Module 3 Notes

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Jan 9, 2024

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1.5 Sig Figs Note Guide Measurement, Significant Figures and Rounding https://youtu.be/b38hFWvEjwI I. Measurement A. Define Precision : B. Define Accuracy : C. Illustrate the difference between accuracy and precision using a dart board. D. The last digit in a measurement is the ________________ digit. II. Significant Figures https://youtu.be/Udnek3sbeQ8?list=PL9A16EF5EA79D5F53 A. Significant Figures include _________ known digits and only ___________estimated digit in a measurement. B. Rules for counting Significant Figures (Complete the chart.) Rule Example 1. 2. 3. 4. 5. 6.

https://youtu.be/wYa1_3OzyRI?list=PL9A16EF5EA79D5F53 III. Rounding A. General Rules for Rounding (Complete the chart.) Number following the keeper is: Then the last digit should: Example (rounded to 3 sig. figs.) Greater than 5 Less than 5 5, followed by nonzero digit(s) 5, not followed by nonzero digit(s) and preceded by an odd digit 5, not followed by nonzero digit(s) and preceded by an even digit https://youtu.be/QLKQpFCXaDU?list=PL9A16EF5EA79D5F53 B. Multiplication and Division The answer to any multiplication and/or division calculation must have the same number of significant figures as the ____________ number of significant figures in the givens.

C. Addition and Subtraction The answer to any addition and/or subtraction calculation can have the same number of decimal places and the given with the ____________number of decimal places. 11. 1.6 NOTES - Dimensional Analysis (or Factor Label Method) https://youtu.be/fEUaQdaOBKo?list=PL9A16EF5EA79D5F53 ( Solving Dimensional Analysis Problems - Unit Conversion Problems Made Easy!; author: sciencespot; 8:46) What are the 3 things you need to perform the Factor Label Method (AKA Dimensional Analysis)? 1) The problem 2) Conversion chart 3) Units Conversion factors get you from representing in one unit, to representing in another unit. The starting unit is the unit that is first and the ending unit is the unit that is last. When cancelling units, you want to cancel ALL units, EXCEPT for the unit you end with. Show the cancellation of units for the following expression: days 1 × hr days × min hr What was the starting unit? What is the ending unit? When you bring in numerical quantities, you will multiply by all numbers in the top , and divide by all numbers in the bottom . MULTIPLY by each number on TOP & DIVIDE by each number on BOTTOM!! To solve the above in a calculator, you would type 1 x 24 x 60 x 60 ÷ 1 ÷ 1 ÷ 1 = 86,400 So from solving the above, we now know that 1 day = 86,400 seconds The following conversion factors were used in the above equation: 1 day = 24 hrs 1 hrs = 60 min 1 min = 60 sec Notice how these conversion factors were used to find the answer and also notice that each conversion factor is numerically equal to 1. This is because the quantity in the numerator is equal to the quantity in the denominator. Thus, multiplying by a conversion factor is like multiplying by 1, which is why dimensional analysis is mathematically sound. It doesn’t actually change the answer. It just expresses it in a different way (with different units). Metric-Metric Conversions Note Guide

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Video Link Part 1 - https://www.youtube.com/watch?v=pEDVddQvimI&feature=youtu.be&list=PL9A16EF5EA79D5F53 https://www.youtube.com/watch?v=pEDVddQvimI&feature=youtu.be&list=PL9A16EF5EA79D5F53 ( Unit Conversion in the Metric System CLEAR & SIMPLE ; author: sciencespot; 11:00) Part 1 I. Examples of Metric Units A. Computers - kilos C. Medicine - grams E. Distance - meters B. Racing - km/h D. Soda/Soft Drinks - mL II. Metric Prefixes Prefix Giga Mega Kilo Hecta Deca Base unit Deci Centi Milli micro nano Abbreviation G M K H D ------ III. Base Units IV. Prefixes + Base Units Measurement Unit Unit Abbreviation Volume cm 3 Deciliter dL Distance/Length meters Kilogram kg Mass kilos Hectometer hm Time sec Nanogram ng Computer memory/information gig Microliter μL Amount of a substance mL millimeter mm IV. Metric Number Line (Copy) ________________________________________________________________________________________ Module 2 Metric-Metric Conversions – Note Guide Video Link Part 2 – https://www.youtube.com/watch?v=pqWzxu2j7w4&feature=youtu.be&list=PL9A16EF5EA79D5F53 (Unit Conversion in the Metric System - Part 2 CLEAR & SIMPLE; author: sciencespot; 6:43) Part 2 Sample Problems - Complete them along with the video 1 km = 1000 m 215 kg = 215,000 g 34.55 s = 34,550 ms 700,000 mL = .7 kL 110.35 µs = 0.11035 ms

Advanced metric prefix conversions 1 Terameter = 1x10 12 meters 1 Gigameter = 1x10 9 meters 1 Megameter = 1x10 6 meters 1 meter = 1x10 6 micrometers 1 meter = 1x10 9 nanometers 1 meter = 1x10 12 picometers 1 meter = 1x10 15 femtometers Notice all of these conversions factors are related to meters . As a simple practice, always convert to and from the base unit. Remember: meter can be substituted by any other type of measurement (i.e. liter, gram, bytes, moles, etc). Sample Problems using the new conversion factors: #1) 0.55 cm = ? pm 0.55 cm× 1 m 100 cm × 1 × 10 12 pm 1 m = 5.5 × 10 9 pm #2) 4.30 × 10 5 kL = ? ML 4.30 × 10 5 kL× 1000 L 1 kL × 1 ML 1 × 10 6 L = 430 ML 1.4 CONCEPTS OF DENSITY https://youtu.be/GnBQ6vIutDM - 2 minutes (Title: Evaluate: Mass, Volume, and Density; Author: ScienceBits) Mass is a measurement of _________________________________________________ The greater the matter in an object the _____________________________________________ Mass is typically measured in ______________________ Volume is a measurement of _________________________________________________ The greater the matter of an object the _________________________________________________________ Volume is typically measured in _______________________________________________ Density is the ratio between ______________________________ Density is a property of materials since ________________________________________ Different objects made of the same material always have the _____________ density regardless of their mass and volume. https://youtu.be/SimFy9wOMXY - 3 minutes (Title: Density; Author: Mark Drollinger) Density of water = 1 g/mL Which of those substances at right would sink in water? Which of those substances at right would float in water? Density of Wood = 0.85 g/mL Density of Ice = 0.93 g/mL Density of Aluminum = 2.7 g/mL Density of Ethanol = 0.94 g/mL Density of Methanol = 0.79 g/mL https://youtu.be/7tVebi3TSsg - 9 minutes (Title: How to perform density calculations; Author: Tyler Dewitt)

A piece of Granite rock has a mass of 15.5 g and a volume of 6.01 cm 3 . What is its density? Gold has a density of 19.3 g/cm 3 . If you have a gold bar with a volume of 44.9 cm 3 , what is its mass? Isopropyl alcohol is a liquid with a density of 0.785 g/cm 3 . How much volume would be taken up by 50.0 grams of isopropyl alcohol? https://youtu.be/4tYXaCADxfE - 3 minutes (Finding density of a cubed object) - (Title: Advanced Density Problem 1; Author: Tyler DeWitt) The piece of wood in the figure has a mass of 96.4 grams. Determine its density. https://youtu.be/TFXC3SV50R0 - 5 minutes (Finding density of an irregular shaped object) - (Title: Advanced Density Problem 2; Author: Tyler DeWitt) You have a graduated cylinder, which is filled with water up to the 150mL mark. You add a hunk of iron, and the water level rises to 425 mL. What is the mass of the iron? SECTION 2: Error and Percent Error Notes https://youtu.be/h--PfS3E9Ao - 7 minutes (Title: Error and Percent Error; Author: Tyler DeWitt) The measurement of how far off a measured value is from an actual value is known as ___________________. There are many possible sources of error that can arise when taking measurements. For example, there could be error in observation , like the slight misreading of a graduated cylinder. There could be error in procedure , like not properly drying a wet solid before weighing it. Error can also stem from the measuring instrument , like a balance that is not properly zeroed. Error can be calculated using the following equation:

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error = measured value − actualvalue Using the above equation, complete the following table: Measured Value Actual Value Error 14.7 feet 14.0 feet 56.3 grams 55.8 grams 345.5 mL 350.0 mL If we truly want to know how accurate our measurements are though, just knowing error is not sufficient. For example, say our error is 2 ft. If we were measuring the height of a 2000 ft. tall tower, only being off by 2 ft would make for a pretty good measurement. On the other hand, if we were measuring the height of a 20 ft. tall house, being off by 2 ft. would make for a pretty sad measurement. Now we turn to a value known as percent error to get better insight into the accuracy of a measurement. Percent error can be calculated using the following equation: ¿ measured value − actual value ∨ ¿ actual value × 100% % error = ¿ Using the above equation, complete the following table: measured value actual value error % error 49.2 ft 52.0 ft 2.7 kg 2.5 kg 3.78 g 2.50 g 48379 ft 50000. ft 910 mL 950 mL Circle the most accurate measured value above. Place an “X” next to the least accurate measured value above. *NOTE: it is possible to have a percentage error of more than 100% SECTION 3: Density Calculations with conversions https://youtu.be/mpR2ZsqQ43k - 10 minutes (Density Calculations - Author: Michael Simmons) Up to this point, all density calculations you’ve done have been pretty straightforward. The units of your givens coincided with all other given units and with the units for the desired final answer. This won’t always be the case though. Examine the following sample problems:

1) Aspirin has a density of 1.40 g/cm 3 . What is the volume, in cubic centimeters, of a 250 mg aspirin tablet? Notice above how the density of aspirin is reported in g /cm 3 , but we are given the mass of a particular aspirin tablet in mg . We must make sure that the units are in agreement to solve this calculation so first the mass of the tablet (mg) must be converted to grams before solving for the volume, the solution is as follows: SOLUTION Since this problem gives the density instead of asking for it, use density as a conversion factor in a dimensional analysis problem. First we must recognize how density can be set up as a conversion factor in the form of a fraction. Density = 1.40 g / cm 3 can be written as two possible fractions as follows: 1.40 g 1 cm 3 ∨ 1 cm 3 1.40 g Now begin the dimensional analysis with the volume (do not start with density because it is a conversion factor): 250 mg× ( 1 g 1000 mg ) × ( 1 cm 3 1.40 g )= 0.1785714286 cm 3 = 0.18 cm 3 ( 2 sig figs ) Be sure to choose the density fraction that will cancel out the volume units: *To solve this, type the following into your calculator: 1234250 ÷ 1000 ÷ 1.40 = 0.1785714286 *The mass (250 mg) has 2 sig figs, and the density (1.40 g/cm 3 ) has three sig figs, therefore the final answer should be rounded to have two sig figs: 0.1785714286 cm 3 = 0.18 cm 3 . Perform all calculations first without rounding, only round off the final answer based on the original values given in the problem. 2) Using the density of aspirin above, what would be the volume, in cubic centimeters, of a massive 500 lb aspirin tablet? (1 lb = 454 g) SOLUTION Since this problem gives the density instead of asks for it, use density as a conversion factor in a dimensional analysis problem. First we must recognize how density can be set up as a conversion factor in the form of a fraction. Density = 1.40 g / cm 3 can be written as two possible fractions as follows: 1.40 g 1 cm 3 ∨ 1 cm 3 1.40 g Now begin the dimensional analysis with the volume (do not start with density because it is a conversion factor): 500 lb× ( 454 g 1 lb ) × ( 1 cm 3 1.40 g )= 162142.8571 cm 3 = 200000 cm 3 ∨ 2 × 10 5 cm 3 ( 1 sig fig ) Be sure to choose the density fraction that will cancel out the volume units: *To solve this, type the following into your calculator: 500 × 454 ÷ 1.40 = 0.0176335743 *The mass (500 lb) has 1 sig fig, and the density (1.40 g/cm 3 ) has three sig figs, therefore the final answer should be rounded to have only one sig fig: 162142.8571 cm 3 = 200000 cm 3 ∨ 2 × 10 5 cm 3 . Perform all calculations first without rounding, only round off the final answer based on the original values given in the problem.

3) Gaseous hydrogen has a density of 0.0899 g/L at 0 o C. How many mL would you need if you wanted 1.0078 g of hydrogen? SOLUTION Since this problem gives the density instead of asks for it, use density as a conversion factor in a dimensional analysis problem. First we must recognize how density can be set up as a conversion factor in the form of a fraction. Density = 0.0899 g / L can be written as two possible fractions as follows: 0.0899 g 1 L ∨ 1 L 0.0899 g Now begin the dimensional analysis with the volume (do not start with density because it is a conversion factor): 1.0078 g× 1 L 0.0899 g × 1000 mL 1 L = 11210.23359 mL = 11200 mL ∨ 1.12 × 10 4 mL ( 3 sig figs ) Be sure to choose the density fraction that will cancel out the volume units: *To solve this, type the following into your calculator: 1.0078 ÷ 0.0899 × 1000 = 11210.23359 *The mass (1.0078 g) has 5 sig figs, and the density (0.0899 g/L) has three sig figs, therefore the final answer should be rounded to have three sig figs: 11210.23359 mL = 11200 mL ∨ 1.12 × 10 4 mL . Perform all calculations first without rounding, only round off the final answer based on the original values given in the problem. 4) Ethanol has a density of 0.789 g/cm 3 at 20 o C. How many cups of ethanol would you need if you wanted 2.50 lbs of ethanol? (1 lb = 454 g; 1 gal = 3.785 L; 1 gal = 4 qts; 1 qt = 4 cups) SOLUTION Since this problem gives the density instead of asks for it, use density as a conversion factor in a dimensional analysis problem. First we must recognize how density can be set up as a conversion factor in the form of a fraction. Density = 0.789 g / cm 3 can be written as two possible fractions as follows: 0.789 g 1 cm 3 ∨ 1 cm 3 0.789 g Now begin the dimensional analysis with the volume (do not start with density because it is a conversion factor): 2.50 lbs× ( 454 g 1 lb ) × ( 1 cm 3 0.789 g ) × ( 1 L 1000 cm 3 ) × ( 1 gal 3.785 L ) × ( 4 qts 1 gal ) × ( 4 cups 1 qt )= 6.080971348 cups = 6.08 cups ( 3 sig figs ) Be sure to choose the density fraction that will cancel out the volume units: *To solve this, type the following into your calculator: 2.50 × 454 ÷ 0.789 ÷ 1000 ÷ 3.785 × 4 × 4 = 6.080971348 *The mass (2.50 lbs) has 3 sig figs, and the density (0.789 g/cm 3 ) has three sig figs, therefore the final answer should be rounded to have three sig figs: 6.080971348 cups = 6.08 cups . Perform all calculations first without rounding, only round off the final answer based on the original values given in the problem.

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