# Handout Unit Conversions (Dimensional Analysis)

Size: px
Start display at page:

Transcription

1 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 System of Units" or "SI" (from the French "Système International"). The metric system has been officially sanctioned for use in the United States since 866, but it remains the only industrialized country that has not adopted the metric system as its official system of measurement. Many sources also cite Liberia and Burma as the only other countries not to have done so. This section will cover conversions () selected units in the metric and American systems, () compound or derived measures, and () between metric and American systems. Also, (4) applications using conversions will be presented. The metric system is based on a set of basic units and prefixes representing powers of 0. Basic metric units length meter (m) mass gram (g) volume liter (L) time second (s) temperature Celsius ( C) or Kelvin ( K) where C=K-7.5 Prefixes (The units that are in bold are the ones that are most commonly used.) prefix symbol value giga G,000,000,000 = 0 9 ( a billion) mega M,000,000 = 0 6 ( a million) kilo k,000 = 0 hecto h 00 = 0 deca da 0 deci centi milli micro nano d c m μ (the Greek letter mu) n = 0. = 0-0 = 0.0 = 0-00 = 0.00 = 0 - (a thousandth),000 = = 0-6 (a millionth),000,000 = = 0-9 (a billionth),000,000,000

2 To get a sense of the size of the basic units of meter, gram and liter consider the following examples. The standard height of a door handle or knob is meter. The weight of a penny is.5 grams. Almost everyone is familiar with liter bottles of soda. The next set of examples illustrates the use of some of the most used prefixes. Examples:. milligram = gram = 0.00 gram, or mg =,000, mg=g. milliliter= liter=0.00 liter, or ml=,000,000 L=0.00 L 4.,000 ml = L g = 0.00 gram 5. centimeter= 00 meter=0.0 meter, or cm = 00 m = 0.0 m 6. kilogram =,000 grams, or kg =,000 g 7. kilometer =,000 meters, or km = 000 m 8. kilobyte = 000 bytes (a byte is a unit used in computers to express the length of a word.) 9. megabyte =,000,000 bytes = 000 kilobytes 0. An adult male is about how tall? A) 75cm B) 75m C) 75mm The correct answer is A) since he is almost twice the standard height of a door knob, so almost meters, that is almost 00 cm.. Choose the most reasonable weight of a newborn baby: A).7g B)L C) 4kg D)0.4m The correct answer is C) since.7g is like a penny, while L measures volume and m is for length.

3 Conversion Tables The American system of measurements is based on the English system. American-->American Capacity (volume) gallon = gal = 4 quarts = 4 qts quart = qt = pints = pt pint = pt = cups = c = 6 fluid ounces = 6 fl oz cup = c = 8 fluid ounces = 8 fl. oz (Note: a fluid ounce is not the same as the weight measure ounce.) fluid ounce = fl oz = tablespoons = tbsp tablespoon = tbsp = teaspoons = tsp Length foot = ft = inches = in mile = mi = 580 feet = 760 yd Mass pound = lb = 6 ounces = 6 oz ton = 000 pounds = 000 lb (This is sometimes called a short ton or ton(us). A long ton or ton(uk) is equal to 40 pounds.) Temperature Temperature is measured in degrees Fahrenheit ( F). Water freezes at F and boils at F SI--> American meter =.096 yards =.808 feet = 9.7 inches kilometer =.67 miles gram =.057 ounces kilogram = 5.7 ounces =.05 pounds liter =.647 gallons =.0567 quarts C 5 9 F SI temperature measure is degree Celsius ( C). Water freezes at 0 C and boils at 00 F Another SI measure for temperature is Kelvin (K) where American--> SI inch = meters =.54 centimeters yard = meters mile = meters = kilometers pound = grams ounce 8.5 grams gallon.784 liters quart.9464 liters fluid ounce.0957 liters = 9.57 milliliters tsp = 4.9 ml Everywhere in the World Time minute = min = 60 seconds = 60 s hour = hr = 60 min day = 4 hr Small amount of liquid Milliliters are used extensively in the sciences and medicine. The abbreviation cc is often used instead of ml. The relation of ml to volume is given by

4 Areas and volumes 4 Recall that area is measured in squares. One square foot or ft represents the area covered by a square foot by foot. Example: square feet = ft means squares foot by foot. The measure of the area of a rectangle ft by 4 ft is ft since it can be covered (tiled) with squares each foot by foot Volume is measured in cubes. One cubic centimeter or cm represents the volume that can be covered by a cube cm by cm by cm. Example: Find the volume of a box cm by cm by 4 cm. The question is, how many cubes cm on a side can be put into this box. cm cm 4 cm = 6 cm. That is, the box will hold 6 cubes cm by cm by cm. A conversion table could be made for areas and another could be made for volumes. The tables would include facts like ft = 44 in, yd = 9 ft, m = 0000 cm, ft = 78 in, etc. Fortunately, as shown below, this is not necessary. This handout will cover one method commonly used in the sciences to convert units. This method uses multiples of " in a convenient form. Examples: a) 4000 in =? ft Notice that ft = in. We write our " as ft so that in in 4000 in will cancel. in 4, 000in ft 4, 000 4, 000in ft. ft. notice that the in canceled in b) 8 ft =? in 8 ft in 8 ft 6in ft Notice that ft = in. This time we write our as in / ft so that the ft cancel leaving only in as the unit. c). mi =? in From the conversion tables on page notice that mi = 580 ft and ft = in. So we should write our in two different ways = 580ft mi and as = in. Using the first fraction we can ft convert miles into feet, while using the second fraction we can further convert the feet into inches. Combining these two we have the following:

5 .mi 580 ft in (.)(580)().mi in 4578in mi ft notice that the mi and the ft cancel 5 d) cm =? km Just like in the previous example we don t have a direct conversion between centimeters (cm) and kilometers (km). However, both are connected through meters (m). Therefore, we will use m the in two different ways: = and =. Using both, we get the following: 00cm 000m 46000cm m km cm km.46km 00cm 000 m (00)(000) notice that the cm and the m cancel e),000,000 fl oz =? gal From the conversion tables on page, we see that pt = 6 fl oz, qt = pt and gal = 4qt. We have to combine all three of these conversions to go from fluid ounces to gallons: fl oz pt qt gal fl oz gal 78.5gal 6 fl oz pt 4 qt (6)()(4) notice that the fl oz, the pt, and the qt cancel f) 8 ft =? yd The following is the standard method for handling areas and volumes. The conversion tables on page say that yd = ft. For square units, we have to use this conversion twice so that ft " cancels with ft ft. 8 ft yd yd 8 8 ft yd yd ft ft ()() Another way to obtain the same result is to create a new conversion formula for our specific prupose. Since yd = ft we immediately have yd = ft ft = 9ft and 8 ft 8 ft yd 8 ft yd 9 ft g),000,000 mm =? km This time we will use two conversions m = 000 mm and km = 000 m. Each of these two conversion will be used twice, since we are using square units: mm m m mm m 000mm 000mm Then we continue: km km m m km. Therefore mm = km. 000m 000m notice that mm " cancels with mm mm in the first row, and m cancels with m m in the second row of calculations above. h) 8 ft =? yd When dealing with cubic units, we have to apply each conversion formula three times. For example, since yd = ft, we can apply this conversion three times so that ft cancels with ft ft ft. 8 ft yd yd yd 8 8 ft yd yd ft ft ft ()()() km

6 Or, as in the example f) above, we can create our own conversion formula yd ft ft ft 7 ft and use it directly: 8 ft 8 ft yd 8 8 ft yd yd 7 ft 7 6 i) 8 ml =? cc This is a straight forward conversion, since cc = ml: 8mL cc 8mL 8cc ml j) L =? cc This time we have to use two conversions in a row: L = 000 ml and ml = cc: L 000mL cc ()(000) L cc 000cc L ml k) m =? cc For cubic units, we use conversion formulas three times: m 00cm 00cm 00cm cc (00)(00)(00) m cc cc m m m cm Alternatively, we can derive our own conversion formula for cubic units. Using m = 00cm, we get. m 00cm 00cm 00cm cm l) 74 F =? C C = 9 5 (F ) C = 9 5 (74 ) C. C m) 9 C =? F F = 5 9 C + F = [ 5 9 (9) + ] F = 84. F Compound Measures We now look at what is sometimes called compound measures: miles per hour = mi/hr, ft/sec, lb/ft, g/cm etc. Examples a) If a car is traveling 90 mi/hr, how many feet will the car travel in sec? In 5 sec? A direct way to convert these units is: 90mi 580 ft hr min (90)(580) 90 mi / hr ft / sec ft / sec hr mi 60 min 60sec (60)(60)

7 Alternatively, we can derive our own conversion formulas separately for miles and for hours: mi = 580ft and hr = 60min = 60 60sec = 600sec. We then replace miles with 580feet and hours with 600sec. Therefore 90 mi ft ft / sec hr 600sec 7 In second the car will travel ft. The car will travel (5 sec )( ft/sec) = 660 ft. in 5 seconds. b) A 90 lb weight is applied to an area /4 in by /4 inch. This pressure is equivalent to how many tons per ft? We have 90 pounds per (/4)(/4) in. We have [90 lb/(/6) in ] = 440 lb/in. 440lb ton in in (440)()() 440 lb / in ton / ft 0.68 ton / ft in 000lb ft ft 000 c) If a machine produces 5 parts in an 8 hour day, how many minutes will it take to produce 0 parts? We will first get minutes per part. 8hours 60 min 8(60) min/ part min/ part 5 parts hour 5 5 The time needed for 0 parts would be (0)(/5) minutes = 64/ minutes = minutes. d) If a machine produces 5 parts in an 8 hour day, how many parts can it produce in 0 minutes? We will first get parts per minute. Notice that we have parts in the numerator since we want parts in the final answer. 5 parts hour 5 5 parts / min parts / min 8hours 60 min 8(60) 5 In 0 minutes, the machine would produce 0 parts = 75 6 parts =. 4 6 e) Water is pouring into a plastic box m by m by. m at the rate of 5 ml per minute. How long will it take in hours to fill this box? The volume of the box is m m. m =. m. In minute, 5 ml will drip into the box. We will convert ml to cm to m and minutes to hours. min (00)(00)(00) ml cm cm cm hr hr. hr 5mL cm m m m 60 min (5)(60) m m. hrs for each m. It will take (.)(.) hr = 40 hr to fill the box Homework:. 000 yd =? in. 000 in =? ft. 000 in =? yd ft =? in yd =? in in =? ft in =? yd ft =? in yd =? in in =? ft. 000 in =? yd. 000 ft =? in

8 .,000,000 mm =? cm. 50 mi =? yd lb/in =? tons/ft 8 4.,000,000 mg =? cg. 50 mi =? in tons / ft =? lb / in 5.,000,000 mm =? m.,000,000 tons =? oz km/hr =? m/sec 6.,000,000 μg =? g 4.,000,000 oz =? tons m/min =? km / hr 7.,000,000 mg =? g 5.,000,000 fl. oz. =? gal m/sec =? km/hr 8.,000,000 cm =? m 6.,000 fl. oz. =? quarts km / hr =? m / min 9.,000,000 ml =? L 7. 4 F =? C 55. cc/sec =? L/hr 0.,000,000 μm =? cm 8. 7 F =? C 56. L / hr =? cc / min.,000,000 mm =? km 9. C =? F 57. m =? L.,000,000 cm =? km C =? F L =? m.,000,000 mg =? kg 4. 5 C =? K m =? ft 4.,000,000 g =? mg K =? C ft =? m 5.,000,000 km =? m ft/sec =? mi/hr 6. 9 qt =? m 6.,000,000 kg =? g mi / hr =? ft / sec. 6. m =? qt 7.,000,000 km =? cm gal / min =? gal/hr 6.,000 kg=? lbs 8.,000,000 ml =? L pints / min =? gal / hr lbs =? kg 9.,000,000 kg =? mg 0.,000,000 cg =? g 47. g/cm =? kg/m kg / m =? g / mm 65.. mg / mm =? oz / in oz / in =? mg / mm 67. A car traveling at a constant speed travels 75 miles in 4 hours. How many minutes will it take for the car to travel 000 feet? 68. A car traveling at a constant speed travels 000 ft in seconds. In miles, how far will this car travel in 4 hours? 69. A car traveling at a constant speed travels 75 miles in 4 hours. How many feet will the car travel in 0 minutes? 70. A car traveling at a constant speed travels 000 ft in seconds. How long in hours will it take to travel 75 miles? 7. If a car is traveling 75 miles per hour, how many feet will it travel in 0 seconds? 7. If a car is traveling 75 kilometers per hour, how many meters will it travel in 0 seconds? 7. A leaky faucet drips at the rate of pint per hour. How many gallons will drip in a 4 hour day? 74. A leaky faucet drips at the rate of 00 ml per hour. How many liters will drip in a 4 hour day?

9 75. A leaky faucet drips at the rate of pint per hour. How long will it take to fill a 0 gallon container? 76. A leaky faucet drips at the rate of 00 ml per hour. How long will it take to fill a 0 liter container? 77. You wish to give a patient 5 liters of fluid intravenously in 4 hours. If this is done at a constant rate, how many cc must be given per minute? 78. You wish to give a patient 4 liters of fluid in 8 hours. If this is done at a constant rate, how many cc must be given per minute? 79. You are giving a patient.5 cc / min of a given solution intravenously. If this continues for 8 hours, how many liters of this solution will you need? 80. You are giving a patient cc / min of a given solution intravenously. If this is done for 4 hours, how many liters of this solution will you need? 8. A recipe calls for 00 ml water. In the English system, how much water is this? 8. A recipe calls for cups water. In the metric system, how much water is this? 8. A car is traveling 00 km / hr, How many feet does this car travel every second? 84. A car is traveling 00 miles / hour. How many meters does this car travel every second? 85. John has a bicycle whose tires are 7 inches in diameter. If John rides his bike mile, how many revolutions does each tire make? A vehicle has a wheel 5 inches in diameter. If the vehicle travels miles, how many revolutions does the wheel make? inches is how many meters? millimeters is how many inches? 89. A large block of butter measures. meters by.4 meters by 5 meters. How many tablespoons of butter are in this block? 90. You wish to form a cube formed from,000,000 tablespoons of butter. What is the length of a side in meters? feet? inches? (Recall: a cube has length = width = height.) 9. An automatic machine produces part every. minutes. How many parts are produced in 8 hours if the machine runs constantly? 9. A machine produces 4500 parts in an 8 hour day. In minutes, how long will it take to produce 00 parts? 9. An automatic machine produces part every. minutes. How long in hours will it take to produce 5000 parts? 94. If a machine produces 45 parts per hour. how many minutes will it take to produce each part? 95. A certain medication recommends that each day a person be given 8 mg for every 00 lbs of weight. John weighs 8 lbs. If his measurements are exact, how many kg of this medication will he take in 65 days? 96. A certain medication recommends that each day a person be given 8 mg for every 00 lbs of weight. If 0,000 people take this medication each day and their average weight is 80 lbs, how many kilograms of this drug are used daily?

10 Solutions: 0 000yd ft in. 000 yd (000)()() in 6000in yd ft 000in ft yd in yd 7 yd in ft ()() yd ft ft in in (000)()()()() in 96000in yd yd ft ft 000in ft ft yd yd yd.77 yd in in ft ft ()()()() 000 yd ft ft ft in in in 9. (000)()()()()()() in in yd yd yd ft ft ft. 000in ft ft ft yd yd yd 000 yd.0yd in in in ft ft ft ()()()()()() mm m 00 cm (000000)(00) cm 00000cm 000mm m mm m m 000m 000mm mg g g 000g 000mg ml L L 000L 000mL mm m km km km 000 mm 000 m (000)(000) mg g kg kg kg 000mg 000 g (000)(000) km 000 m (000000)(000) m m km km 000m 00cm 7. (000000)(000)(00) cm cm 0 cm km m kg 000 g (000000)(000) g g kg. 50 mi 580 ft yd (50)(580) yd 88000yd mi ft

11 000000tons 000lb 6oz 0. (000000)(000)(6) oz oz. 0 oz ton lb fl oz pt qt gal gal 78.5gal 6 fl oz pt 4 qt (6)()(4) 7. C = 5 9 (F ) ; C = 5 9 (4 ) C 5.6 C 9. F = 9 5 C + ; F = 9 5 () + F = 5.6 F 4. K = C + 7.5; K = K = 98.5 K ft mi 60sec 60min (00)(60)(60) mi 68.8 mi / hr gal 60min (5)(60) gal / hr 00 gal / hr sec 580 ft min hr 580hr min hr g kg 00cm 00cm 00 cm ()(00)(00)(00) 47. kg / m 000 kg / m cm 000g m m m lb ton in in (00)()() 49. tons / ft 4.4 tons / ft in 000lb ft ft km 000 m hr min (00)(000) m/ sec 7.78 m/ sec hr km 60min 60sec (60)(60) m km 60sec 60min (00)(60)(60) km / hr 60 km / hr sec 000m min hr cc ml L 60sec 60min ()(60)(60) L / hr 7. L / hr sec cc 000ml min hr 000 m 00 cm 00 cm 00 cm ml L ()(00)(00)(00) m m m cm 000 ml 000 L 000 L 4m 9.7 in 9.7 in ft ft 4(9.7)(9.7) ft 4.05 ft m m in in ()() 9qt L 000 ml cm m m m 9(000) m.0567 qt L ml 00cm 00cm 00 cm (.0567)(00)(00)(00) ,000 kg. lbs,00lbs kg 65.. mg g kg lbs oz mm mm mm m m m.85 oz mm 000 mg 000 g kg lb m m m 9.7 in 9.7 in 9.7 in in 4hours mile 60min (4)(60) 67. min/ ft min/ ft ; 75miles 580 ft hour (75)(580) The car will take approximately.6 minutes to travel 000 feet miles 580 ft hour (75)(580) ft / min 850 ft / min ; 4hours mile 60 min (4)(60)

12 In 0 minutes the car would travel (0)(850) ft = 8500 ft mi 580 ft hr min (75)(580) ft 0 ft hr mi 60 min 60 sec (60)(60) sec sec In 0 seconds the car will travel (0)(0) ft. = 00 ft. 7. pt 4 4 qt gal hours gal / day gal hour pt 4qt day ()(4) day 75. hour pt 4 qt 8 hours / gal ; It would take (0)(8) hours = 80 hours to fill a 0 gallon container. pt qt gal 77. 5L hour 000mL cc (5)(000) cc / min.47 cc / min 4hours 60min L ml (4)(60) cc 60min ml L (.5)(60) L / hour.5 L / hour.you need (8)(.5) L =. L in 8 hours. min hour cc 000mL ml pt cups 8. pt pt, also pt 4 cups and 00 ml Tbs 0Tbs 480 ml pt 0mL 00 km.64 miles 580 ft hr min (00)(.64)(580) ft hr km mile 60min 60sec (60)(60)sec 8. ft 9.4 sec 85. C = π d = π r ; C = π 7 in. ; revolution = rev = circumference = 7 π in. ; mile 580 (580)() 747 ft in rev rev rev mile ft 7in in m 000 m 5.4in 9.7in Volume =. m x.4 m x 5 m = 9. m ; 9.m 00cm 00cm 00cm ml tbsp (9.)(00)(00)(00) tbsp,600,000 tbsp m m m cm 5mL 5 9. part 60 min 60 parts 6. parts (8)(6.) parts ; 08.8 parts in 8 hours.min hr. hr hour 8hours 9..min. (.08)(5000) hr hr.08 hr hrs ; part 60min 60 part part 5000 parts It will take approximately 9 hours to produce 5000 parts mg 8lbs 9.04 mg 00lbs each day; 9.04mg each day x 65 days = mg mg g kg kg kg 000mg 000 g (000)(000) In one year, John would take approximately.007 kg.

### 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

### 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,

### 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

### 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

### 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

### 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.

### 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.

### 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.

### 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

### 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

### 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

### 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

### 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:

### 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

### 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:

### 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

### 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

### Sample Questions Chapter 2. Stoker

Sample Questions Chapter 2. Stoker 1. The mathematical meaning associated with the metric system prefixes centi, milli, and micro is, respectively, A) 2, 4, and 6. B) 2, 3, and 6. C) 3, 6, and 9. D) 3,

### 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,

### 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

### 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,

### 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,

### 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

### 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

### 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,

### EXERCISE # 1.Metric Measurement & Scientific Notation

EXERCISE # 1.Metric Measurement & Scientific Notation Student Learning Outcomes At the completion of this exercise, students will be able to learn: 1. How to use scientific notation 2. Discuss the importance

### How to Solve Drug Dosage Problems

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

### 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

### CHAPTER 2: MEASUREMENT AND PROBLEM SOLVING

CHAPTER 2: MEASUREMENT AND PROBLEM SOLVING Problems: 1-64, 69-88, 91-120, 123-124 2.1 Measuring Global Temperatures measurement: a number with attached units When scientists collect data, it is important

### Measurements 1. BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com. In this section we will look at. Helping you practice. Online Quizzes and Videos

BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Measurements 1 In this section we will look at - Examples of everyday measurement - Some units we use to take measurements - Symbols for units and converting

### Unit conversion problems, by Tony R. Kuphaldt (2006)

Unit conversion problems, by Tony R. Kuphaldt (2006) This worksheet and all related files are licensed under the Creative Commons Attribution License, version.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/.0/,

### 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

### 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

### 10 g 5 g? 10 g 5 g. 10 g 5 g. scale

The International System of Units, or the SI Units Vs. Honors Chem 1 LENGTH In the SI, the base unit of length is the Meter. Prefixes identify additional units of length, based on the meter. Smaller than

### 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

### Appendix 1: Units of Measure Used in the Lead-Based Paint Field

Appendix 1: Units of Measure Used in the Lead-Based 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

### EXAMPLE 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

### 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

### 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

### 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

### 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,

### 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

### 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

### Nursing 131 Household to Metric Conversion

Nursing 3 Household to Metric Conversion Slide 2 & 3 In the metric system liquid volumes are measured in milliliters or liters. Weight is measured in micrograms, milligrams, grams, or kilograms. liter

### .001.01.1 1 10 100 1000. milli centi deci deci hecto kilo. Explain that the same procedure is used for all metric units (meters, grams, and liters).

Week & ay Week 15 ay 1 oncept/skill ompare metric measurements. Standard 7 MG: 1.1ompare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles

### 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

### GRADE 6 MATHEMATICS CORE 1 VIRGINIA STANDARDS OF LEARNING. Spring 2006 Released Test. Property of the Virginia Department of Education

VIRGINIA STANDARDS OF LEARNING Spring 2006 Released Test GRADE 6 MATHEMATICS CORE 1 Property of the Virginia Department of Education 2006 by the Commonwealth of Virginia, Department of Education, P.O.

### Metric Conversion: Stair-Step Method

ntroduction to Conceptual Physics Metric Conversion: Stair-Step Method Kilo- 1000 Hecto- 100 Deka- 10 Base Unit grams liters meters The Metric System of measurement is based on multiples of 10. Prefixes

### Units of Measurement and Conversions

Units of Measurement and Conversions OBJECTIVES/RATIONALE Basic math principles are important in providing quality client care when pharmaceuticals are involved and knowledge of various measurement systems

### Systems of Measurement

Systems of Measurement Course Principles of Health Science Unit X Vital Signs Essential Question What s math got to do with it? TEKS 130.202 (c)1a, 1B, 1D Prior Student Learning Basic understanding of

### 2006 Core Knowledge National Conference, Measurement, 4 th Grade 1

Measurement Grade Level or Special Area: Grade 4 Mathematics Written by: Caroline Ruppert Tuiolosega, Aurora Academy Charter School, Aurora, Colorado Length of Unit: Seven lessons; eight one-hour days

### 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,

### History of U.S. Measurement

SECTION 11.1 LINEAR MEASUREMENT History of U.S. Measurement The English system of measurement grew out of the creative way that people measured for themselves. Familiar objects and parts of the body were

### FCAT 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

### 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

### Section 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

### Sorting Cards: Common Measures

Sorting Cards: Common Measures The mass, capacity, length and time cards (pages 2-3) were originally used as a starter activity in a pre-gcse maths class (Level 1 and Level 2 numeracy), after we had done

### Converting English and Metric Recipes

Appendix E Converting English and Metric Recipes In this chapter, you will learn the following to World Class standards: Knowing the English to Metric Conversion Making the Mathematical Conversion Between

### Chapter 1 An Introduction to Chemistry

1 Chapter 1 An Introduction to Chemistry 1.1 What Is Chemistry, and What Can Chemistry Do for You? Special Topic 1.1: Green Chemistry 1.2 Suggestions for Studying Chemistry 1.3 The Scientific Method 1.4

### 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

### 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

### CONNECT: Currency, Conversions, Rates

CONNECT: Currency, Conversions, Rates CHANGING FROM ONE TO THE OTHER Money! Finances! \$ We want to be able to calculate how much we are going to get for our Australian dollars (AUD) when we go overseas,

### 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.

### 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

### 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

### 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,

### 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.

### DATA EXPRESSION AND ANALYSIS

NAME Lab Day DATA EXPRESSION AND ANALYSIS LABORATORY 1 OBJECTIVES Understand the basis of science and the scientific method. Understand exponents and the metric system. Understand the metric units of length,

### 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

### 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

### 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

### Don t Make Me Think: Essential Pharmacy Math for Pharmacy Technicians Made Easy

J & D Educational Services, Inc. In association and co-sponsorship with Texas Tech University HSC School of Pharmacy Provides continuing education for certified pharmacy technicians. Texas Tech University

### www.parklandsd.org/web/physics/

Course: AP Physics 1 2016 2017 Physics Teachers: Mrs. Dogmanits & Mr. Wetherhold Summer Assignment DO NOT TAKE A TEXTBOOK FROM THE LIBRARY! USE THE ONLINE TEXT. 1. The AP Physics 1 textbook is available

### 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

### Student 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

### 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

### Metric 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

### Name: Seventh Grade Science Teacher: Page 1

Name: Seventh Grade Science Teacher: Page 1 Why should you do this Packet? Dear future 8 th grade student, You are most likely asking yourself, what the heck is this and why do I have to do it? Let me

### Cattle 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

### Measurement. 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:

### Story Problems With Remainders

Mastery Drill 8 8 Story Problems With Remainders What we do with the remainder after working a division story problem depends on the story. Three hungry boys divided ten pieces of pizza equally among themselves.

### Measurement. Length. Inch pulgada (pulg) A customary unit for measuring length. The plural is inches. English Español

CHAPTER 13 Measurement connected.mcgraw-hill.com Investigate Animations The BIG Idea How are units of measure related? Vocabulary Math Songs Multilingual eglossary Learn Personal Tutor Virtual Manipulatives

### Grade 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

### The following book is required for purchase prior to the beginning of the semester:

Dear Student: As a faculty member of the Johns Hopkins University School of Nursing, we are pleased to welcome you to the School. In preparation for a key nursing course, Principles and Applications in

### 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

### \$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

### 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

### 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

### Math Concepts for Science

1 Math Concepts for Science Math for Science webpages originally created by Stephanie S. Baiyasi, D.V.M., Instructor, Science Division, Delta College Karen Constan, B.A., Staff Tutor, Teaching/Learning

### 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

### Chapter 1 Chemistry: The Study of Change

Chapter 1 Chemistry: The Study of Change This introductory chapter tells the student why he/she should have interest in studying chemistry. Upon completion of this chapter, the student should be able to:

### 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

### 100 cm 1 m. = 614 cm. 6.14 m. 2.54 cm. 1 m 1 in. 1 m. 2.54 cm 1ft. 1 in = 242 in. 614 cm. 242 in 1 ft. 1 in. 100 cm = 123 m

Units and Unit Conversions 6. Define the problem: If the nucleus were scaled to a diameter of 4 cm, determine the diameter of the atom. Develop a plan: Find the accepted relationship between the size of

### Grade 4 Mathematics Measurement: Lesson 3

Grade 4 Mathematics Measurement: Lesson 3 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

### Perimeter, Area, and Volume

Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all

### Calculating Area, Perimeter and Volume

Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly

### Chapter 8 Unit Conversions

99 Chapter 8 Unit Conversions Review Skills 8.1 Unit Analysis An Overview of the General Procedure Metric-Metric Unit Conversions English-Metric Unit Conversions 8.2 Rounding Off and Significant Figures

### SCIENTIFIC MEASUREMENTS 2004, 1990 by David A. Katz. All rights reserved.

SCIENTIFIC MEASUREMENTS 2004, 1990 by David A. Katz. All rights reserved. A BRIEF HISTORY OF MEASUREMENT Measurement was among one of the first intellectual achievements of early humans. People learned