DIMENSIONAL ANALYSIS #2


 Nigel Houston
 2 years ago
 Views:
Transcription
1 DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we might say that the area of a room is 28 ft 2. Generally, when you see a unit of measure with an exponent of 2, it is a measurement of area. Similarly, volume is measured in cubic units. The volume of a tank might be written as 200 cubic feet or 200 ft. Generally, when you see a unit of measure with an exponent of, it is a measurement of volume. The technique of dimensional analysis can be used to convert from one unit of area or volume to another unit of area or volume. However, it is important to remember that more than one dimension is being considered. EXAMPLE : Determine the number of square inches in square foot. SOLUTION: This problem is equivalent to solving ft 2? in. 2 To solve this problem, remember that square foot means the area of a square that measures foot on each side. The area of the square is A lw ( ft)( ft) ft 2. ft ft 2 ft To convert from square feet to square inches, we must consider that each of the two dimensions of the square is foot, and each foot is equivalent to 2 inches. We can perform the conversion using unit fractions, but we must use the conversion factor of 2 inches twice, once for each dimension of the square. ft ft 2 ( ft)( ft) (2 in. )(2 in. ) ( ft)( ft) ()()(2)(2) in.2 ()() 44 in 2 So there are 44 square inches in square foot. Notice that the unit fraction we used to perform the conversion had foot twice in the denominator (equivalent to ft 2 ) and 2 inches twice in the numerator. REMEMBER: To convert from one unit of area to another unit of area, always use the conversion factor two times. The exponent of 2 on the unit is a reminder that there are two dimensions to consider. printed /6/2004 Copyright LinnBenton Community College Mathematics Department. Used with permission.
2 Performing a conversion between two different units of volume is very similar. Volume involves three dimensions and is expressed in cubic units. For example, cubic meter means the volume of a cube that measures meter by meter by meter. The volume of that cube is given by V lwh ( m)( m)( m) m. m m m m When we perform a conversion using cubic meters, we must remember that there are three dimensions to the cube, each of which measures meter. So the conversion factor must be used three times, as shown in the next example. EXAMPLE 2: Convert 5,800,000 cubic millimeters to cubic meters. SOLUTION: This problem is equivalent to solving 5,800,000 mm? m. We begin by writing 5,800,000 mm 5,800, 000 mm as. Now we multiply by a unit fraction that relates mm to m and that has mm in the denominator. From the measurement and conversion table, we know that m 000 mm, so we write a unit fraction using the conversion factor of 000 three times, once for each dimension. 5,800, 000 mm ( m)( m)( m) (000 mm)(000 mm)(000 mm) (5,800,000)()()() m (000)(000)(000) m So 5,800,000 cubic millimeters is equivalent to cubic meters. The conversion we wrote above with the unit fraction relating mm and m can be written more briefly as shown below. 5,800, 000 mm m 000(000)(000) mm or even as 5,800,000() m (000)(000)(000) m 5,800, 000 mm m (000) mm 5,800,000() m (000)(000)(000) m The important thing is to be sure to use the conversion factor three times. REMEMBER: To convert from one unit of volume to another unit of volume, always use the conversion factor three times. The exponent of is a reminder that there are three dimensions to consider. printed /6/2004 Copyright LinnBenton Community College Mathematics Department. Used with permission. 2
3 We can chain unit fractions to perform conversions with square and cubic units as we did in the earlier problems. The next example illustrates this process. EXAMPLE : The displacement of an engine is often measured in liters or in cubic inches. Suppose that a compact car has a.8 L engine. What is the displacement of this engine in cubic inches? SOLUTION: This problem is equivalent to the conversion:.8 L? in. Notice only the unit on the righthand side has an exponent of. We can compare liters and cubic inches, however, since a liter is a measure of capacity. Remember that ml cm. We will use this relationship to perform the conversion. First we will convert from liters to cubic centimeters by multiplying by two unit fractions.. 8 L 000 ml L cm ml If we multiplied these fractions, liters and milliliters would cancel and we would be left with cubic centimeters. Now we must convert from cubic centimeters to cubic inches, so we multiply by a unit fraction with cubic inches in the numerator and cubic centimeters in the denominator.. 8 L 000 ml L cm ml in. (2.54) cm.8(000)()() in. ()()(2. 54) 0 in. Multiplying these fractions together gives us the equivalent displacement in cubic inches (rounded to the nearest whole number). Therefore, the displacement of the engine in the compact car is approximately 0 cubic inches. printed /6/2004 Copyright LinnBenton Community College Mathematics Department. Used with permission.
4 PROBLEM SET 2 Answers to the oddnumbered problems are given at the end of the problem set. Dimensional Analysis #2, Continued WARMUP EXERCISES Use dimensional analysis to perform the following conversions. Show the procedure that you used, including all of your unit fractions. If an answer is not exact, round to two decimal places.. 0 ft 2 to in in. 2 to cm mm to cm 4. m to L 5. 6 mi 2 to km gal to yd cm to qt acres to yd 2 PROBLEMS Use dimensional analysis to solve each of the following problems. Show the procedure that you used, including all of your unit fractions. Answer the question in a complete sentence. 9. Frank just moved to the U.S. and wants to buy a 40hectare farm. How many acres should he tell the real estate agent he wants to buy? Round your answer to the nearest acre. 0. A room measures 6 ft by 2 ft. a. Find the area of the room in square yards. Round your answer up to the nearest whole number. b. What would it cost to carpet the room if the carpet sells for $2.99 per square yard? Round your answer to the nearest cent.. A basement for a 0 ft by 40 ft house is to be dug at a depth of 7 feet. How many cubic yards of earth need to be hauled away? Assume that the surface of the ground is level. Round your answer to the nearest cubic yard. 2. A cylindrical tank is 8 meters long and 4 meters in diameter. How many liters of liquid will the tank hold? Round your answer to the nearest thousand. EXTRA PROBLEMS Use dimensional analysis to perform the following conversions. Show the procedure that you used, including all of your unit fractions. If an answer is not exact, round to two decimal places.. 50 cm 2 to m yd to ft m to in in. to L Use dimensional analysis to solve each of the following problems. Show the procedure that you used, including all of your unit fractions. Answer the question in a complete sentence. Round your answers to the nearest whole number. 7. Ann s back yard is 60 feet by 70 feet. What is the area of her backyard in square meters? 8. A fish tank measures 25 inches by 6 inches by 2 inches. How many cubic feet of water will it hold? How many gallons will it hold? printed /6/2004 Copyright LinnBenton Community College Mathematics Department. Used with permission. 4
5 ANSWERS TO ODDNUMBERED PROBLEMS: (NOTE: For some of these problems there are several ways to set up the problem. Therefore, your unit fractions may look different from the sequence of unit fractions shown here. Your final answer, however, should be approximately the same as the one given below.). 0 ft2 (2)2 in. 2 ft in mm cm (0) mm cm 5. 6 mi2 (.609)2 km 2 mi km cm ml cm L 000 ml.057 qt L 2.64 qt ha 0,000 m2 ha (9.7) 2 in. 2 m 2 ft 2 (2) 2 in. 2 acre 4,560 ft 2 99 acres Frank needs a farm of approximately 99 acres.. Volume (0 ft)(40 ft)(7 ft) 8400 ft 8400 ft yd () ft yd Approximately cubic yards of dirt must be hauled away.. 50 cm2 m 2 (00) 2 cm m m (00) cm m in. (2.54) cm in. 7. Area (60 ft)(70 ft) 4200 square feet ft 2 (2)2 in. 2 ft 2 m 2 (9.7) 2 in m 2 The area of Ann s back yard is approximately 90 square meters. printed /6/2004 Copyright LinnBenton Community College Mathematics Department. Used with permission. 5
Converting Units of Measure Measurement
Converting Units of Measure Measurement Outcome (lesson objective) Given a unit of measurement, students will be able to convert it to other units of measurement and will be able to use it to solve contextual
More informationTallahassee Community College PERIMETER
Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides
More informationMeasurement/Volume and Surface Area LongTerm Memory Review Grade 7, Standard 3.0 Review 1
Review 1 1. Explain how to convert from a larger unit of measurement to a smaller unit of measurement. Include what operation(s) would be used to make the conversion. 2. What basic metric unit would be
More informationTo Multiply Decimals
4.3 Multiplying Decimals 4.3 OBJECTIVES 1. Multiply two or more decimals 2. Use multiplication of decimals to solve application problems 3. Multiply a decimal by a power of ten 4. Use multiplication by
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationNegative Exponents and Scientific Notation
3.2 Negative Exponents and Scientific Notation 3.2 OBJECTIVES. Evaluate expressions involving zero or a negative exponent 2. Simplify expressions involving zero or a negative exponent 3. Write a decimal
More informationQuick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More informationCHAPTER 4 DIMENSIONAL ANALYSIS
CHAPTER 4 DIMENSIONAL ANALYSIS 1. DIMENSIONAL ANALYSIS Dimensional analysis, which is also known as the factor label method or unit conversion method, is an extremely important tool in the field of chemistry.
More informationTask: Representing the National Debt 7 th grade
Tennessee Department of Education Task: Representing the National Debt 7 th grade Rachel s economics class has been studying the national debt. The day her class discussed it, the national debt was $16,743,576,637,802.93.
More informationLesson 21. Circles. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 1 Circles Objectives Understand the concepts of radius and diameter Determine the circumference of a circle, given the diameter or radius Determine
More informationHFCC Math Lab General Math Topics 1. Metric System: Shortcut Conversions of Units within the Metric System
HFCC Math Lab General Math Topics  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:
More information4.5.1 The Metric System
4.5.1 The Metric System Learning Objective(s) 1 Describe the general relationship between the U.S. customary units and metric units of length, weight/mass, and volume. 2 Define the metric prefixes and
More informationArea and Circumference
4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert
More informationFCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication
FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby
More informationArea of Parallelograms (pages 546 549)
A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular
More informationSection 1 Tools and Measurement
Section 1 Tools and Measurement Key Concept Scientists must select the appropriate tools to make measurements and collect data, to perform tests, and to analyze data. What You Will Learn Scientists use
More informationCalculating Area and Volume of Ponds and Tanks
SRAC Publication No. 103 Southern Regional Aquaculture Center August 1991 Calculating Area and Volume of Ponds and Tanks Michael P. Masser and John W. Jensen* Good fish farm managers must know the area
More informationStudent Exploration: Unit Conversions
Name: Date: Student Exploration: Unit Conversions Vocabulary: base unit, cancel, conversion factor, dimensional analysis, metric system, prefix, scientific notation Prior Knowledge Questions (Do these
More informationChapter 1 Lecture Notes: Science and Measurements
Educational Goals Chapter 1 Lecture Notes: Science and Measurements 1. Explain, compare, and contrast the terms scientific method, hypothesis, and experiment. 2. Compare and contrast scientific theory
More informationIntroduction. Percent Increase/Decrease. Module #1: Percents Bus 130 1
Module #1: Percents Bus 130 1 Introduction In this module, we are going to use the process of excavating soil to demonstrate the mathematical concept of percent changes and problem solving skills. When
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
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 informationMeasurement. Introduction... 3
Introduction... 3 Unit 1: Length Customary System Lesson 1: Length... 3 Lesson 2: Perimeter... 3 Lesson 3: Length Estimation... 4 Lesson 4: Selection of Units... 4 Lesson 5: Changing Units... 5 Unit 2:
More informationJones and Bartlett Publishers, LLC. NOT FOR SALE OR DISTRIBUTION.
Chapter 3 Metric System You shall do no unrighteousness in judgment, in measure of length, in weight, or in quantity. Just balances, just weights, shall ye have. Leviticus. Chapter 19, verse 35 36. Exhibit
More informationUnits of Measurement: A. The Imperial System
Units of Measurement: A. The Imperial System Canada uses the metric system most of the time! However, there are still places and occasions where the imperial system of measurement is used. People often
More informationCylinder Volume Lesson Plan
Cylinder Volume Lesson Plan Concept/principle to be demonstrated: This lesson will demonstrate the relationship between the diameter of a circle and its circumference, and impact on area. The simplest
More informationArea is a measure of how much space is occupied by a figure. 1cm 1cm
Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number
More informationCHAPTER 2: MEASUREMENT AND PROBLEM SOLVING
CHAPTER 2: MEASUREMENT AND PROBLEM SOLVING Problems: 164, 6988, 91120, 123124 2.1 Measuring Global Temperatures measurement: a number with attached units When scientists collect data, it is important
More informationGrade 8 FCAT 2.0 Mathematics Sample Questions
Grade FCAT. Mathematics Sample Questions The intent of these sample test materials is to orient teachers and students to the types of questions on FCAT. tests. By using these materials, students will become
More informationExercise Worksheets. Copyright. 2002 Susan D. Phillips
Exercise Worksheets Copyright 00 Susan D. Phillips Contents WHOLE NUMBERS. Adding. Subtracting. Multiplying. Dividing. Order of Operations FRACTIONS. Mixed Numbers. Prime Factorization. Least Common Multiple.
More informationRevision Notes Adult Numeracy Level 2
Revision Notes Adult Numeracy Level 2 Place Value The use of place value from earlier levels applies but is extended to all sizes of numbers. The values of columns are: Millions Hundred thousands Ten thousands
More informationMultiplying Fractions
. Multiplying Fractions. OBJECTIVES 1. Multiply two fractions. Multiply two mixed numbers. Simplify before multiplying fractions 4. Estimate products by rounding Multiplication is the easiest of the four
More informationArea of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in
More informationRAINWATER HARVESTING FOR DRYLANDS  VOLUME 1. By Brad Lancaster, 2006. Appendix 3. WaterHarvesting Calculations
RAINWATER HARVESTING FOR DRYLANDS  VOLUME 1 By Brad Lancaster, 2006 Appendix 3 WaterHarvesting Calculations List of Equations and Other Information Box A3.1. Abbreviations, Conversions, and Constants
More informationArea & Volume. 1. Surface Area to Volume Ratio
1 1. Surface Area to Volume Ratio Area & Volume For most cells, passage of all materials gases, food molecules, water, waste products, etc. in and out of the cell must occur through the plasma membrane.
More informationHealthcare Math: Using the Metric System
Healthcare Math: Using the Metric System Industry: Healthcare Content Area: Mathematics Core Topics: Using the metric system, converting measurements within and between the metric and US customary systems,
More informationConversions between the common units of length used in the Imperial system are listed below 12 in = 1 ft 3 ft = 1 yard 1760 yards = 1 mile
THE METRIC SYSTEM The metric system or SI (International System) is the most common system of measurements in the world, and the easiest to use. The base units for the metric system are the units of: length,
More informationnorth seattle community college
INTRODUCTION TO FRACTIONS If we divide a whole number into equal parts we get a fraction: For example, this circle is divided into quarters. Three quarters, or, of the circle is shaded. DEFINITIONS: The
More informationMOST COMMON METRIC UNITS USED IN THE MEDICAL FIELD *BASE. deci. King Henry Died (from a) Disease Called Mumps. (k) (h) (da) gram (g) (d) (c) (m)
MOST COMMON METRIC UNITS USED IN THE MEDICAL FIELD Micro (mc) microgram 0 6 One millionth 0.00000 Milli (m) milligram milliliter* millimeter 0 3 One thousandth 0.00 Centi (c) centimeter 0 2 One hundredth
More informationPerimeter. 14ft. 5ft. 11ft.
Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine
More information$566.30. What is the monthly interest rate on the account? (Round to the nearest hundredth of a percent.) 4 = x 12. 7)
Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1)What percent of 6 is 27? 1) 2)64.288 is 28.7% of what number? 2) 3)112% of what number is
More informationFractions to decimals
Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of
More informationArea and Volume Equations
Area and Volume Equations MODULE 16? ESSENTIAL QUESTION How can you use area and volume equations to solve realworld problems? LESSON 16.1 Area of Quadrilaterals 6.8.B, 6.8.D LESSON 16. Area of Triangles
More informationChapter 1 Problems. 1micron 1 10 6 m =1 10 9 microns. =1 10 4 cm. 1micron 1 10 6 m = 9.144 105 microns. 1 ft
Chapter 1 Problems 1.3 The micrometer is often called the micron. (a) How man microns make up 1 km? (b) What fraction of a centimeter equals 1µm? (c) How many microns are in 1.0 yard We begin by calculating
More informationSPCC Plan  Calculation Guidance
SPCC Plan  Calculation Guidance The following example compares two different design criteria: one based on the volume of the tank and one based on precipitation. Scenario: A 20,000gallon horizontal tank
More informationArea of Circles. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and record in the blanks above.
Name: Area of Circles Label: Length: Label: Length: A Part 1 1. Label the diameter and radius of Circle A. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and recd
More informationDon t worry! There is no right or wrong answer.be honest so that I can figure out the best way to help you next year!
AP Environmental Science Summer Assignment 20162017 Mrs. Carlson, rcarlson@g.aledoisd.org Welcome to AP Environmental Science! This class is highly intensive, with a lot of material that needs to be covered.
More informationGrade 6 FCAT 2.0 Mathematics Sample Questions
Grade FCAT. Mathematics Sample Questions The intent of these sample test materials is to orient teachers and students to the types of questions on FCAT. tests. By using these materials, students will become
More informationGrade 4  Module 5: Fraction Equivalence, Ordering, and Operations
Grade 4  Module 5: Fraction Equivalence, Ordering, and Operations Benchmark (standard or reference point by which something is measured) Common denominator (when two or more fractions have the same denominator)
More informationMathSphere MATHEMATICS. Equipment. Y6 Fractions 6365 Round decimals. Equivalence between decimals and fractions
MATHEMATICS Y6 Fractions 6365 Round decimals. Equivalence between decimals and fractions Paper, pencil, ruler Fraction cards Calculator Equipment MathSphere 6365 Round decimals. Equivalence between fractions
More informationMetric Rules. Activity 7. In this activity you will: Introduction. The Problem. Math Concepts Measurement. Science Concepts Data collection
. Math Concepts Measurement Geometry Activity 7 Science Concepts Data collection Metric Rules Materials TI73 calculator Yardstick Meter stick In this activity you will: Collect data by measuring different
More informationGEOMETRY  MEASUREMENT Middle School, Science and Math Monica Edwins, Twin Peaks Charter Academy, Longmont Colorado
GEOMETRY  MEASUREMENT Grade Level: Written by: Length of Unit: Middle School, Science and Math Monica Edwins, Twin Peaks Charter Academy, Longmont Colorado Six class periods I. ABSTRACT This unit could
More informationGeometry  Calculating Area and Perimeter
Geometry  Calculating Area and Perimeter In order to complete any of mechanical trades assessments, you will need to memorize certain formulas. These are listed below: (The formulas for circle geometry
More informationOral and mental starter
Lesson Objectives Order fractions and position them on a number line (Y6) Vocabulary gauge, litre numerator, denominator order Resources OHT. individual whiteboards (optional) Using fractions Oral and
More informationMetric Units of Length
7.2 Metric Units of Length 7.2 OBJECTIVES. Know the meaning of metric prefixes 2. Estimate metric units of length 3. Convert metric units of length NOTE Even in the United States, the metric system is
More information6.4 Factoring Polynomials
Name Class Date 6.4 Factoring Polynomials Essential Question: What are some ways to factor a polynomial, and how is factoring useful? Resource Locker Explore Analyzing a Visual Model for Polynomial Factorization
More informationMath. So we would say that the volume of this cube is: cubic units.
Math Volume and Surface Area Two numbers that are useful when we are dealing with 3 dimensional objects are the amount that the object can hold and the amount of material it would take to cover it. For
More informationCOMMON CORE STATE STANDARDS FOR MATHEMATICS 35 DOMAIN PROGRESSIONS
COMMON CORE STATE STANDARDS FOR MATHEMATICS 35 DOMAIN PROGRESSIONS Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Operations and Algebraic Thinking Represent and solve problems involving
More informationBasic Math for the Small Public Water Systems Operator
Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the
More informationAll the examples in this worksheet and all the answers to questions are available as answer sheets or videos.
BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Numbers 3 In this section we will look at  improper fractions and mixed fractions  multiplying and dividing fractions  what decimals mean and exponents
More informationKeystone National High School Placement Exam Math Level 1. Find the seventh term in the following sequence: 2, 6, 18, 54
1. Find the seventh term in the following sequence: 2, 6, 18, 54 2. Write a numerical expression for the verbal phrase. sixteen minus twelve divided by six Answer: b) 1458 Answer: d) 16 12 6 3. Evaluate
More informationChapter 1: Order of Operations, Fractions & Percents
HOSP 1107 (Business Math) Learning Centre Chapter 1: Order of Operations, Fractions & Percents ORDER OF OPERATIONS When finding the value of an expression, the operations must be carried out in a certain
More informationBASIC MATH FORMULAS  CLASS I. A. Rectangle [clarifiers, ponds] I = length; w = width; A = area; area in square ft [sq ft]
WASTEWATER MATH CONVERSION FACTORS 1. 1 acre =43,560 sq ft 2. 1 acre =2.47 hectares 3. 1 cu ft [of water] = 7.48 gallons 4. 1 cu ft [of water] = 62.4 Ibs/ft 3 5. Diameter =radius plus radius, D =r + r
More informationNumerator Denominator
Fractions A fraction is any part of a group, number or whole. Fractions are always written as Numerator Denominator A unitary fraction is one where the numerator is always 1 e.g 1 1 1 1 1...etc... 2 3
More informationEXAMPLE EXERCISE 3.1 Metric Basic Units and Prefixes
EXAMPLE EXERCISE 3.1 Metric Basic Units and Prefixes Give the symbol for each of the following metric units and state the quantity measured by each unit: (a) gigameter (b) kilogram (c) centiliter (d) microsecond
More informationMath Questions & Answers
What five coins add up to a nickel? five pennies (1 + 1 + 1 + 1 + 1 = 5) Which is longest: a foot, a yard or an inch? a yard (3 feet = 1 yard; 12 inches = 1 foot) What do you call the answer to a multiplication
More informationGENERAL MATH PROBLEM CATEGORIES AND ILLUSTRATED SOLUTIONS MEASUREMENT STANDARDS WHICH MUST BE MEMORIZED FOR THE BROKER TEST
Chapter 17 Math Problem Solutions CHAPTER 17 GENERAL MATH PROBLEM CATEGORIES AND ILLUSTRATED SOLUTIONS MEASUREMENT STANDARDS WHICH MUST BE MEMORIZED FOR THE BROKER TEST Linear Measure 12 inches = 1 ft
More informationPractice Tests Answer Keys
Practice Tests Answer Keys COURSE OUTLINE: Module # Name Practice Test included Module 1: Basic Math Refresher Module 2: Fractions, Decimals and Percents Module 3: Measurement Conversions Module 4: Linear,
More informationAppendix 1: Units of Measure Used in the LeadBased Paint Field
Appendix 1: Units of Measure Used in the LeadBased Paint Field Many of the units, terms, and concepts used in these Guidelines are new to the users. Most of the measures cited are in the Metric System
More informationExcel Invoice Format. SupplierWebsite  Excel Invoice Upload. Data Element Definition UCLA Supplier website (Rev. July 9, 2013)
Excel Invoice Format Excel Column Name Cell Format Notes Campus* Supplier Number* Invoice Number* Order Number* Invoice Date* Total Invoice Amount* Total Sales Tax Amount* Discount Amount Discount Percent
More informationCattle Producer's Library  CL 1280 CONVERSIONS FOR COMMONLY USED WEIGHTS AND MEASURES
Cattle Producer's Library  CL 1280 CONVERSIONS FOR COMMONLY USED WEIGHTS AND MEASURES Ron Torell, Northeast Area Livestock Specialist University of Nevada, Reno Bill Zollinger, Extension Beef Specialist
More information26 Integers: Multiplication, Division, and Order
26 Integers: Multiplication, Division, and Order Integer multiplication and division are extensions of whole number multiplication and division. In multiplying and dividing integers, the one new issue
More informationPAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE
PAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE 1 Property of Paychex, Inc. Basic Business Math Table of Contents Overview...3 Objectives...3 Calculator...4 Basic Calculations...6 Order of Operation...9
More informationOD 1401 9 PRECISION MEASURING INSTRUMENTS
SUBCOURSE EDITION OD 1401 9 PRECISION MEASURING INSTRUMENTS PRECISION MEASURING INSTRUMENTS SUBCOURSE OD1401 EDITION 9 Unites States Army Combined Arms Support Command Fort Lee, VA 238011809 5 CREDIT
More informationENGLISH CONTENT. Instructions for Using Your Computer Watch
ENGLISH CONTENT Instructions for Using Your Computer Watch Two Rotation System of Scale Ring Rotate System Crown Rotate System Ring Rotate System Crown Rotate System Figure 1 Instructions for Using your
More informationFourth Grade Math Standards and "I Can Statements"
Fourth Grade Math Standards and "I Can Statements" Standard  CC.4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and
More informationGrade 6 Math. Oak Meadow. Coursebook. Oak Meadow, Inc. Post Office Box 1346 Brattleboro, Vermont 053021346 oakmeadow.
Grade 6 Math Oak Meadow Coursebook Oak Meadow, Inc. Post Office Box 1346 Brattleboro, Vermont 053021346 oakmeadow.com Item #b064010 Grade 6 Contents Introduction... ix Lessons... Lesson 1... 1 Multiplication
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Thursday, August 16, 2012 8:30 to 11:30 a.m.
INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name
More informationChapter 8 Unit Conversions
Chapter 8 Unit Conversions [M]athematics is the easiest of sciences, a fact which is obvious in that no one s brain rejects it. Roger Bacon (c. 1214c. 1294), English philosopher and scientist Stand firm
More informationChapter 1: Chemistry: Measurements and Methods
Chapter 1: Chemistry: Measurements and Methods 1.1 The Discovery Process o Chemistry  The study of matter o Matter  Anything that has mass and occupies space, the stuff that things are made of. This
More informationIntroduction to fractions A fraction is the ratio of two whole numbers, i.e. one whole number divided by another whole number:
Fractions & Percentages Topics Covered: Fractions Simplifying fractions Equivalent fractions Improper fractions & mixed numers Operations with Fractions (addition, sutraction, multiplication, division)
More informationAppendix A: Units of Measure, Scientific Abbreviations, Symbols, Conversions, Variables, and Equations
119 : Units of Measure, Scientific Abbreviations, Symbols, Conversions, Variables, and Equations These abbreviations are for scientific and technical writing, and are not applicable to general style. Technical
More information1.05 Dimensional Analysis or Unit Factor Method
1.05 Dimensional Analysis or Unit Factor Method 12in = 1 ft 1 dime= 10 pennies 1 in = 2.54 cm Dr. Fred Garces Chemistry 100 Miramar College 100 yd = 300 ft *If you plan to be in the nursing field please
More informationScale Factors and Volume. Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor
Scale Factors and Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor Find the volume of each prism 1. 2. 15cm 14m 11m 24m 38cm 9cm V = 1,848m 3 V = 5,130cm
More informationHow to Solve Drug Dosage Problems
How to Solve Drug Dosage Problems General Information    page 2 Converting between units 
More informationTEKS TAKS 2010 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM
7 th Grade Math TAKSSTAARSTAARM Comparison Spacing has been deleted and graphics minimized to fit table. (1) Number, operation, and quantitative reasoning. The student represents and uses numbers in
More informationInterpreting Graphs. Interpreting a Bar Graph
1.1 Interpreting Graphs Before You compared quantities. Now You ll use graphs to analyze data. Why? So you can make conclusions about data, as in Example 1. KEY VOCABULARY bar graph, p. 3 data, p. 3 frequency
More informationGeorgia Online Formative Assessment Resource (GOFAR) AG geometry domain
AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent
More informationArea of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of
More information1.6 The Order of Operations
1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative
More informationSubject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1
Subject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1 I. (A) Goal(s): For student to gain conceptual understanding of the metric system and how to convert
More informationSection 1.5 Exponents, Square Roots, and the Order of Operations
Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.
More informationDrafting Terminology. Drafters. Drafting Technologists and Technicians
Drafting Terminology Drafters Drafting Technologists and Technicians Acknowledgments Winnipeg Technical College and the Department of Labour and Immigration of Manitoba wish to express sincere appreciation
More informationHow many are your works, Lord! In wisdom you made them all; the earth is full of your creatures. Psalm 104:24, niv
WELCOME When you look around, do you ever wonder where everything came from and how it was made? Have you ever contemplated why a tree is hard, a sponge is soft, and a breeze is invisible? By faith we
More informationAnswer Key For The California Mathematics Standards Grade 7
Introduction: Summary of Goals GRADE SEVEN By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use
More informationWhat You ll Learn. Why It s Important
These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why
More informationCooperative Extension Service The University of Georgia College of Agricultural and Environmental Sciences Athens
Using Cooperative Extension Service The University of Georgia College of Agricultural and Environmental Sciences Athens Chemicals are applied to ponds and lakes to control aquatic weeds; to control fish
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationA PRACTICAL GUIDE TO db CALCULATIONS
A PRACTICAL GUIDE TO db CALCULATIONS This is a practical guide to doing db (decibel) calculations, covering most common audio situations. You see db numbers all the time in audio. You may understand that
More informationUnit 7 The Number System: Multiplying and Dividing Integers
Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will
More information