3. Ways to increase the precision and accuracy of your data:Using the proper measuring devices for the taskUsing calibrated and properly maintained, clean equipmentEnsuring measurements are within the detection range of the instrument usedUsing the average of multiple data recordings of the same sample (more than triplicate)4. Percent error Quantities measured during an experiment are called experimental values. The difference between an accepted value and an experimental value is called an error. The ratio of an error to an accepted value is called, percent error. When you calculate percent error, ignore any plus or minus signs because only the size of the error (or its absolute value) counts. The equation for percent error is as follows:Ex: Actual length of the pen =10.3 cm, Eric’s measurement = 10.2 cm. percent error = I 10.2 -10.3 I x 100 = 0.1 x 100 = 0.970 %10.310.35. Two types of experimental errors:Random (indeterminate) error = a value has an equal probability of being high or low based on human error for example.Systematic (determinate) error = an error that occur in one direction each time and is always either high or low. (Ex: measuring mass on a scale that has a chewing gum stuck on the under surface)6. SCIENTIFIC NOTATIONIn scientific notation, an exponent is used to easily indicate complex numbersAll numbers in scientific notation are expressed as one whole number that is not zero, followed by a decimal that is followed by one or more numbers X (minus or positive)10th power of an exponent:Examples: 0.00002478 in scientific notation = 2.478 x 10-5 (note: that when decimal is followed by zeros, you have to move the decimal point to the RIGHT so you get a 10- power)83409800000000 in scientific notation = 8.34098 x 1013 (note: that when a decimal is absent, you have to move the decimal point to the LEFT from the last digit in the number, so you get a 10+ power)7. Significant figures (Sig-figs)The more digits reported, the more precise the measurement. The digits reported in a measurement are called significant figures. The significant figures of a number are?the number of important single digits in a measurement that tell how accurate it is. There are 6 rules associated with figuring out significant figures of a number. 5 Rules for Identifying Significant Figures All non-zero numbers are always significant. (EX: 123.45 contains five sig-figs)Any zeros between significant figures are significant (*zeros between sig-figs are highlighted. EX: 82800.05 contains seven sig-figs, 8.05 contains three sig-figs)All final zeros to the right of a decimal and at the end of the number are significant. (**Final zeros are underlined in the EX: 123.50 contains six sig-figs, 90.500 contains four sig-figs)Place-holder zeros are NOT significant. To remove a place-holder zeros, numbers are written in scientific notation. (EX place holders are underlined: 0.90000 contains five sig-figs, 49000 contains two sig-figs)Counting numbers and defined constants have an infinite number of significant figures. (EX: The =10.0000000…? with an infinite number of zeros. Thus, this quantity has an infinite number of sig-figs)Addition and subtraction of Significant figures:? The answer should be rounded off so as to contain the same number of decimal places as the number with the LEAST number of decimal places.? Thus:? 11.31?+?33.264 +?4.1 =?48.674?Rounded off to 48.7Multiplication and Division of Significant figures:? The answer should be rounded off to contain the same number of Sig figs as the least number of decimal places.Thus:? 5.282?x 3.42?=?18.06444?Rounded off to =18.1Rounding Rules for all numbersIn a series of calculations carry the extra digits through the final result and then, round.If the digit to be removed is:Less than 5, the preceding digit stays the same (Ex. 1.33 rounds to 1.3)Is equal or greater than 5, the preceding digit is increased by 1(Ex. 1.36 rounds to 1.4)Full Name:__________________________ Period:__ Seat___ Date:________ (Due 8-23-19)8-20-2019 Unit 2-Problem set 1:Which of the following measurements is most accurate?4.03 cm b. 20000 cmc . 9.87501d. 0.520043190Circle the digit that is uncertain in each measurement given below:7095b. 70780 cmc . 7.47502d. 0.70466140Katie repeatedly measured the mass of the unknown metal sample using a digital balance and obtained the values, 20.9g (Trial-1), 29.5 (Trial-2), and 19.1g ()Trial-3 and 26.9g (trial-4). The actual mass of the object is 21.8g.Explain why you think her data is precise or accurate.What is the percent error of the measurement of Trial-1?The actual mass of an Erlenmeyer flask is 33.9mg. A student’s experimental mass readings for this Erlenmeyer flask are given below: Trial-1: 34.1 mgTrial-2: 33.8 mgTrial-3: 33.7 mgAre these data precise or accurate?(b) Calculate the percent error for each trial. On a bathroom scale a man always weighs 2.5 lbs. less than the scale at the doctor’s office. Assume that the scale at the doctor’s office is showing precise and accurate measurements. The person’s actual weight is 125 lbs. What is the percent error of the bathroom scale?Write the following numerical figures in scientific notation:0.00037801 mol ________________195.3077 nL ___________________30000 cm3 ________________1.05 m/s ________________2 Kg ___________________0.309 pmol _______________Convert the following figures from scientific notation numerical figures:2.391 x 10-3 M________________3.0117 x 102 ng ________________9.00451 x 108cm3 _______________2.03 100 m/s ________________4.94 x 10-6 mg________________9.2441 x104 L _______________Round the following numbers to the nearest two decimal places:3.00814 kL _______________3.004814 Kg _______________800.213 L_______________0.0013 mmol ________________Underline sig-figs and state the total number of significant figures for each:0.0201 ______3000 ______3000.00 _______0.0000492_______0.020000010 _____4.3650 ________30 kittens: _______Perform the following Significant figure mathematical functions 0.0000492 + 20.0501 _____________300.42 – 2.006 _____________30 + 3.9 _____________40102.0 – 20.1 _____________30 x 3.970 _____________1120 ÷ 30000 _____________15020 ÷ 0.04 _____________8. METRIC (SI) UNITS OF MEASUREMENT Date: 8-26-2019You probably know your height in feet and inches and mass in pounds and ounces. These are units from the archaic Imperial (British) system of measurements that the rest of the world has abandoned. Why we still use the Imperial measurement system in America is very disturbing if we deem ourselves an advanced civilization! Nations outside the United States, however, use the extremely logical and easy to use, metric system of measurements. The METRIC system is a decimal based system of units that was invented in France during the 1900s. Scientists today use a revised form of the metric system called the Système Internationale d’Unités, or SI. When we study chemistry, we will ONLY use the metric system of measurements.Metric BASE UNITS:There are seven base units in SI. A base unit is a unit of measure that is based on an object or event in the physical world. Table 2-1 lists the 6 of the SI base units you need to know, their abbreviations, and the quantities they are used to measure. SI is based on a decimal system. So are the prefixes in Table 2-2, which are used to extend the range of SI units to greater or lesser amounts.Table 2-1QuantitySI Base unit (symbol)Timesecond (s)Lengthmeter (m)Massgram (g)Temperaturekelvin (K)Volumeliter (L)Amount of substance mole (mol)Metric PREFIXES Table 2-2 Metric Prefixes Used with SI UnitsPrefixSymbol Represented Value As a Decimal As an Exponentkilok 10001000103 BASE unit- 11100decid 1/100.110-1centic1/1000.0110-2millim1/10000.00110-3micro?1/10000000.00000110-6nanon1/10000000000.00000000110-9picop1/10000000000000.00000000000110-12Example: If we use the Base unit Meter for length,kilo 1 km = 1000 mBase unit 1m = 1 meterdeci 10 dm = 1 mcenti 100 cm = 1 mmilli 1000 mm = 1 mmicro 1000 000 ?m = 1 mnano 1000 000 000 nm = 1 mpico 1000 000 000 000 pm = 1 mWe can use factors to express the relationship between meters and kilometers as shown:1 km = 1000m can be written as: 1km/ 1000m or 1000m/1km which both mean the same.Practice problem: Convert 30.49 m to km. Convert 2.906 mol to ?mol***See Dimensional analysis section for inter converting between metric values.Temperature Only Celsius/centigrade (0 C) and Kelvin (K) scales are used in Chemistry. Both of these are Metric units but only Kelvin is used as the BASE unit for temperature. We do NOT use the non-metric, Fahrenheit scale as it is not a decimal scale. You must be able to interconvert between Kelvin and Centigrade scales. The Celsius scale is based on the freezing and boiling points of water. The freezing-point of water = 0 0CThe boiling-point of water = 100 0C On the Kelvin scale, water freezes at about 273 K and boils at about 373 K. One kelvin is equal in size to one degree on the Celsius scale. 0 K is called Absolute zero and?is thought to be the coldest temperature, possible. To convert from degrees Celsius to kelvins, add 273 to the Celsius measurement. To convert from kelvins to degrees Celsius, subtract 273 from the measurement in kelvins. See the problems shown here:Practice problems:Convert -20.3 centigrade into Kelvin:Convert 397.8 K in to Celsius:Baby Sam has a fever of 102.6 0C. convert this value into Kelvin:Amount of substance (mole)Is the quantity of anything that has the same number of particles found in 12.0 grams of carbon-12 isotope. That number of particles is Avogadro's Number, which is roughly 6.02x1023. A?mole?of carbon atoms is 6.02x1023?carbon atoms. Ex: A?mole?of?chemistry teachers is 6.02x1023?chemistry?teachers.Practice problem: Find the number of moles in 2.4 x 1029 atoms of carbon? Derived units Not all quantities can be measured using SI base units. For example, density and volume of solid objects are measured using units that are a combination of base units. An SI unit that is defined by a combination of base units is called a derived unit. The SI unit for volume is the liter. A liter is a cubic meter, that is, a cube whose sides are all one meter in length. Density is a ratio that compares the mass of an object to its volume. The SI units for density are often grams per cubic centimeter (g/cm3) or grams per milliliter (g/mL). One centimeter cubed is equivalent to one milliliter (1 cm3 = 1 mL). Fun fact: 1g of Pure water has a volume of 1 cm3 or 1ml. ] Practice problems:At 170C, 216 g of olive oil has a volume of 100 ml. Calculate the density of olive oil.Which of the following are derived units: m/s (velocity)mol/ L (molarity) 36.9 K (temperature)N/m (Work = Newton/meters) 45.9 km2 (area = km x km) 32cm3 (Volume = cm x cm x cm9. DIMENSIONAL ANALYSIS Dimensional analysis is a method of problem solving that focuses on the units that are used to describe matter. Dimensional analysis often uses conversion factors. A conversion factor is a ratio of equivalent values used to express the same quantity in different units. A conversion factor is always equal to 1. Multiplying a quantity by a conversion factor does not change its value—because it is the same as multiplying by 1— but the units of the quantity can change.Example: Converting From One Unit to Another UnitQ: How many centigrams are in 5 kilograms?Two conversion factors are needed to solve this problem. Remember that there are 1000 grams in a kilogram and 100 centigrams in a gram. To determine the number of centigrams in 1 kilogram, set up the first conversion factor so that kilograms cancel out. Set up the second conversion factor so that grams cancel out.Practice problems:Mount Everest is 8847 m high. How many centimeters high is the mountain?Your friend is 1.56 m tall. How many millimeters tall is your friend?A family consumes 12.5L of milk per week. How many microliters of milk do they need to buy for one week?How many hours are there in one week? Convert 3.047 pg into kgConvert 3.091 km into cm10. REPRESENTING DATA (GRAPHS)A graph is a visual display of data. Representing your data in graphs can reveal a pattern if one exists. You will encounter several different kinds of graphs in your study of chemistry.Correct way to draw a graph:Based on the spread of data values, which type of graph to use? Determine independent variable is on x- axis and Dependent variable ( the tested variable) is on the y-axis.What number is used as the minimum and maximum range for each axis?Place the Title (on top), Label x and y axis and write the units beside the measurement.TYPES OF GRAPHS:Pie chart (Circle graph)A Pie chart is used to show the parts of a fixed whole. This kind of graph is sometimes called a pie chart because it is a circle divided into wedges that look like pieces of pie. Each wedge represents a percentage of the whole. The entire graph represents 100 percent. These graphs have immediate visual impact and are easy to understand but does not show data trends or patterns. dioxide (CO2):?Fossil fuel use is the primary source of CO2. ?CO2?can also be emitted from direct human-induced impacts on forestry and other land use, such as through deforestation, land clearing for agriculture, and degradation of soils. Likewise, land can also remove CO2?from the atmosphere through reforestation, improvement of soils, and other activities.Methane (CH4): Agricultural activities, waste management, energy use, and biomass burning all contribute to CH4?emissions.Nitrous oxide (N2O): Agricultural activities, such as fertilizer use, are the primary source of N2O emissions. Fossil fuel combustion also generates N2O.Fluorinated gases (F-gases): Industrial processes, refrigeration, and the use of a variety of consumer products contribute to emissions of F-gases, which include hydrofluorocarbons (HFCs), perfluorocarbons (PFCs), and sulfur hexafluoride (SF6).Q1: According to this graph what gas is the largest contributor of the greenhouse effect?CO2 b. N2O c. CH4 d. none of these e. F-gasesQ2: According to the data, which human activity produces the most amount of greenhouse gases? Q3: which of the following is likely to reduce man-made CO2 gas production?Growing backyard food forests in every homeSwitching to electric carsEating less beefReplanting forests Bar graphs A bar graph is often used to show how a quantity varies with time, location, or temperature. In this situation, the quantity being measured appears on the vertical axis. The independent variable—time, for example— appears on the horizontal axis. If the data in the x-axis are interconnected or continuous in a bar graph, then it is called a histogram. If the data on the x-axis are not inter-connected, it is a regular bar-graph.Q1: Why is there a gap between age 80 and 90?: The FBI data shown below can be represented in a pie chart, true or false?________Q3: why do you think the FBI chose to use a bar graph for this?______________________________________Line graphs (*Used for scientific data representation)The points on a line graph represent the intersection of data for two variables. When you design an experiment, only one variable is tested (unknown variable) while changing another variable that the experimenter can control. For example, you want to know if the volume of extra virgin olive oil changes with temperature. So, the variable you are experimenting is __________ and the variable you are controlling is, _____________. To do this experiment, you will take a known mass of olive oil and measure how its volume changes with temperature. To study the relationship between temperature and volume, you will draw a graph. Always, the independent variable is plotted on the horizontal (x) axis while the dependent variable is plotted on the vertical (y) axis. The points on a line graph are connected by a best fit line, which is a line drawn so that as many points fall above the line as below it.Q3: Why does ice float on water?If a best fit line is straight, there is a linear relationship between the variables. This relationship can be described by the steepness, or slope, of the line. If the line rises to the right, the slope is positive. A positive slope indicates that the dependent variable increases as the independent variable increases. Thus, the variables are directly proportional.If the line falls to the right, the slope is negative. A negative slope indicates that the dependent variable decreases as the independent variable increases. Thus, the variables are inversely proportional. You can use two data points to calculate the slope of a line.Practice Problems: Calculate the slope of each line using the points given.(24 cm3 , 36 g), (12 cm3 , 18 g)(25.6 cm3 , 28.16 g), (17.3 cm3 , 19.03 g)(15s, 147 m), (21 s, 205.8 m)d. (55 kJ, 18.75° C), (75 kJ, 75.00° C)x-y scatter plots: (*Most important type of graph for scientific data representation)A?scatter plot?(also called an?XY graph, or?scatter-diagram) is a two-dimensional?chart?that shows the relationship between two variables. In a?scatter graph, both horizontal and vertical axes are value axes that?plot?numeric data.Questions: Can you represent the data in the table shown here with a histogram?______ Explain why_________________________________________________________________What 20.5 0C, how much sales can be expected?____________Scientific notation problems: Regular notation Convert to Scientific Notation15 cm24500000 M3750200101 nL46890300000000050.1 kg60.0002170.0000000000000001068 Scientific notation Convert to Regular notation and UNITS83.70 x 10-4 s93.8 x 105 g/cm3104.004876 x 10-18 km116.022 x 1023 atoms122.004502 x 10-313. Which SI units would you use to measure the following quantities? the amount of water you drink in one day_____the distance from New York to San Francisco______the mass of an apple________the number of atoms in a substance _________the duration of the CBS Nightly News broadcast ______14. How does adding the prefix kilo- to an SI unit affect the quantity being described?15. What units are used for density in the SI system? Are these base units or derived units? Explain your answer.16. A student takes three mass measurements. The measurements have errors of 0.42 g, 0.38 g, and 0.47 g. What information would you need to determine whether these measurements are accurate or precise? 17. What conversion factor is needed to convert minutes to hours? 18. What kind of graph would you use to represent the following data?the segments of the population who plan to vote for a certain candidate______________the average monthly temperatures of two cities ______________the amount of fat in three different kinds of potato chips ______________the percent by mass of elements in Earth’s atmosphere ______________your scores on math quizzes during a year ______________the effect of a hormone on tadpole growth ______________ Problem Solution using SIG-FIG rules and correct UNITS193.8096 cm + 0.52 cm2034.2 km x 4980003.259 km211.22 kg ÷ 0.3902 L2212.80446 nm - 30.222 nmProblemSolution in Dimensional analysis format23Convert 3.62 m to cm 24Convert 480.10 cm to m25Convert 4.608 ml to L26Convert 73.008L into L27Convert 5.3 g into kg28. The depreciation of Sarah’s car value over time is shown in the table below. Display the data in an appropriate graph. Is the value of the car inversely or directly proportional to the years owned?What is the value of the car in June 15, 2004?Due: 8-29-2019 Full Name:__________________________________ Seat ___ Period: ____ Score: ______ /50 LAB3: Unit-2 Measuring the Density of Liquids and Solids Safely equipment: None needed as we will not be using any harmful chemicalsToday, you will be learning how to calculate the DENSITY of liquids and solids. If you mix oild and water and shake them up, what happens? Why does that happen? Maybe you can answer this question by comparing a physical property of oil and water like density. You will have to compare the densityLab#3_Learning objectives:Explain the difference and relationship between mass and density using an equation.Take accurate measurements of mass using a digital balanceTaking measurements of liquid volumes by reading a meniscusTaking length measurements of a regular shaped object to calculate its volume using the correct mathematical formulaPerforming density calculation using the density equationRelate hydrophobicity and miscibility to densityDensity is a derived unitSI measurement system is built on seven fundamental standards called?base units. All other SI units are derived by multiplying, dividing or powering the?base?units in various combinations. Some Examples of Derived units:Mechanical work is?force?applied multiplied by distance moved is written as= N x m = NmSpeed is distance divided by time written as= m/s or ms-1Area is length multiplied by width and has the unit = m x m = m2Density is mass divided by volume = g/ml or g / cm3DENSITY OF A LIQUID:Experiment: Determine if there is a difference in density between TAP water and Olive oil :Your hypothesis: _____________________________________________________________ ______________________________________________________________Experimental Procedure: Place the graduated cylinder on the balance and press “T” to tare. [Make sure the scale in on grams by pressing “M” till a small g symbol appear on the bottom of the screen.]Carefully pour the liquid in the beaker into the graduated cylinder.Measure the volume of water by placing your eye at the base of the meniscus in correct units.Measure the mass of the water in correct units.Calculate the density of TAP water using the formula shown above. You must show all steps of your calculation.Mass of water:_________ Volume of water:________Density of water = ________ Calculating Density of an irregular shaped object (rock)Measure the Mass of the dry object using the digital balance. Record the volume of water in the graduated cylinder in ml. Place the rock inside the cylinder and record the volume of the water and the rock in ml. Calculate the density of the rock.Mass of rock:_________ Volume of water alone:________Volume of water + rock:_______Volume of rock alone:_______Density of Rock:________ = _________Calculating Density of a regular shaped solid wood object (cuboid shaped)Volume of a cube = length x width x heightProcedure: Measure the Mass of the solid object using the digital balance and measure the length,height and width of the object using the ruler. Then find the density of the object. Mass of object :_________ Length :________ Width: __________ Height:_________Volume of objectDensity of object:________ = _________ ................
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