Chapter 2 Dimensional Analysis
|
|
- Magnus Bradley
- 6 years ago
- Views:
Transcription
1 Chapter 2 Dimensional Analysis 1. Introduction There are many methods one can use to solve mathematical problems in chemistry. Sometimes called "story problems", to the novice they can seem difficult, if not impossible! But with a good "plan of attack" they can be made "child's play". Let's look at four methods of problem solving. 1. Pure Logic This is the most difficult method and definitely not for beginners. By this method you reason out what to do with the numbers according to your knowledge about the quantities involved. 2. Formulas This method is commonly taught in math classes. One memorizes a formula for each type of problem and "plugs in" values to get the answer. Unfortunately there would be too many formulas to memorize to use this method in chemistry. 3. Proportions Some older chemistry books use this method. Proportions can be set up for many of the quantities we study, but they can be confusing to apply. 4. Dimensional Analysis This is by far the most common method used today and will be our primary way of "attacking" chemistry problems throughout the year. In dimensional analysis (sometimes called the factor-label method) you will learn to custom build a formula for each problem as you solve it. 2. Dimensional Analysis Suppose you visited a village deep in Africa and found that instead of money the people traded in various types of animals. You assemble the following trading table: 4 pigs = 9 ducks 1 goat = 3 ducks 2 pigs = 5 chickens Problem How many chickens could you trade for? Solution One could use pure logic but it would be easier with dimensional analysis! If you wish, you could try to figure out the answer to this problem by pure logic; then turn to the net page to see how you can do it using dimensional Dimensional Analysis Chapter 2 1
2 analysis. Two Mathematical Ideas to Apply First ---- If the top of a fraction equals the bottom of a fraction, the value of the fraction is "one". Second ---- If the letter on top of one fraction is the same as the letter on the bottom of another fraction, they cancel. 7 7 = 1 Eamples Each equals "one" if = 3 y = = 1 3y - 2 The "B" c ancels 2 B C 3 A 5 B In dimensional analysis we write each equivalency (such as 4 pigs = 9 ducks) as a fraction. We treat the units (pigs, goats, etc.) as algebraic letters allowing them to cancel. The parts of the problem therefore fit together like pieces of a puzzle. The Problem The Table: How many chickens could you trade for? 4 pigs = 9 ducks 1 goat = 3 ducks 2 pigs = 5 chickens Step 1 We start by listing the given information at the left edge of the page and the unit of what we want to find at the right edge of the page. Thus our task will be to go from goats to chickens. GIVEN FIND chic kens Step 2 We multiply by the fraction, "3 ducks over 1 goat". This is based on one of the equivalencies in our table. Goats are placed on the bottom of the fraction so that they will cancel with the goats given in the problem. Since the fraction we are multiplying by has a value of one, the answer so far (18 ducks) is equal to the original. 2 Chapter 2 Dimensional Analysis 3 ducks = 18 ducks 1 goat Step 3 Similarly, we multiply by another fraction, "4 pigs over 9 ducks". This cancels out the "ducks" and introduces "pigs". 3 ducks 1 goat 4 pigs 9 ducks Step 4 Then we multiply by another fraction, "5 chickens over 2 pigs". This cancels out the "pigs" and introduces "chickens". 3 ducks 4 pigs 5 chickens = chickens 1 goat 9 ducks 2 pigs Each time we have multiplied by a fraction equal to "1" so that the answer will be equal to the we started out with. Each time one unit cancels and another is introduced, until the unit becomes what we are looking for, "chickens". On the Calculator press the keys in the following order: = 20 We have custom built a formula to solve the problem. Writing fractions and canceling
3 units has forced us to arrange the numbers in a particular fashion. Multiplying and dividing the numbers as they are arranged gives the answer: 20 chickens. Use this epanded table to work out the problems below. Choose only the equivalencies you need to write fractions which will cancel units to bring you to the unit of the answer. Problems 4 pigs = 9 ducks 9 goats = 2 horse 1 goat = 3 ducks 5 ducks = 3 geese 2 pigs = 5 chickens 1 cow = 12 geese 20 rabbits = 1 pig 5 horses = 3 bulls 3 goats = 2 sheep 1 bull = 32 pigeons 1. How many goats could be traded for 18 geese? 2. Eight sheep would be worth how many pigs? 3. How many rabbits could you get for 2 horses? 3. Converting Measurements One useful application of dimensional analysis is converting measurements in either the English or Metric system. Most of us can do simple one step conversions, like feet to inches, by pure logic. But when several steps are involved, such as to convert miles to inches, use dimensional analysis. Sample Problem 2 How many meters are in 2.5 yards? Solution To solve this problem we will need to recall certain equivalencies which should be familiar to you. A partial list of these equivalences are on the net page. A more complete list is contained in the appendi of this book. It is best to decide a path through the problem by picking out the appropriate equivalencies in the appropriate order before starting to set up the problem. Since we are starting with yards and have to convert to meters these equivalencies are: 1 yard = 3 feet, 1 foot = ches, 1 inch = 2.54 centimeters, and 1 meter = 100 centimeters. Step 1 Convert the 2.5 yards to feet by multiplying by "3 feet over 1 yard". Hold off on the actual multiplication until the whole problem is set up. 2.5 yd 3 ft 1 yd Step 2 Convert feet to inches by multiplying by "ches over 1 foot". 2.5 yd 3 ft 1 yd 1 ft Step 3 Convert inches to centimeters by multiplying by "2.54 centimeters over 1 inch". 2.5 yd 3 ft 1 yd 1 ft 2.54 cm Step 4 Convert centimeters to meters by multiplying by "1 meter over 100 centimeters". This process has forced us to arrange the numbers in a particular fashion to custom build a formula 1 in Dimensional Analysis Chapter 2 3
4 for this problem. At this point you can use your calculator to get the answer: 2.3 meters. 2.5 yd 3 ft 1 yd 1 ft 2.54 cm 1 in 1 m 100 cm = m English and Metric Conversion Table ches = 1 foot 1 kilometer = 1000 meters 3 feet = 1 yard 1 hectometer = 100 meters 16.5 feet = 1 rod 1 dekameter = 10 meters 5280 feet = 1 mile 10 decimeters = 1 meter 40 rods = 1 furlong 100 centimeters = 1 meter 6 feet = 1 fathom 1000 millimeters = 1 meter 1 gallon = 231 inch 3 1 milliliter = 1 centimeter 3 16 ounces = 1 pint 2 pints = 1 quart 1000 milliliters = 1 liter 4 quarts = 1 gallon English to metric conversion: 2.54 centimeters = 1 inch *For the most part, the equivalencies in this table are eact and therefore will not affect the number of significant figures in the answer to the problems in this chapter. The eceptions are marked with a. Problems Use only the equivalencies listed in the above table. 4. How many rods will equal 247 inches? 5. How many centimeters in 34.2 decimeters? 6. A horse race is 55.0 furlongs. How many yards is that? 7. How many ounces are in 1.00 gallon? 8. A "Five K Race" is 5.00 kilometers long. How many miles is that? metric abbreviations km kilomenter hm hectometers dam dekameters m meters dm decimeters cm centimeters mm millimeters ml milliliters L liters Square units are squares with one unit along each side. Thus 1 square foot equals 1 foot times 1 foot. Cubic units are cubes of one unit along each of the three dimensions. Thus 1 cubic foot equals 1 foot times 1 foot times 1 foot. Sample Problem 3 How many square feet in 238 square inches? Solution Write square feet as ft 2 and write square inches as in 2. Remember that units must cancel and that, from algebra, an "X 2 " on top will cancel with two "X's" on the bottom. Therefore: Step 1 Start with 238 square inches. 238 in 2 Step 2 Multiply by "1 foot over ches".? 4 Chapter 2 Dimensional Analysis
5 238 in 2 1 ft Step 3 Multiply by "1 foot over ches", again. 238 in 2 1 ft 1 ft = ft 2 Notice that the same co nversion facto r is u sed twice to cancel th e sq uare u nits. Again we have custom build a formula for the problem. Multiplying and dividing the numbers as they are arranged ( ) gives us the answer: 1.65 square feet. Sample Problem 4 How many square feet are in 3.25 square meters? Solution Remember to plan a path through the problem, before starting to write the set up. We will start with meters, convert to centimeters, then to inches, then to feet multiplying by each conversion factor twice since we are working with square units m cm 100 cm 1 in 1 in 1 ft 1 ft 1 m 1 m 2.54 cm 2.54 cm = 35.0 ft 2 Sample Problem 5 Convert 56.0 cubic inches to cubic centimeters. Solution Use the conversion factor, "2.54 centimeters over 1 inch", three times in cm 2.54 cm 2.54 cm 918 cm 3 = 1 in 1 in 1 in Mied Problems Use only the equivalencies in the table earlier in this chapter. Some of the problems use the same conversion factor more than once, some do not. 9. An area on the ocean bottom is charted as being fathoms 2 in size. How many yards 2 is that? square centimeters is how many square dekameters? 11. How many fathoms are in 63 dekameters? 12. A bo has a volume of 4.6 ft 3. How many gallons does it contain? 13. A cup of coffee is measured to have a volume of 618 milliliters. What is the volume in cubic decimeters? 14. How many rods in 26 miles? 15. Using the defined equality "640 acres = 1 square mile", how many square yards are in 1.00 acre? 16. Hiking trails are often marked on maps in rods. How many kilometers long Dimensional Analysis Chapter 2 5
6 is a trail marked as 82 rods on the map? 17. Coke and Pepsi are now sold in 2.00 liter bottles. What is this volume in quarts? 18. A farm covers a area of two-tenths (0.200) of a square mile. What is the area in square feet? 19. How many liters are contained in a bo measuring 1.2 meters by 2.5 meters by 1.8 meters? (Hint: Find the volume of the bo in cubic meters first. ) 20. What is the volume of an ounce cup in milliliters? 21. How many ounces are in 3.9 in 3? 22. How many hectometers are in 56 furlongs? JPF 9/13/ Chapter 2 Dimensional Analysis
1 centimeter (cm) 5 10 millimeters (mm) 1 meter (m) centimeters. 1 kilometer (km) 5 1,000 meters. Set up equivalent ratios and cross multiply.
Domain 2 Lesson 16 Convert Measurements Common Core State Standard: 6.RP.3.d Getting the Idea The tables below show some conversions for units of length in both the customary system and the metric system.
More informationUnit 1 - INTRODUCTION MEDICAL MATH Listening guide
Unit 1 - INTRODUCTION MEDICAL MATH Listening guide Name Period 1. List one important reason that healthcare workers must be proficient in math. 2. Number forms: 3. Basic math: Counting numbers and zero
More informationMetric System: Shortcut Conversions of Units within the Metric System
HFCC Math Lab NAT 04 Metric System: Shortcut Conversions of Units within the Metric System In this handout, we will work with three basic units of measure in the metric system: meter: gram: liter: The
More informationEnglish & Metric Systems. Systems of Measurement. The Metric System. Mathematics and Millennials 6th. The quickest and most comprehensive way to learn
English & Metric Systems Mathematics and Millennials 6th Systems of Measurement The quickest and most comprehensive way to learn about various systems of measurement is actually easy! At Wikipedia do a
More informationWhile the U.S. continues using inch-pound measures, the other 94% of the world has adopted the METRIC SYSTEM
Metric System While the U.S. continues using inch-pound measures, the other 94% of the world has adopted the METRIC SYSTEM Let s see how well you know the English measurement system. What units do we use
More information1. Metric system- developed in Europe (France) in 1700's, offered as an alternative to the British or English system of measurement.
Basics Review of Math I. MATHEMATICS REVIEW A. Decimal Fractions, basics and definitions 1. Decimal Fractions - a fraction whose deonominator is 10 or some multiple of 10 such as 100, 1000, 10000, etc.
More informationDear Parent, Paige Hudson Answers Metric System Worksheet Answers L g km
Dear Parent, The following worksheets are meant to assist you as you teach your students about units of measurement. This packet is in no way exhaustive, as this topic is typically covered with your math
More informationReteach. Chapter 11. Grade 5
Reteach Chapter Grade 5 esson Reteach Convert Customary Units of ength Customary Units of ength foot (ft) = inches (in.) mile (mi) = 5,80 ft yard (yd) = 6 in. mile (mi) =,760 yd yard (yd) = ft Multiply
More informationSection 3.2 Objectives
CHAPTER ~ Formulas, Proportions, and Percent Section - Proportions Section Objectives Determine if a proportion is true or false Solve proportions for an unknown Solve unit conversion problems using proportions
More informationMetric System & Scientific Notation
+ Metric System & Scientific Notation + What Americans Are Used To The English Standard System Inches and gallons and pounds (oh my!) Many different units Inches, feet, yards, miles, Ounces, cups, pints,
More informationModule 4 Conversion Factors
Module 4 Conversion Factors Prerequisite Module 4 requires Lessons 1A and 1B (on exponential fundamentals) and 2A and 2B (on metric fundamentals). Lesson 2C and Module 3 will be helpful, but not essential,
More informationMeasurement: Things To Know Vocabulary: units dimension US Customary System Metric System
Objectives: 1. Identify units of measurement in the US Customary and Metric systems. 2. Compare attributes of objects to units of measurement of length, area, and volume. 3. Convert units of measured quantities
More informationSection Volume, Mass, and Temperature
Section 11.5 - Volume, Mass, and Temperature Surface Area is the number of square units covering a three dimensional figure; Volume describes how much space a three-dimensional figure contains. The unit
More informationUnit 3.4 Dimensional Analysis
Unit 3.4 Dimensional Analysis How can a number of track laps be converted to a distance in meters? You are training for a 10-kilometer run by doing laps on a 400- meter track. You ask yourself How many
More informationLength is the distance from one point to another. Length has standard units of measurement such as inches or centimeters.
Page 1 Measurements are a standard set by different cultures to address their own needs. In the United States, we use the U. S. Customary system of units. However, the metric system is used worldwide.
More information13) = 4 36 = ) = 5-8 = -3 =3 15) = = -58 = 58 16) = 81-9 = 72 = 72
Practice Practice Practice 3 ) (-3) + (-6) = -9 ) () + (-5) = -3 3) (-7) + (-) = -8 4) (-3) - (-6) = (-3) + 6 = + 3 5) (+) - (+5) = -3 6) (-7) - (-4) = (-7) + 4 = -3 7) (5)(-4) = - 8) (-3)(-6) = +8 9)
More informationThe Metric System & Conversions
Purpose of this lab: The purpose of this lab exercise is for you to become familiar with basic measurements in metric units (SI), English units, and conversions between the two systems. Assignment Objectives:
More informationModule 4 Conversion Factors
Module 4 Conversion Factors Prerequisites: Module 4 requires knowledge of exponential math and metric fundamentals in Lessons 1A, 1B, 2A, and 2B. The other lessons in Modules 1-3 will be helpful, but not
More informationSolving Problems with Labeled Numbers
Solving Problems with Labeled Numbers When solving problems with labeled numbers (those with units such as grams or liters), the labels are treated in the same way as P or y in algebra. The problem is
More informationMath 6, Unit 9 Notes: Measurement and Geometry
Math 6, Unit 9 Notes: Measurement and Geometry Customary and Metric Units of Measure Objective: (6.3)The student will estimate corresponding units of measure between customary and metric systems for temperature,
More informationHandout Unit Conversions (Dimensional Analysis)
Handout Unit Conversions (Dimensional Analysis) This section will cover conversions () selected units in the metric and American systems, () compound or derived measures, and () between metric and American
More informationmay be sent to:
B A S I C M A T H A Self-Tutorial by Luis Anthony Ast Professional Mathematics Tutor LESSON 7: UNITS OF MEASUREMENT Copyright 2006 All rights reserved. No part of this publication may be reproduced or
More informationClinical Calculation 5 th Edition
Clinical Calculation 5 th Edition Chapter 1 Dimensional Analysis Pages 1-18 Introduction Clinical calculations: refers to the solving of computational problems associated with administration of medications.
More informationEnglish Measurement Relationships
Math 30 Prealgebra Sec 10.1: Using Unit Fractions with U.S. and Metric Units Defn A unit fraction is a fraction that shows the relationship between units and is equal to 1. Ex English Measurement Relationships
More informationChapter 6. Ratio, Proportion and Measurement
Chapter 6. Ratio, Proportion and Measurement 6.1 Ratios 6.2 Proportion 6.3 American Units of Measurement 6.4 Metric Units of Measurement 6.5 Converting between American and Metric Units 1 6.1 Ratios 1.
More informationMEASUREMENTS. Significant Figures
SIGNIFICANT FIGURES MEASUREMENTS Significant Figures Every measured value, that you record on paper, reflects the precision of the measuring device used to obtain that value. Every calculated value that
More informationSection 8.1. Basic Terms and Conversions Within the Metric System. Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 8.1 Basic Terms and Conversions Within the Metric System INB Table of Contents Date Topic Page # May 28, 2014 Test #1 20 May 28, 2014 Test #1 Corrections 21 May 28, 2014 Section 8.1 Examples 22
More informationMATH MATH.
A = πr 2 A = πr 2 www.bloggymomma.com www.bloggymomma.com Liquid Equivalents 8 fluid ounces (fl.oz.) = 1 cup (c.) 2 cups (c.) = 1 pint (pt.) 2 pints (pt.) = 1 quart (qt.) 4 quarts (qt.) = 1 gallon (gal.)
More informationLearning Plan 4 Chapter 9
Learning Plan 4 Chapter 9 Question The population of a country reached 309.5 million people. The total area is 3.25 million square miles. What is the population density for the country? Round to the nearest
More informationAltitude. Area. surface inside closed boundaries measured in squares. Area is 21 squares. height above sea level or the Earth s surface
Altitude L 6 height above sea level or the Earth s surface Cruising altitude is 30,000 feet. Area surface inside closed boundaries measured in squares Area is 21 squares L 4 Axis plural Axes 2 intersecting
More informationM E A S U R E M E N T M A N I A
B u s i n e s s C u l i n a r y A r c h i t e c t u r e C o m p u t e r G e n e r a l I n t e r e s t C h i l d r e n L i f e S c i e n c e s B i o g r a p h y A c c o u n t i n g F i n a n c e M a t h
More informationObtain and improve measurement skills in just 5 minutes a day!
Obtain and improve measurement skills in just 5 minutes a day! has been designed to help students attain, improve and apply measurement skills in just a few minutes each day. The system includes: Mathematics
More informationSlide 1 / 82 Slide 2 / 82. Step 2 - PLAN how you will solve the problem. Step 3 - SOLVE it!
Slide 1 / 82 Slide 2 / 82 Algebra I Relationships Between Quantities 2015-11-02 www.njctl.org Slide 3 / 82 Slide 4 / 82 Table of Contents Click on the topic to go to that section Relationships Between
More information2 Standards of Measurement
What You ll Learn the SI units and symbols for length, volume, mass, density, time, and temperature how to convert related SI units 2 Standards of Measurement (A), 2(D), 2(C), 2(E) Before You Read If someone
More informationNotes Chapter 2: Measurements and Calculations. It is used to easily and simply write very large numbers, and very small numbers.
Scientific Notation Notes Chapter 2: Measurements and Calculations It is used to easily and simply write very large numbers, and very small numbers. It begins with a number greater than zero & less than
More informationI. Qualit a Qualit t a ive iv vs. Quantit Quan a tit tiv a e tiv Measurements
I. Qualitative vs. Quantitative Measurements Qualitative Measurement 1) Qualitative measurement = a measurement that gives descriptive, NONnumeric results a)ex: Jillian ran a fast race. b)ex: The light
More informationThe Metric System, Measurements, and Scientific Inquiry (Chapter 23)
GEOLOGY 306 Laboratory Instructor: TERRY J. BOROUGHS NAME: The Metric System, Measurements, and Scientific Inquiry (Chapter 23) For this assignment, you will require: a calculator & a metric ruler. Objectives:
More informationG302 - Basics Review of Math and Algebra
G302 - Basics Review of Math and Algebra I. MATHEMATICS REVIEW A. Decimal Fractions, basics and definitions 1. Decimal Fractions - a fraction whose deonominator is 10 or some multiple of 10 such as 100,
More informationLaboratory1: Exercise 1
3 September 2007 MAR 110 Lab1: Exercise 1 - Conversions 1 1-1. THE METRIC SYSTEM Laboratory1: Exercise 1 Metric - English Conversion [based on the Chauffe & Jefferies (2007)] The French developed the metric
More informationChapter 3 Metric Units and Conversions
Chapter 3 Metric Units and Conversions 3.1 The Metric System and Prefixes Metric system: a simple decimal system of measurement that uses the following basic units: Quantity Basic Unit Symbol length meter
More informationName Date Class 5, 4, 7, 8
7 What Is an Average? Suppose that your class is doing an experiment to determine the boiling point of a particular liquid. Working in groups, your classmates come up with several answers that are all
More informationPSSA Released Items 16 Multiple Choice Questions, 1 Open-Ended Response
Page 1 of 21 2016-2017 PSSA Released Items 16 Multiple Choice Questions, 1 Open-Ended Response Directions Do not use a calculator. You may refer to the formula sheet shown below. Show your work on this
More informationCCR Math - Grade 7 Practice Test
R Math - Grade 7 Practice Test You may use a calculator for questions -7.. Use the picture below to answer the question. A B What is the probability of spinning a? A. B.. D. 5 3 5 3 5 A 3 Go on to the
More information1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =
Extra Practice for Lesson Add or subtract. ) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = Multiply. 7) (5)(-4) = 8) (-3)(-6) = 9) (-)(2) = Division is
More informationGrade 5 FSA Mathematics Reference Sheet
Grade 5 FSA Mathematics Reference Sheet Customary Conversions 1 foot = 12 inches 1 yard = 3 feet 1 mile = 5,280 feet 1 mile = 1,760 yards 1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon
More information2 Standards for Measurement. Careful and accurate measurements of ingredients are important both when cooking and in the chemistry laboratory!
2 Standards for Measurement Careful and accurate measurements of ingredients are important both when cooking and in the chemistry laboratory! Chapter Outline 2.1 Scientific Notation 2.2 Measurement and
More informationChapter 2: Approaches to Problem Solving Lecture notes Math 1030 Section B
Section B.1: Standardized Unit Systems: U.S. and Metric Different system of standardized units There are different systems of standardized units: the international metric system, called SI (from the French
More informationChemistry is a course based on regular laboratory investigations of matter, chemical reactions, and the role of energy in reactions.
Honors Chemistry Summer Assignment Chemistry is a course based on regular laboratory investigations of matter, chemical reactions, and the role of energy in reactions. Honors Chemistry Summer Assignment
More informationMath Series Measurement. Measuring Lengths and Distances
Math Series Measurement Measuring Lengths and Distances Copyright 2019 Oklahoma Department of Career and Technology Education Resource Center for CareerTech Advancement All rights reserved. Printed in
More informationMath Math in the Liberal Arts
Math 1303 - Math in the Liberal Arts Final Exam - 2014.12.10 Name: Metric Units Prefix Symbol Meaning kilo k 1000 base unit hecto h 100 base unit deka da 10 base unit base unit deci d 1 of base unit 10
More informationChapter 1 (Part 2) Measurements in Chemistry 1.6 Physical Quantities
Chapter 1 (Part 2) Measurements in Chemistry 1.6 Physical Quantities This is a property that can by physically measured. It consists of a number and a unit of measure. (e.g. ) Units Units are very important.
More informationresources Symbols < is less than > is greater than is less than or equal to is greater than or equal to = is equal to is not equal to
Symbols < is less than > is greater than is less than or equal to is greater than or equal to resources = is equal to is not equal to is approximately equal to similar a absolute value: = ; - = (x, y)
More informationTake notes on all slides with stars Lesson 1: Length
Take notes on all slides with stars Lesson 1: Length T. Trimpe 2008 http://sciencespot.net/ English vs. Metric Units Which is longer? A. 1 mile or 1 kilometer B. 1 yard or 1 meter 1 mile 1.6 kilometers
More informationGrading Homework. The Metric System. SI Base Units. SI Units. Lesson 1: Length 9/5/2012
The Metric System Complete your Identify Variables Worksheet We will be Grading after the bell rings! Grading Homework Remove all Writing Utensils from your Table You will be provided a red pen Correct
More informationWILDLIFE BIOLOGY. Monday 11 Sep 2017
WILDLIFE BIOLOGY Monday 11 Sep 2017 Entry Task Phones in your bag & bags on the outer counters. At your desk you will need pencil/pen (blue/black ink) composition notebook On the cover of your composition
More informationLESSON F6.1 UNITS OF MEASUREMENT
LESSON F6. UNITS OF MEASUREMENT LESSON F6. UNITS OF MEASUREMENT 545 546 TOPIC F6 INTERPRETING DATA Overview We have already worked with quantities that included units such as centimeters and inches. To
More informationChapter 02 - The Chemist's Toolbox
1. When adding and subtracting, the number of significant figures in the answer is determined by. a. the most precise number b. the least precise number c. the number with the most significant figures
More informationChapter 1 Review Problems (Done in Class)
Chapter 1 Measurement Review Problems Chapter 1 Review Problems (Done in Class) Section - problems Sec 1, p. 8 # 2, 5, 6, 8, 9 Sec 2, p. 12 # 1, 3, 4, 5, 7, 8 Sec 3, p.17 # 3, 4, 5 Sec 4, p. 23 # 3, 6,
More informationEnglish 5 th Grade A-L Vocabulary Cards and Word Walls Revised: 11/18/14
English 5 th Grade A-L Vocabulary Cards and Word Walls Revised: 11/18/14 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State
More informationGrade 11 Mathematics Practice Test
Grade Mathematics Practice Test Nebraska Department of Education 204 Directions: On the following pages are multiple-choice questions for the Grade Practice Test, a practice opportunity for the Nebraska
More informationAlgebra 1 FSA Mathematics Practice Test Questions
Algebra 1 FSA Mathematics Practice Test Questions The purpose of these practice test materials is to orient teachers and students to the types of questions on paper-based FSA tests. By using these materials,
More informationchapter 3 Measurement I. Making Measurements Using the Metric System Introduction
Measurement JJ Introduction If you become a nurse, a physical therapist, a biologist, or just about anything to do with science, you will be asked to measure things. Measuring things may seem trivial,
More informationModule 5 Word Problems
Module 5 Word Problems Prerequisite: Complete Modules 2 and 4 before starting Module 5. Timing: Begin Module 5 as soon as you are assigned word-problem calculations. Introduction In this module, you will
More informationThe Metric System. Mr. Hold-Key
The Metric System Mr. Hold-Key About it The metric system is a universal. Except for the U.S.A Developed in the late 18th century by French scientists Until then it was a chaotic system of various measurements
More informationChapter 2 Measurement and Problem Solving. What Is a Measurement? Scientific Notation 8/20/09. Introductory Chemistry, 3 rd Edition Nivaldo Tro
Introductory Chemistry, 3 rd Edition Nivaldo Tro Measurement and Problem Solving Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA 2009, Prentice Hall What Is a Measurement? Quantitative
More informationPower Standard #6 Practice Test
Name Date 1) Liter Power Standard #6 Practice Test d. A metric unit that is used for cats and kittens 2) Gram d. A metric unit that is used for crackers 3) Meter d. A metric unit that is used for meteors
More informationMETRIC CHART. The metric system has three units or bases.
METRIC SYSTEM THE METRIC SYSTEM The metric system is much easier. All metric units are related by factors of 10. Nearly the entire world (95%), except the United States, now uses the metric system. Metric
More informationThe Nature of Science
chapter 1 The Nature of Science section 2 Standards of Measurement Before You Read If someone asked you how wide your desk is, how would you measure it? Would you measure using inches, centimeters, feet,
More informationThe metric system, science, and you!
The metric system, science, and you! SCIENTIFIC MEASUREMENT Long ago, standardized units of measurement were based on parts of the body What s the problem with this? In science class, we use the Metric
More informationStandards of the past
Metric Prefixes Measurement Must have a standard. A standard is an exact quantity people agree to use for comparison. A standard means two people using the same object should get close to the same results.
More informationWORKSHEET #1. Dougherty Valley HS Chemistry Chemistry Math. 1) Solve for the variables using the expression below.
Chemistry Math #1 Solve for the variables using the expression below. =1 a = b = x = y = z = ---------------------------------------------------------------------------------------------------------------------------------------
More informationIntegrated General Biology
Integrated General Biology A Contextualized Approach FIRST EDITION Jason E. Banks Julianna L. Johns Diane K. Vorbroker, PhD Chapter 4 On-Target: Units, Accuracy, and Conversion Section 4.1 Directions for
More informationGeneral Chemistry Unit 8 Measurement ( )
General Chemistry Unit 8 Measurement (2017-2018) Significant Figures Scientific Notation Unit Analysis Unit of Measure Accuracy and Precision Density Percent Error 1 Adding Numbers: Add numbers as you
More informationIn recording measurements, it is necessary to understand 1. SIGNIFICANCE of numbers 2. importance of UNITS.
CHEMISTRY IS LARGELY A QUANTITATIVE SCIENCE Theories and ideas are tested by measurement Measurements are usually quantitative have numbers Science is built on a foundation of mathematics. In recording
More informationMeasuring SKILLS INTRODUCTION
SKILLS INTRODUCTION Measuring If you enjoy sports, you know how exciting it is when an athlete swims faster, runs longer, or hits a ball farther than other competitors. You also know that people aren t
More informationChapter 2 Measurements and Solving Problems
History of Measurement Chapter 2 Measurements and Solving Problems Humans once used handy items as standards or reference tools for measurement. Ex: foot, cubit, hand, yard. English System the one we use.
More informationSection 1.6 Systems of Measurement. A system of measurement is a set of units which can be used to specify any physical attribute of an object.
Section 1.6 Systems of Measurement A system of measurement is a set of units which can be used to specify any physical attribute of an object. There are two systems of measurement used in the United States
More informationThe Metric System and Measurement
The Metric System and Measurement Introduction The metric system is the world standard for measurement. Not only is it used by scientists throughout the world, but most nations have adopted it as their
More informationPre-Lab 0.2 Reading: Measurement
Name Block Pre-Lab 0.2 Reading: Measurement section 1 Description and Measurement Before You Read Weight, height, and length are common measurements. List at least five things you can measure. What You
More informationAP Physics 1 Mr. Perkins June 2014 SUMMER WORK FOR AP PHYSICS 1 STUDENTS
AP Physics 1 Mr. Perkins June 2014 SUMMER WORK FOR 2014-2015 AP PHYSICS 1 STUDENTS 1. Read Chapter 1 of Textbook (Giancoli pp.1-17). Make a list of questions about any topics you would like clarified on
More informationMeasurements in Chemistry Chapter 2
Measurements in Chemistry Chapter 2 Problem-Set Solutions 2.1 It is easier to use because it is a decimal unit system. 2.2 Common measurements include mass, volume, length, time, temperature, pressure,
More informationCHAPTER EIGHT THE METRIC SYSTEM
CHAPTER EIGHT THE METRIC SYSTEM Exercise Set 8.1 1. The metric system. 2. The U.S. customary system. 3. It is the worldwide accepted standard of measurement. There is only 1 basic unit of measurement for
More informationHW: page 168 (12-24 evens, 25-28) Extra Credit # 29 & 31
Lesson 5-1 Rational Numbers pages 166-168 Review our number system and real numbers. Our Number System Real Complex Rational Irrational # Integers # Whole # Natural Rational Numbers the word "rational"
More informationScientific Units of Measurement & Conversion
Scientific Units of Measurement & Conversion Principle or Rationale: Scientific measurements are made and reported using the metric system and conversion between different units is an integral part of
More informationFind the Surface Area of a Prism
Find the Surface Area of a Prism The of a solid is the area of the surface of the solid. A is a polyhedron with two parallel congruent bases. The bases are two faces of the polyhedron. The other faces
More informationVocabulary Cards and Word Walls Revised: June 29, 2011
Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,
More informationCustomary Units of Measurement
Customary Units of Measurement What would it be like to have no system of measurement? If we are to measure something, we need a unit of measure. standard unit of measure: one that people have agreed to
More informationMetric System length meter Mass gram Volume liter
Metric System The basic unit of length in the metric system in the meter and is represented by a lowercase m. Mass refers to the amount of matter in an object. The base unit of mass in the metric system
More informationMindTrap. Read the question. Think about the question. Please Do not yell out the answer
Metric System Read the question Think about the question MindTrap Please Do not yell out the answer Dee Septor, the famous magician, filled an ordinary glass to the top. Holding the glass above his head
More informationRelationships Between Quantities
Relationships Between Quantities MODULE 1? ESSENTIAL QUESTION How do you calculate when the numbers are measurements? CORE STANDARDS LESSON 1.1 Precision and Significant Digits CORE N.Q.3 LESSON 1.2 Dimensional
More informationAlaska Mathematics Standards Vocabulary Word List Grade 4
1 add addend additive comparison area area model common factor common multiple compatible numbers compose composite number counting number decompose difference digit divide dividend divisible divisor equal
More informationGrade 6 Mathematics Practice Test
Grade 6 Mathematics Practice Test Nebraska Department of Education 206 Directions: On the following pages are questions for the Grade 6 Practice Test, a practice opportunity for the Nebraska State Accountability
More informationStudy Guide. Summer Packet 06/03/2014 Area of Triangle - B
Study Guide Summer Packet 06/03/2014 Area of Triangle - B This skill requires the student to find the area of a triangle, which is one half the area of a rectangle that has the same base and height. The
More informationScientific Notation. Part A: Express each of the following in standard form x x x
Name: Course: Scientific Notation Part A: Express each of the following in standard form. 1. 5.2 x 10 3 5. 3.6 x 10 1 2. 9.65 x 10 4 6. 6.452 x 10 2 3. 8.5 x 10 2 7. 8.77 x 10 1 4. 2.71 x 10 4 8. 6.4 x
More informationMeasurements in Chemistry Chapter 2
Measurements in Chemistry Chapter 2 Problem-Set Solutions 2.1 It is easier to use because it is a decimal unit system. 2.2 Common measurements include mass, volume, length, time, temperature, pressure,
More informationMA 40S APPLIED UNIT F: DESIGN AND MEASUREMENT CLASS NOTES
1 MA 40S APPLIED UNIT F: DESIGN AND MEASUREMENT CLASS NOTES 1. Introduction. In Grade 1 Applied you learn some powerful mathematics. But it remains necessary to re-enforce the most basic practical type
More informationSEVENTH EDITION and EXPANDED SEVENTH EDITION
SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 8-1 Chapter 8 The Metric System 8.1 Basic Terms and Conversions within the Metric System SI System and U.S. Customary System Most countries of the world
More informationGRADE 5. Mathematics. Administered April 2013 RELEASED
GRADE Mathematics Administered April 0 RELEASED Copyright 0, Texas Education Agency. All rights reserved. Reproduction of all or portions of this work is prohibited without express written permission from
More information2.1 Units of Measurement. Copyright 2011 Pearson Education, Inc.
Chapter 2 Measurements 2.1 Units of Measurement 1 Measurement You make a measurement every time you measure your height read your watch take your temperature weigh a cantaloupe 2 Measurement in Chemistry
More informationChapter 1 (Part 2) Measurements in Chemistry
Chapter 1 (Part 2) Measurements in Chemistry 1.7 Physical Quantities English Units Those of us who were raised in the US are very accustomed to these. Elsewhere in the world, these are very confusing.
More information