Dimensional Analysis #3

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Dimensional Analysis #3"

Transcription

1 Dimensional Analysis #3 Many units of measure consist of not just one unit but are actually mixed units. The most common examples of mixed units are ratios of two different units. Many are probably familiar to you. For example, you drive your car at a speed of 55 miles per hour. You get gas mileage of 28 miles per gallon. You pay $.38 per gallon for gasoline. You inflate your car tires to a pressure of 35 pounds per square inch. You drive an average of 2,000 miles per year. Each of these mixed units involves two different types of units. We can write each of these mixed units as a unit fraction. For example, a speed of 55 miles per hour could be written as or Either of these two ratios expresses the relationship between miles and hours; that is, that in one hour the car will travel a distance of 55 miles. Some other mixed units are products of two or more units. For example, torque is measured in footpounds, electricity usage is measured in kilowatt-hours, and production is measured in man-hours. In each of these mixed units two different units are multiplied together, but the unit is generally written with a hyphen; that is, you will usually see foot-pounds not foot pounds or foot pounds. We can use the method of dimensional analysis to convert from one mixed unit to another mixed unit of similar type. To perform a conversion on a mixed unit expressed as a ratio, we will often have to chain several unit fractions to eliminate units in both the numerator and the denominator of the fraction. EXAMPLE : The speed limit on many highways is 55 mph. Convert this speed to feet per second. SOLUTION: First, note that the mixed unit we are given, 55 mph or 55 mi/hr, has a unit of distance in the numerator and a unit of time in the denominator. We can convert this mixed unit to any other mixed unit which has a unit of distance in the numerator and a unit of time in the denominator. The unit of ft/sec is of this type. To perform the conversion, we must multiply by unit fractions as we did in the previous two sections. We want to choose unit fractions so that the unit of miles will cancel and we are left with feet in the numerator. We will also want to multiply by other unit fractions so that the unit of hours will cancel and we will be left with the unit of seconds in the denominator. We can eliminate either the miles or the hours first. In this example, we will first eliminate the miles by multiplying by a unit fraction that has miles in the denominator ft mi If we were to multiply these two fractions, the result would be a fraction with feet in the numerator and hours in the denominator (ft/hr). Next we must multiply by a unit fraction or fractions that will eliminate hours and yield seconds. Since there are 60 seconds in minute and 60 minutes in hour, we will multiply by two unit fractions to convert from hours to seconds ft mi 60min min 60sec

2 Dimensional Analysis #3, Continued When we multiply these four unit fractions together, miles, hours and minutes will cancel, and we will be left with ft/sec, which is the unit we wanted. 55 mi 5280 ft mi 60min min 55(5280)()() ft = ft sec 60sec ()(60)(60)sec Therefore, a speed limit of 55 mph is equivalent to about ft/sec. REMEMBER: To convert from one mixed unit in fraction form to a different mixed unit in fraction form, you may eliminate the units in the numerator or in the denominator first. Just multiply by as many unit fractions as are necessary to convert both. EXAMPLE 2: A chemistry book gives the density of copper as 8.94 g/cm 3. What would this density be if expressed in kg/m 3? SOLUTION: The density of copper can be written as the ratio 8.94g cm 3 We must convert from grams to kilograms and from cubic centimeters to cubic meters. It makes no difference which conversion we perform first. For this example, we will first convert from grams to kilograms by multiplying by a unit fraction with grams in the denominator. 8.94g cm kg 3 000g Next we will convert from cubic centimeters to cubic meters by multiplying by a unit fraction with cubic centimeters in the numerator. Remember that since these are cubic units, we must use the 00 cm conversion factor of three times. m 8.94g cm kg 3 000g (00)3 cm 3 m 3 Now when we multiply these fractions together, the units of grams and cubic centimeters will cancel, and we will be left with the desired units of kilograms per cubic meter g cm 3 kg 000 g (00)3 cm 3 m 3 = 8940 kg m 3 Therefore, the density of copper is 8940 kg/m 3. The technique of dimensional analysis can be used to solve many problems that might be solved by formulas or by other methods. If we know what unit is required for an answer, we can multiply by the right unit fractions to get that unit. The next problem gives an example of this method. 2

3 Dimensional Analysis #3, Continued EXAMPLE 3: Suppose that a bathroom faucet is dripping at a rate of 40 drops per minute. At this rate, how long would it take to drain a 40-gallon water tank. (We will use the fact that 5 drops ml) SOLUTION: Since the volume of water in the tank is expressed in gallons and the dripping of the faucet is expressed in terms of drops per minute, we must convert the gallons to drops or the drops per minute to gallons per minute. For this example, we will convert drops/min to gal/min as shown below. 40drops min ml 5drops L 000 ml.057qt L gal 4qt gal min This new rate can be expressed as a unit fraction in two different ways gal min or min gal We can use the second fraction to determine the time it would take to drain the water tank in minutes. 40gal min gal We can multiply by still more unit fractions to express the time in hours, days, or any other unit of time. We will calculate the time in hours, rounding to the nearest whole number. 40gal min gal 60min 946hr Therefore, at the given rate, it would take approximately 946 hours of continuous dripping for the 40-gallon water tank to be drained. 3

4 PROBLEM SET 3 Answers to the odd-numbered problems are given at the end of the problem set. Dimensional Analysis #3, Continued WARM-UP 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.. 30 m/sec to km/hr 2. 7 kg/m 2 to lbs/ft ft/min to cm/sec 4. 3 cents/ft to cents/cm g/cm 3 to lb/in mi/gal to km/l 7. $90/day to cents/min 8. 2 ft 3 /sec to gal/min 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. Gasoline costs $.469 per gallon. How many cents per liter does the gas cost? Round your answer to the nearest cent. 0. The national debt is about $3,233,000,000,000. If a person can count one dollar per second, how many years would it take to count the number of dollars in the national debt? (Assume that the person doing the counting takes no break in counting.) Round your answer to the nearest year.. A farmer has irrigation rights of 2 acre-feet per year. One acre-foot is the amount of water that would cover one acre to a depth of one foot. How many gallons of water would the farmer have to pump to use all of the allotted irrigation water in one year? Round your answer to the nearest thousand gallons. 2. A bicycle tire is inflated to 20 psi (lbs per square inch). What would this pressure be in Newtons per square meter? Round your answer to the nearest hundred. 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 m/sec to in/sec gal/min to ft 3 /sec cm 3 /min to mm 3 /sec /in. to $/yard 4

5 Dimensional Analysis #3, Continued 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. 7. A bolt must be tightened to 60 ft lbs of torque. To the nearest tenth, what is this torque in N m? SOLUTIONS TO ODD-NUMBERED 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.) The gasoline costs about 39 cents/liter.. The farmer must pump 489,000 gallons of water to use all of the allotted irrigation water The bolt must be tightened to about 8.3 N m of torque. ANSWERS TO EVEN NUMBERED PROBLEMS lbs / ft / cm km / L gal / min 0. It would take 02,57.76 years psi is approximately 827,000 N / m ft 3 /sec $ / y 5

6 MEASUREMENT AND CONVERSION TABLE U. S. CUSTOMARY SYSTEM yd = 3 ft 3 tsp = T ft = 2 in 6 T cup fathom = 6 ft cup = 8 oz (liquid capacity) mi = 5, 280 ft pt = 2 cups acre = 43,560 ft qt = 2 pt lb = 6 oz (dry weight) gal = 4 qt ton = 2000 lb gal 23 in ft 7.48 gal METRIC SYSTEM m =,000,000 microns ( ) hectare (ha) = 0,000 m m = 000 mm kg = 000 g m = 00 cm g = 000 mg m = 0 dm kl = 000 L km = 000 m L = 000 ml cm = 0 mm cm = ml m = 000 L CONVERSION BETWEEN THE U. S. CUSTOMARY AND THE METRIC SYSTEM in. = 2.54 cm lb g m in. oz g mi.609 km kg lb kwh = 3,43 Btu pt cm lb. = N (Newtons) L.057 qt tsp = 5 ml ft L

DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 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

More information

DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 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

More information

Dimensional Analysis is a simple method for changing from one unit of measure to another. How many yards are in 49 ft?

Dimensional Analysis is a simple method for changing from one unit of measure to another. How many yards are in 49 ft? HFCC Math Lab NAT 05 Dimensional Analysis Dimensional Analysis is a simple method for changing from one unit of measure to another. Can you answer these questions? How many feet are in 3.5 yards? Revised

More information

Handout Unit Conversions (Dimensional Analysis)

Handout Unit Conversions (Dimensional Analysis) Handout Unit Conversions (Dimensional Analysis) The Metric System had its beginnings back in 670 by a mathematician called Gabriel Mouton. The modern version, (since 960) is correctly called "International

More information

MATH FOR NURSING MEASUREMENTS. Written by: Joe Witkowski and Eileen Phillips

MATH FOR NURSING MEASUREMENTS. Written by: Joe Witkowski and Eileen Phillips MATH FOR NURSING MEASUREMENTS Written by: Joe Witkowski and Eileen Phillips Section 1: Introduction Quantities have many units, which can be used to measure them. The following table gives common units

More information

Converting Units of Measure Measurement

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 information

INTERIM UNITS OF MEASURE As suggested by Federal Standard 376B January 27, 1993. hectare (ha) Hundred for traffic buttons.

INTERIM UNITS OF MEASURE As suggested by Federal Standard 376B January 27, 1993. hectare (ha) Hundred for traffic buttons. SI - The Metrics International System of Units The International System of Units (SI) is a modernized version of the metric system established by international agreement. The metric system of measurement

More information

Measurement. Customary Units of Measure

Measurement. Customary Units of Measure Chapter 7 Measurement There are two main systems for measuring distance, weight, and liquid capacity. The United States and parts of the former British Empire use customary, or standard, units of measure.

More information

CH 304K Practice Problems

CH 304K Practice Problems 1 CH 304K Practice Problems Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. How many millimeters are there in 25 feet? a. 7.6 10 2 mm b.

More information

MEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were:

MEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were: MEASUREMENT Introduction: People created systems of measurement to address practical problems such as finding the distance between two places, finding the length, width or height of a building, finding

More information

Prealgebra Textbook. Chapter 6 Odd Solutions

Prealgebra Textbook. Chapter 6 Odd Solutions Prealgebra Textbook Second Edition Chapter 6 Odd Solutions Department of Mathematics College of the Redwoods 2012-2013 Copyright All parts of this prealgebra textbook are copyrighted c 2009 in the name

More information

Unit Conversions. Ben Logan Feb 10, 2005

Unit Conversions. Ben Logan <ben.logan@gmail.com> Feb 10, 2005 Unit Conversions Ben Logan Feb 0, 2005 Abstract Conversion between different units of measurement is one of the first concepts covered at the start of a course in chemistry or physics.

More information

MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.

MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile. MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units

More information

APPENDIX I SI AND ENGLISH UNITS AND CONVERSION FACTORS

APPENDIX I SI AND ENGLISH UNITS AND CONVERSION FACTORS APPENDIX I SI AND ENGLISH UNITS AND CONVERSION FACTORS The International System of Units (Systéme International d Unités, or SI) recognizes seven basic units from which all others are derived. They are:

More information

Appendix C: Conversions and Calculations

Appendix C: Conversions and Calculations Appendix C: Conversions and Calculations Effective application of pesticides depends on many factors. One of the more important is to correctly calculate the amount of material needed. Unless you have

More information

18) 6 3 4 21) 1 1 2 22) 7 1 2 23) 19 1 2 25) 1 1 4. 27) 6 3 qt to cups 30) 5 1 2. 32) 3 5 gal to pints. 33) 24 1 qt to cups

18) 6 3 4 21) 1 1 2 22) 7 1 2 23) 19 1 2 25) 1 1 4. 27) 6 3 qt to cups 30) 5 1 2. 32) 3 5 gal to pints. 33) 24 1 qt to cups Math 081 Chapter 07 Practice Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 18) 6 3 4 gal to quarts Convert as indicated. 1) 72 in. to feet 19)

More information

Conversion Formulas and Tables

Conversion Formulas and Tables Conversion Formulas and Tables Metric to English, Introduction Most of the world, with the exception of the USA, uses the metric system of measurements exclusively. In the USA there are many people that

More information

Objective To introduce a formula to calculate the area. Family Letters. Assessment Management

Objective To introduce a formula to calculate the area. Family Letters. Assessment Management Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

More information

APPENDIX H CONVERSION FACTORS

APPENDIX H CONVERSION FACTORS APPENDIX H CONVERSION FACTORS A ampere American Association of State AASHTO Highway & Transportation Officials ABS (%) Percent of Absorbed Moisture Abs. Vol. Absolute Volume ACI American Concrete Institute

More information

Metric System Conversion Factors 1

Metric System Conversion Factors 1 AGR39 1 J. Bryan Unruh, Barry J. Brecke, and Ramon G. Leon-Gonzalez 2 Area Equivalents 1 Acre (A) = 43,560 square feet (ft 2 ) = 4,840 square yards (yd 2 ) = 0.405 hectares (ha) = 160 square rods (rd 2

More information

Fractions, Ratios, and Proportions Work Sheets. Contents

Fractions, Ratios, and Proportions Work Sheets. Contents Fractions, Ratios, and Proportions Work Sheets The work sheets are grouped according to math skill. Each skill is then arranged in a sequence of work sheets that build from simple to complex. Choose the

More information

Conversions. 12 in. 1 ft = 1.

Conversions. 12 in. 1 ft = 1. Conversions There are so many units that you can use to express results that you need to become proficient at converting from one to another. Fortunately, there is an easy way to do this and it works every

More information

1. Metric system- developed in Europe (France) in 1700's, offered as an alternative to the British or English system of measurement.

1. Metric system- developed in Europe (France) in 1700's, offered as an alternative to the British or English system of measurement. GS104 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,

More information

Math Review Sheets Math 20 Basic Mathematics (Arithmetic)

Math Review Sheets Math 20 Basic Mathematics (Arithmetic) Math Review Sheets Math 0 Basic Mathematics (Arithmetic) The purpose of this Review Sheet is to provide students a comprehensive review of items that are taught in Math 0 classes. It is the KCC Math Department

More information

UNIT (1) MEASUREMENTS IN CHEMISTRY

UNIT (1) MEASUREMENTS IN CHEMISTRY UNIT (1) MEASUREMENTS IN CHEMISTRY Measurements are part of our daily lives. We measure our weights, driving distances, and gallons of gasoline. As a health professional you might measure blood pressure,

More information

Activity Standard and Metric Measuring

Activity Standard and Metric Measuring Activity 1.3.1 Standard and Metric Measuring Introduction Measurements are seen and used every day. You have probably worked with measurements at home and at school. Measurements can be seen in the form

More information

Chapter 2 Measurement and Problem Solving

Chapter 2 Measurement and Problem Solving Introductory Chemistry, 3 rd Edition Nivaldo Tro Measurement and Problem Solving Graph of global Temperature rise in 20 th Century. Cover page Opposite page 11. Roy Kennedy Massachusetts Bay Community

More information

UNIT 1 MASS AND LENGTH

UNIT 1 MASS AND LENGTH UNIT 1 MASS AND LENGTH Typical Units Typical units for measuring length and mass are listed below. Length Typical units for length in the Imperial system and SI are: Imperial SI inches ( ) centimetres

More information

Chapter 7. g-----grams, unit measure of weight m----meters, unit measure of length l---liters, unit measure of volume

Chapter 7. g-----grams, unit measure of weight m----meters, unit measure of length l---liters, unit measure of volume Chapter 7 g-----grams, unit measure of weight m----meters, unit measure of length l---liters, unit measure of volume ) find cm, cm, 5mm, 60mm, 05mm, dm,.dm,.5cm, 0.5cm One liter of coke. The amount of

More information

To Multiply Decimals

To 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 information

One basic concept in math is that if we multiply a number by 1, the result is equal to the original number. For example,

One basic concept in math is that if we multiply a number by 1, the result is equal to the original number. For example, MA 35 Lecture - Introduction to Unit Conversions Tuesday, March 24, 205. Objectives: Introduce the concept of doing algebra on units. One basic concept in math is that if we multiply a number by, the result

More information

REVIEW SHEETS INTRODUCTORY PHYSICAL SCIENCE MATH 52

REVIEW SHEETS INTRODUCTORY PHYSICAL SCIENCE MATH 52 REVIEW SHEETS INTRODUCTORY PHYSICAL SCIENCE MATH 52 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts which are taught in the specified math course.

More information

Dividing Decimals 4.5

Dividing Decimals 4.5 4.5 Dividing Decimals 4.5 OBJECTIVES 1. Divide a decimal by a whole number 2. Divide a decimal by a decimal 3. Divide a decimal by a power of ten 4. Apply division to the solution of an application problem

More information

Calculating Area and Volume of Ponds and Tanks

Calculating 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 information

Measurement/Volume and Surface Area Long-Term Memory Review Grade 7, Standard 3.0 Review 1

Measurement/Volume and Surface Area Long-Term 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 information

1.05 Dimensional Analysis or Unit Factor Method

1.05 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 information

CHEMISTRY B- FACTOR LABEL PACKET NAME: HR: PAGE 1. Chemistry B. Factor Label Packet

CHEMISTRY B- FACTOR LABEL PACKET NAME: HR: PAGE 1. Chemistry B. Factor Label Packet CHEMISTRY B- FACTOR LABEL PACKET NAME: HR: PAGE 1 Chemistry B Factor Label Packet CHEMISTRY B- FACTOR LABEL PACKET NAME: HR: PAGE 2 PERIODIC TABLE OF ELEMENTS WITH OXIDATION NUMBERS +1 0 H +2 +3-3 He Li

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)

$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 information

Pump Formulas Imperial and SI Units

Pump Formulas Imperial and SI Units Pump Formulas Imperial and Pressure to Head H = head, ft P = pressure, psi H = head, m P = pressure, bar Mass Flow to Volumetric Flow ṁ = mass flow, lbm/h ρ = fluid density, lbm/ft 3 ṁ = mass flow, kg/h

More information

Units of Measurement: A. The Imperial System

Units 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 information

Exercise Worksheets. Copyright. 2002 Susan D. Phillips

Exercise 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 information

CHAPTER 4 DIMENSIONAL ANALYSIS

CHAPTER 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 information

CHEM 101 / 105 LECT 1

CHEM 101 / 105 LECT 1 CHEM 101 / 105 LECT 1 Rules of the road: Your Loyola computer account (activate it). Class Web site (visit and send me an e-mail B4 Tues.) spavko1@luc.edu Chapter 1. Chemistry is... Matter is... Classifications

More information

AP* Environmental Science Mastering the Math

AP* Environmental Science Mastering the Math AP* Environmental Science Mastering the Math Part I: Dimensional Analysis (aka Factor-Label or Unit Cancellation Method) Sample Problem 1 A large, coal-fired electric power plant produces 1 million kilowatt-hours

More information

Activity 3.2 Unit Conversion

Activity 3.2 Unit Conversion Activity 3.2 Unit Conversion Introduction Engineers of all disciplines are constantly required to work with measurements of a variety of quantities length, area, volume, mass, force, time, temperature,

More information

Metric Mania Conversion Practice. Basic Unit. Overhead Copy. Kilo - 1000 units. Hecto - 100 units. Deka - 10 units. Deci - 0.

Metric Mania Conversion Practice. Basic Unit. Overhead Copy. Kilo - 1000 units. Hecto - 100 units. Deka - 10 units. Deci - 0. Metric Mania Conversion Practice Overhead Copy Kilo - 1000 Hecto - 100 Deka - 10 To convert to a larger unit, move decimal point to the left or divide. Basic Unit Deci - 0.1 To convert to a smaller unit,

More information

Preferred SI (Metric) Units

Preferred SI (Metric) Units Quantity Unit Symbol LENGTH meter m Preferred SI (Metric) Units Metric-U.S. Customary Unit Equivalents 1 m = 1000 mm = 39.37 in. = millimeter mm 25.4 mm = 1 inch micrometer μm 1 μm = 10-6 m Remarks 3.281

More information

Measurement: Converting Distances

Measurement: Converting Distances Measurement: Converting Distances Measuring Distances Measuring distances is done by measuring length. You may use a different system to measure length differently than other places in the world. This

More information

How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

How 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 pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

More information

METRIC CONVERSION TABLE Multiply By To Obtain Millimetres 0.03937 Inches Millimetres 0.003281 Feet Metres 3.281 Feet Kilometres 0.

METRIC CONVERSION TABLE Multiply By To Obtain Millimetres 0.03937 Inches Millimetres 0.003281 Feet Metres 3.281 Feet Kilometres 0. Linear Measure Square Measure or Area Volume or Capacity Mass Density Force* Pressure* or Stress* Temperature METRIC CONVERSION TABLE Multiply By To Obtain Millimetres 0.03937 Inches Millimetres 0.003281

More information

Imperial and metric quiz

Imperial and metric quiz Level A 1. Inches are a metric measure of length. 2. Pints are smaller than gallons. 3. 1 foot is the same as: A) 12 inches B) 14 inches C) 16 inches D) 3 yards 4. foot is usually shortened to: A) 1 f

More information

Note: Because approximations are used, your answers may vary slightly from the answers given in the back of the book.

Note: Because approximations are used, your answers may vary slightly from the answers given in the back of the book. 2.5C 9.7 Exercise Set FOR EXTRA HELP Note: Because approximations are used, your answers may vary slightly from the answers given in the back of the book. Objective Convert as indicated. If necessary,

More information

4.5.1 The Metric System

4.5.1 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 information

2.2 Scientific Notation: Writing Large and Small Numbers

2.2 Scientific Notation: Writing Large and Small Numbers 2.2 Scientific Notation: Writing Large and Small Numbers A number written in scientific notation has two parts. A decimal part: a number that is between 1 and 10. An exponential part: 10 raised to an exponent,

More information

MOST 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 *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 information

Energy and Cost Required to Lift or Pressurize Water

Energy and Cost Required to Lift or Pressurize Water University of California Tulare County Cooperative Extension Energy and Cost Required to Lift or Pressurize Water Bill Peacock, Tulare County Farm Advisor Pub. IG6-96 Power Requirements to Lift Water It

More information

HFCC Math Lab General Math Topics -1. Metric System: Shortcut Conversions of Units within the Metric System

HFCC 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 information

MATHEMATICAL EXCURSIONS Math and the Tourist

MATHEMATICAL EXCURSIONS Math and the Tourist MATHEMATICAL EXCURSIONS Math and the Tourist When you travel to a foreign country, besides different languages and customs, you may encounter a different currency, system of weights and measures, and temperature

More information

Conversion Factors. The following conversion tables are for your use: Conversion Tables and Formulas Decimal and Millimeter Equivalents of Fractions

Conversion Factors. The following conversion tables are for your use: Conversion Tables and Formulas Decimal and Millimeter Equivalents of Fractions Conversion Factors Safety Home>Conversion Factors The following conversion tables are for your use: Conversion Tables and Formulas Decimal and Millimeter Equivalents of Fractions CONVERSION TABLES AND

More information

For. Level 3. Published by SAI Interactive, Inc., 340 Frazier Avenue, Chattanooga, TN 37405.

For. Level 3. Published by SAI Interactive, Inc., 340 Frazier Avenue, Chattanooga, TN 37405. Introduction For Level 3 Published by SAI Interactive, Inc., 340 Frazier Avenue, Chattanooga, TN 37405. Copyright 2000 by SAI Interactive, Inc. KeyTrain is a registered trademark of SAI Interactive, Inc.

More information

How to Solve Drug Dosage Problems

How to Solve Drug Dosage Problems How to Solve Drug Dosage Problems General Information ----------------------------------------- ----- ------------------ page 2 Converting between units -----------------------------------------------------------

More information

ENGLISH CONTENT. Instructions for Using Your Computer Watch

ENGLISH 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 information

Metric System Math Review -Dimensional Analysis

Metric System Math Review -Dimensional Analysis Metric System Math Review -Dimensional Analysis In 1960 the International Bureau of Weights and Measures (Sevres, France) adopted the "International System of Units", also known as "SI" units. 7 base units

More information

Metric Units of Weight and Volume

Metric Units of Weight and Volume 7.3 Metric Units of Weight and Volume 7.3 OBJECTIVES 1. Use appropriate metric units of weight 2. Convert metric units of weight 3. Estimate metric units of volume 4. Convert metric units of volume The

More information

Free Pre-Algebra Lesson 3 page 1. Example: Find the perimeter of each figure. Assume measurements are in centimeters.

Free Pre-Algebra Lesson 3 page 1. Example: Find the perimeter of each figure. Assume measurements are in centimeters. Free Pre-Algebra Lesson 3 page 1 Lesson 3 Perimeter and Area Enclose a flat space; say with a fence or wall. The length of the fence (how far you walk around the edge) is the perimeter, and the measure

More information

Jones and Bartlett Publishers, LLC. NOT FOR SALE OR DISTRIBUTION.

Jones 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 information

CONVERSION INFORMATION

CONVERSION INFORMATION CONVERSION INFORMATION Compiled by Campbell M Gold (2008) CMG Archives http://campbellmgold.com IMPORTANT The health information contained herein is not meant as a substitute for advice from your physician,

More information

2. Length, Area, and Volume

2. Length, Area, and Volume Name Date Class TEACHING RESOURCES BASIC SKILLS 2. In 1960, the scientific community decided to adopt a common system of measurement so communication among scientists would be easier. The system they agreed

More information

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms.

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts

More information

Equivalents & Conversion Factors 406 Capacity Formulas for Steam Loads 407 Formulas for Control Valve Sizing 408-409

Equivalents & Conversion Factors 406 Capacity Formulas for Steam Loads 407 Formulas for Control Valve Sizing 408-409 Engineering Data Table of Contents Page No. I II Formulas, Conversions & Guidelines Equivalents & Conversion Factors 406 Capacity Formulas for Steam Loads 407 Formulas for Control Sizing 408-409 Steam

More information

Metric System Conversion Factors

Metric System Conversion Factors 133 Metric System Conversion Factors Area Equivalents 1 acre = 43,560 ft 2 = 4840 yd 2 = 0.4047 hectares = 160 rods 2 = 4047 m 2 = 0.0016 sq. mile 1 acre-inch = 102.8 m 3 = 27,154 gal = 3630 ft 3 1 hectare

More information

HESI PREP TEST. SLC Lake Worth Math Lab

HESI PREP TEST. SLC Lake Worth Math Lab 1 PREP TEST 2 Explanation of scores: 90% to 100%: Excellent Super job! You have excellent Math skills and should have no difficulty calculating medication administration problems in your program. 80% to

More information

Changing Fractions to Decimals on a Calculator

Changing Fractions to Decimals on a Calculator Changing Fractions to Decimals on a Calculator You can change fractions to decimals on a calculator. Do you remember how to change a fraction to a decimal? Divide the numerator by the denominator. For,

More information

A Mathematical Toolkit. Introduction: Chapter 2. Objectives

A Mathematical Toolkit. Introduction: Chapter 2. Objectives A Mathematical Toolkit 1 About Science Mathematics The Language of Science When the ideas of science are epressed in mathematical terms, they are unambiguous. The equations of science provide compact epressions

More information

Chapter 8 Unit Conversions

Chapter 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. 1214-c. 1294), English philosopher and scientist Stand firm

More information

Excel Invoice Format. SupplierWebsite - Excel Invoice Upload. Data Element Definition UCLA Supplier website (Rev. July 9, 2013)

Excel 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 information

Metric Prefixes. 10 12 Tera- T 10 2 centi- c 10 9 Giga- G 10 3 milli- m 10 6 Mega- M 10 6 micro- µ 10 3 kilo- k 10 9 nano- n

Metric Prefixes. 10 12 Tera- T 10 2 centi- c 10 9 Giga- G 10 3 milli- m 10 6 Mega- M 10 6 micro- µ 10 3 kilo- k 10 9 nano- n Metric Prefixes Meaning Name Abbreviation Meaning Name Abbreviation 10 12 Tera- T 10 2 centi- c 10 9 Giga- G 10 3 milli- m 10 6 Mega- M 10 6 micro- µ 10 3 kilo- k 10 9 nano- n These are the most commonly

More information

Multiply circumference by 0.3183. Or divide circumference by 3.1416. Multiply diameter by 3.1416. Or divide diameter by 0.3183.

Multiply circumference by 0.3183. Or divide circumference by 3.1416. Multiply diameter by 3.1416. Or divide diameter by 0.3183. RULES RELATIVE TO THE CIRCLE TO FIND DIAMETER TO FIND CIRCUMFERENCE TO FIND RADIUS TO FIND SIDE OF AN INSCRIBED SQUARE TO FIND SIDE OF AN EQUAL SQUARE Multiply circumference by 0.383. Or divide circumference

More information

FLORIDA DEPARTMENT OF ENVIRONMENTAL PROTECTION Wastewater Treatment Formulas/Conversion Table

FLORIDA DEPARTMENT OF ENVIRONMENTAL PROTECTION Wastewater Treatment Formulas/Conversion Table Revised February 2014 FLORIDA DEPARTMENT OF ENVIRONMENTAL PROTECTION Wastewater Treatment Formulas/Conversion Table Measurement Conversion Measurement Conversion Measurement Conversion 12 in= 1 ft 27 cu.

More information

DRUG CALCULATION PRESENTATION. By: Donna Hess RN, MS

DRUG CALCULATION PRESENTATION. By: Donna Hess RN, MS DRUG CALCULATION PRESENTATION By: Donna Hess RN, MS FIRST RULE: ALWAYS CHECK YOUR ANSWER! Second Rule: DOES YOUR ANSWER MAKE SENSE? Rules to Remember: When writing a whole number as a fraction, place the

More information

Healthcare Math: Using the Metric System

Healthcare 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 information

Chapter 3 Review Math 1030

Chapter 3 Review Math 1030 Section A.1: Three Ways of Using Percentages Using percentages We can use percentages in three different ways: To express a fraction of something. For example, A total of 10, 000 newspaper employees, 2.6%

More information

H.C.C.T.P. Highway Construction Careers Training Program. Entrance Exam. Study Guide

H.C.C.T.P. Highway Construction Careers Training Program. Entrance Exam. Study Guide H.C.C.T.P. Highway Construction Careers Training Program Entrance Exam Study Guide Entrance Exam Study Guide How to use this study guide: This study guide is to prepare you for the math section on your

More information

Homework 1 Solutions

Homework 1 Solutions Homework 1 Solutions Chapter 1B Multiple Negations. Explain the meaning of the given statement, then answer the question that follows. 23. Sarah did not decline the offer to go to dinner. Did Sarah go

More information

hp calculators HP 35s Unit Conversions Metric units and Imperial units Conversion keys Practice working problems involving conversions

hp calculators HP 35s Unit Conversions Metric units and Imperial units Conversion keys Practice working problems involving conversions Metric units and Imperial units Conversion keys Practice working problems involving conversions Performing conversions that are not built in Special considerations for temperature conversions Metric units

More information

Chapter 1 Problems. To do all three sections of this problem, we can first convert the radius to kilometers. r = 6.37 10 6 1km 1000m = 6.

Chapter 1 Problems. To do all three sections of this problem, we can first convert the radius to kilometers. r = 6.37 10 6 1km 1000m = 6. Chapter 1 Problems 1.1 The Earth is approximately a sphere of radius 6.37 x 10 6 m. (a) What is is its circumference in kilometers? (b) What is its surface area in square kilometers? (c) What is its volume

More information

Authors: Editor: Graphics: Jason March, B.A. Tim Wilson, B.A. Linda Shanks. Tim Wilson Jason March Eva McKendry

Authors: Editor: Graphics: Jason March, B.A. Tim Wilson, B.A. Linda Shanks. Tim Wilson Jason March Eva McKendry Student Name: Date: Contact Person Name: Phone Number: Lesson 15 Rates and Ratios Objectives Understand what a rate and a ratio are Solve word problems that involve rates and ratios Authors: Jason March,

More information

Practice Tests Answer Keys

Practice 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 information

Conversions 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

Conversions 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 information

Chapter 1 Lecture Notes: Science and Measurements

Chapter 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 information

Unit Conversions Practice

Unit Conversions Practice Make the following conversions: 1) Convert 16.7 inches to feet Unit Conversions Practice 2) Convert 25 yards to feet (there are 3 feet in a yard) 3) Convert 90 centuries to years 4) Convert 84 miles to

More information

GEOMETRY - MEASUREMENT Middle School, Science and Math Monica Edwins, Twin Peaks Charter Academy, Longmont Colorado

GEOMETRY - 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 information

Revision Notes Adult Numeracy Level 2

Revision 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 information

Tallahassee Community College PERIMETER

Tallahassee 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 information

Ratios (pages 288 291)

Ratios (pages 288 291) A Ratios (pages 2 29) A ratio is a comparison of two numbers by division. Ratio Arithmetic: to : Algebra: a to b a:b a b When you write a ratio as a fraction, write it in simplest form. Two ratios that

More information

Solving Equations With Fractional Coefficients

Solving Equations With Fractional Coefficients Solving Equations With Fractional Coefficients Some equations include a variable with a fractional coefficient. Solve this kind of equation by multiplying both sides of the equation by the reciprocal of

More information

BASIC MATH FORMULAS - CLASS I. A. Rectangle [clarifiers, ponds] I = length; w = width; A = area; area in square ft [sq ft]

BASIC 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 information

Customary Length, Weight, and Capacity

Customary Length, Weight, and Capacity 15 CHAPTER Lesson 15.1 Customary Length, Weight, and Capacity Measuring Length Measure each object to the nearest inch. 1. The crayon is about inches long. 2. 3. The toothbrush is about The rope is about

More information

PROBLEM SOLVING BY DIMENSIONAL ANALYSIS

PROBLEM SOLVING BY DIMENSIONAL ANALYSIS PROBLEM SOLVING BY DIMENSIONAL ANALYSIS Problem solving in chemistry almost always involves word problems or story-problems. Although there is no single method for solving all types of problems encountered

More information

4-1 Ratios, Rates, and Unit Rates

4-1 Ratios, Rates, and Unit Rates Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up Divide. Round answers to the nearest tenth. 1. 420 23.3 2. 73 3.5 18 21 3. 380 23.8 4. 430 23.9 16 18 Learn to work with rates and

More information