# UNIT ANALYSIS & CONVERSION RCT STUDY GUIDE Identify the values and abbreviations for SI prefixes.

Save this PDF as:

Size: px
Start display at page:

Download "UNIT ANALYSIS & CONVERSION RCT STUDY GUIDE Identify the values and abbreviations for SI prefixes."

## Transcription

1 LEARNING OBJECTIVES: Identify the commonly used unit systems of measurement and the base units for mass, length, and time in each system Identify the values and abbreviations for SI prefixes Given a measurement and the appropriate conversion factor(s) or conversion factor table, convert the measurement to the specified units Using the formula provided, convert a given temperature measurement to specified units. INTRODUCTION A knowledge of the unit analysis and conversion process is a necessity for the Radiological Control Technician. It is useful for air and water sample activity calculations, contamination calculations, and many other applications. This lesson will introduce the different unit systems, the fundamental units in each system, and the unit analysis and conversion process. Many calculations accomplished in radiological control are actually unit conversions, not complex calculations to be memorized. UNITS AND MEASUREMENTS Units are used in expressing physical quantities or measurements, i.e., length, mass, etc. All measurements are actually relative in the sense that they are comparisons with some standard unit of measurement. Two items are necessary to express these physical quantities: a number which expresses the magnitude and a unit which expresses the dimension. A number and a unit must both be present to define a measurement. Measurements are algebraic quantities and as such may be mathematically manipulated subject to algebraic rules Issued 05/95

2 Fundamental Quantities All measurements or physical quantities can be expressed in terms of three fundamental quantities. They are called fundamental quantities because they are dimensionally independent. They are: Length Length (L) Mass (M) (not the same as weight) Time (T) Mass Time Figure 1. Fundamental Units Derived Quantities Other quantities are derived from the fundamental quantities. Derived quantities are formed by multiplication and/or division of fundamental quantities. For example: Area is the product of length times length (width), which is L L or L 2 Volume is area times length, which is length times length times length, or L 3 Velocity is expressed in length per unit time, or L/T Density is expressed in mass per unit volume, or M/L Issued 05/95

3 Identify the commonly used unit systems of measurement and the base units for mass, length, and time in each system. SYSTEMS OF UNITS The units by which physical quantities are measured are established in accordance with an agreed standard. Measurements made are thereby based on the original standard which the unit represents. The various units that are established, then, form a system by which all measurements can be made. English System The system that has historically been used in the United States is the English System, sometimes called the English Engineering System (EES). Though no longer used in England, many of the units in this system have been used for centuries and were originally based on common objects or human body parts, such as the foot or yard. Though practical then, the standards for these units were variable as the standard varied from object to object or from person to person. Even though fixed standards have since been established for these antiquated units, no uniform correlation exists between units established for the same quantity. For example, in measuring relatively small lengths there are inches, feet and yards. There are twelve inches in a foot, and yet there are only three feet in a yard. This lack of uniformity makes conversion from one unit to another confusing as well as cumbersome. However, in the U.S., this system is still the primary system used in business and commerce. Table 1. English System Base Units Physical Unit Abbr. Quantity Length: foot ft. Mass: pound lb. Time: second sec Issued 05/95

4 International System of Units (SI) Since the exchange of scientific information is world-wide today, international committees have been set up to standardize the names and symbols for physical quantities. In 1960, the International System of Units (abbreviated SI from the French name Le Système Internationale d'unites) was adopted by the 11th General Conference of Weights and Measures (CGPM). The SI or modernized metric system, is based on the decimal (base 10) numbering system. First devised in France around the time of the French Revolution, the metric system has since been refined and expanded so as to establish a practical system of units of measurement suitable for adoption by all countries. The SI system consists of a set of specifically defined units and prefixes that serve as an internationally accepted system of measurement. Nearly all countries in the world use metric or SI units for business and commerce as well as for scientific applications Identify the values and abbreviations for SI prefixes. SI Prefixes The SI (or modernized) system is completely decimalized and uses prefixes for the base units of meter (m) and gram (g) as well as for derived units, such as the liter (l) which 3 equals 1000 cm. SI prefixes are used with units for various magnitudes associated with the measurement being made. Units with a prefix whose value is a positive power of ten are called multiples. Units with a prefix whose value is a negative power of ten are called submultiples. For example, as a point of reference, the meter is a little longer than a yard. Try using a yard stick to measure the size of a frame on film for a camera. Instead you would use inches, because it is a more suitable unit. With the metric system, in order to measure tiny lengths, such as film size, the prefix milli- can be attached to the meter to make a millimeter, or 1/1000 of a meter. A millimeter is much smaller and is ideal in this situation. On the other hand, we would use a prefix like kilo- for measuring distances traveled in a car. A kilometer would be more suited for these large distances than the meter Issued 05/95

5 Table 2. SI Prefixes PREFIX FACTOR SYMBOL PREFIX FACTOR SYMBOL yotta Y deci 10-1 d zetta Z centi 10-2 c 18-3 exa 10 E milli 10 m 15-6 peta 10 P micro 10 µ 12-9 tera 10 T nano 10 n 9-12 giga 10 G pico 10 p 6-15 mega 10 M femto 10 f 3-18 kilo 10 k atto 10 a 2-21 hecto 10 h zepto 10 z 1-24 deka 10 da yocto 10 y Prior to the adoption of the SI system, two groups of units were commonly used for the quantities length, mass and time: MKS and CGS. The units for these subsystems are given below. Table 3. Metric Subsystems Physical CGS MKS Quantity Length: centimeter meter Mass: gram kilogram Time: second second SI Units In the SI system there are seven fundamental physical quantities. These are length, mass, time, temperature, electric charge, luminous intensity, and molecular quantity (or amount of substance). In the SI system there is one-and only one-si unit for each physical quantity. The SI system base units are those in the metric MKS system. Table 4 lists these seven fundamental quantities and their associated SI unit. The units for these seven fundamental quantities provide the base from which the units for other physical quantities Issued 05/95

6 are derived. For most applications the RCT will only be concerned with the first four quantities as well as the quantities derived from them. Radiological Units In the SI system, there are derived units for quantities used for radiological control. These are the becquerel, the gray and the sievert. The SI unit of activity is the becquerel, which is the activity of a radionuclide decaying at the rate of one spontaneous nuclear transition per second. The gray is the unit of absorbed dose, which is the energy per unit mass imparted to matter by ionizing radiation, with the units of one joule per kilogram. The unit for dose equivalent is the sievert, which is the absorbed dose of ionizing radiation multiplied by the dimensionless factors and other multiplying factors with the units of joule per kilogram. These quantities and their applications will be discussed in detail in Lesson Other units There are several other SI derived units that are not listed in table 4. It should be noted that the SI system is evolving and that there will be changes from time to time. The standards for some fundamental units have changed in recent years and may change again as technology improves our ability to measure even more accurately Issued 05/95

7 Table 4. International System (SI) Units Physical Quantity Unit Symbol Dimensions Base units Length: meter m m Mass: kilogram kg kg Time: second s or sec. s Temperature: kelvin K K or K Electric current: ampere A or amp A or (C/s) Luminous intensity: candela cd cd Molecular quantity: mole mol mol Selected derived units Volume: cubic m m meter 3 3 Force: newton N kg m/s 2 Work/Energy: joule J N m Power: watt W J/s Pressure: pascal Pa N/m 2 Electric charge: coulomb C A s Electric potential: volt V J/C Electric resistance: ohm V/A Frequency: hertz Hz s -1 Activity: becquerel Bq disintegration/s Absorbed dose: gray Gy J/kg Dose equivalence: sievert Sv Gy Q N Issued 05/95

8 Given a measurement and the appropriate conversion factor(s) or conversion factor table, convert the measurement to the specified units. UNIT ANALYSIS AND CONVERSION PROCESS Units and the Rules of Algebra Remember that a measurement consists of a number and a unit. When working problems with measurements, it should be noted that the units follow the same rules as the values. Some examples are provided below. (cm) (cm) cm 2 ft 3 ft 1 yr ft 2 yr 1 As mentioned above, measurements are subject to algebraic laws of operation and can therefore be multiplied, divided, etc., in order to convert to a different system of units. Obviously, in order to do this, the units must be the same. For example, a square measures one foot in length and 18 inches in width. To find the area of the square in square inches we must multiply the length by the width. However, the measurements are in different units, and cannot be multiplied. We can convert feet to inches. We know that there are 12 inches in one foot. We can use this ratio to convert 1 foot to 12 inches. We can then calculate the area as 12 inches 18 2 inches, which equals 216 in, which is a valid measurement. Steps for Unit Analysis and Conversion 1) Determine given units and desired units. 2) Build (or obtain) conversion factor(s) -- see Conversion Tables at end of lesson Issued 05/95

9 A conversion factor is a ratio of two equivalent physical quantities expressed in different units. When expressed as a fraction, the value of all conversion factors is 1. Because it equals 1, it does not matter which value is placed in the numerator or denominator of the fraction. Examples of conversion factors are: 365 days 1 year 12 inches 1 foot 1 foot E4 cm 3 Building conversion factors involving the metric prefixes for the same unit can be tricky. This involves the conversion of a base unit to or from a subunit or superunit. To do this, use the following steps: a) Place the base unit in the numerator and the subunit/ superunit in the denominator (or vice versa). Example: 1 gram to milligrams g mg b) Place a 1 in front of the subunit/superunit. g 1 mg c) Place the value of the prefix on the subunit/ superunit in front of the base unit. -3 m (milli-) = 10 or 1E-3 1E 3 g 1 mg Issued 05/95

10 Also remember that algebraic manipulation can be used when working with metric prefixes and bases For example, 1 centimeter = 10 meters. This means that 1 meter = 1/10 centimeters, or 100 cm. Therefore, the two conversion factors below are equal: 1E 2 m 1 cm 1 m 100 cm EXAMPLE 1. 3) Set up an equation by multiplying the given units by the conversion factor(s) to obtain desired units. When a measurement is multiplied by a conversion factor, the units (and probably the magnitude) will change; however, the actual measurement itself does not change. For example, 1 ft and 12 inches are still the same length; only different units are used to express the measurement. By using a "ladder" or "train tracks," a series of conversions can be accomplished in order to get to the desired units. By properly arranging the numerator and denominator of the conversion factors, given and intermediate units will cancel out by multiplication or division, leaving the desired units. Some examples of the unit analysis and conversion process follow. Convert 3 years to seconds. Step 1 - Determine given and desired units Given units: years Desired units: seconds. Step 2 - Build/obtain conversion factor(s) We can use multiple conversion factors to accomplish this problem: 1 year = days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds Issued 05/95

11 Step 3 - Analyze and cancel given and intermediate units. Perform multiplication and division of numbers. 3 years days 1 year 24 hours 1 day 60 minutes 1 hour 60 seconds 1 minute 94,672, Issued 05/95

12 EXAMPLE 2. What is the activity of a solution in µci if it has 2000 dpm ml gallon? Step 1 - Determine given and desired units. Given units: Desired units: dpm gallon µci ml Step 2 - Build conversion factor(s) dpm gal 1 liter = gallons 1 dpm = 4.5 E-07 µci 1 liter = 1000 ml Step 3 - Analyze and cancel given and intermediate units. Perform multiplication and division of numbers. 4.5E 7 µci 1 dpm gal 1 1 1,000 ml 2.38E 7 µci ml Practical exercises and their solutions are provided at the end of this lesson Issued 05/95

13 Using the formula provided, convert a given temperature measurement to specified units. TEMPERATURE MEASUREMENTS AND CONVERSIONS Temperature measurements are made to determine the amount of heat flow in an environment. To measure temperature it is necessary to establish relative scales of comparison. Three temperature scales are in common use today. The general temperature measurements we use on a day-to-day basis in the United States are based on the Fahrenheit scale. In science, the Celsius scale and the Kelvin scale are used. Figure 2 shows a comparison of the three scales. The Fahrenheit scale, named for its developer, was devised in the early 1700's. This scale was originally based on the temperatures of human blood and salt-water, and later on the freezing and boiling points of water. Today, the Fahrenheit scale is a secondary scale defined with reference to the other two scientific scales. The symbol F is used to represent a degree on the Fahrenheit scale. About thirty years after Fahrenheit scale, Anders Celsius, a Swedish astronomer suggested that it would be simpler to use a temperature scale divided into one hundred degrees between the freezing and boiling points of water. For many years his scale was called the centigrade scale. In 1948 an international conference of scientists named it the Celsius in honor of its inventor. The Celsius degree, C, was defined as 1/100 of the temperature difference between the freezing point and boiling point of water. In the 19th century, an English scientist, Lord Kelvin, established a more fundamental temperature scale that used the lowest possible temperature as a reference point for the beginning of the scale. The lowest possible temperature, sometimes called absolute zero, was established as 0 K (zero Kelvin). This temperature is C below zero, or C. Accordingly, the Kelvin degree, K, was chosen to be the same as a Celsius degree so that there would be a simple relationship between the two scales. Note that the degree sign ( ) is not used when stating a temperature on the Kelvin scale. Temperature is stated simply as kelvins (K). The kelvin was adopted by the 10th Conference of Weights and Measures in 1954 and is the SI unit of thermodynamic temperature. Note that the degree Celsius ( C) is the SI unit for expressing Celsius temperature and temperature intervals. The temperature interval one degree Celsius equals one kelvin exactly. Thus, 0 C = K by definition Issued 05/95

14 Kelvin Celsius Fahrenheit Water boils 373 K 100 C 212 F Human body temp. 310 K 37.0 C 98.6 F Room temp. 293 K 20.0 C 68.0 F Water freezes 273 K 0 C 32.0 F 255 K C 0 F 233 K -40 C -40 F Liquid nitrogen 123 K -150 C -238 F Absolute zero 0 K -273 C -460 F K C F Figure 2. Comparison of Kelvin, Celsius and Fahrenheit scales Issued 05/95

15 To convert from one unit system to another, the following formulas are used: Table 5. Equations for Temperature Conversions ( F 32) F to C C or 1.8 C ( F 32) 5 9 C to F F 1.8( C) 32 or F 9 5 ( C) C to K K C EXAMPLE 3. Convert 65 Fahrenheit to Celsius. C C C (65 F 32) C REFERENCES: 1. "Health Physics and Radiological Health Handbook"; Scinta, Inc; DOE-HDBK (June 1992) "Classical Physics" DOE Fundamental Handbook; US Department of Energy 3. "Nuclides and Isotopes"; Fourteenth Edition, General Electric Company; "Chemistry: An Investigative Approach"; Houghton Mifflin Co., Boston; "Introduction to Chemistry: sixth ed.; Dickson, T. R.; John Wiley & Sons, Inc.; "Physics"; 2nd ed.; Giancoli, Douglas C.; Prentice Hall, Inc.; "Modern Physics"; Holt, Rinehart and Winston, Publishers; NIST Special Publication 330; "The International System of Units"' National Institute of Standards and Technology; Issued 05/95

16 PRACTICAL EXERCISES: Convert the following measurements: mm to feet ounces to kg microsieverts (µsv) to millirem (mrem) years to minutes disintegrations per minute (dpm) to millicuries (mci) Issued 05/95

17 micrometer (µm) to inches E-4 ergs to kev F to K 9. 2E-3 rad to milligray (mgy) C to F Issued 05/95

18 Use unit analysis and conversion to solve the following problems. 11. Light travels at 186,000 miles per second. How many feet will light travel in one minute? 12. A worker earns a monthly salary of \$2500. If the worker gets paid every two weeks and works no overtime, what will be the gross amount for a given pay period? 13. An air sampler has run for 18 hours, 15 minutes at 60 liters per minute. When collected an analyzed the sample reads 7685 disintegrations per minute (dpm). What is the concentration of the sample in micocuries/cm 3? Issued 05/95

19 PRACTICAL EXERCISE SOLUTIONS: mm to feet: 67 mm 1 1 m 1E3 mm ft 1 m 0.22 ft ounces to kg 1843 oz g 1 oz 1 kg 1E3 g kg microsieverts (µsv) to millirem (mrem) 3.5E3 µsv 1 1 Sv 1E6 µsv 1E2 rem 1 Sv 1E3 mrem 1 rem 3.5E2 mrem 350 mrem years to minutes year days 1 year 24 hours 1 day 60 minutes 1 hour minutes dis./min. to millicuries (mci) 5E3 dis min 1 Ci 2.22E12 dis min 1E3 mci 1 ci 2.25E 6 mci Issued 05/95

20 Issued 05/95

21 micrometer (µm) to inches 2350 µ E 5 inches 1 µ inches 9.25E 2 inches E-4 ergs to kev 2.5E 4 ergs E11 ev 1 erg 1 kev 1E3 ev 1.55E5 kev F to K C (205 F 32) C K 96.1 C K 9. 2E-3 rad to milligray (mgy) 2E 3 rad Gy 1 rad 1E3 mgys 1 Gy 2E 2 mgy 0.02 mgy C to F F ( 25 C) F Issued 05/95

22 Use unit analysis and conversion to solve the following: 11. Light travels at 186,000 miles per second. How many feet will light travel in one minute? 186,000 miles sec 5280 ft 1 mile 60 sec 1 minute 5.89E10 ft min 12. A worker earns a monthly salary of \$2500. If the worker gets paid every two weeks and works no overtime, what will be the gross amount for a given pay period? 2500 dollars month 12 months 1 year 1 year 52 weeks 2 weeks pay period dollars pay period 13. An air sampler has run for 18 hours, 15 minutes at 60 liters per minute. When collected an analyzed the sample reads 7685 dis./min. What is the concentration of the sample in micocuries/cm 3? 15 minutes 1 1 hour 60 minutes 0.25 hour 18 hours 0.25 hours hours hours 1 60 minutes 1 hour 60 l 1 minute 65,700 l 7685 dpm 6.57E4 l 1 Ci 2.22E12 dpm 1E6 µci 1 Ci 1l 1E3 ml ml 1 cc 5.26E 11 µci cc Issued 05/95

24 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Length -8 angstroms (Å) 10 cm -10 Å 10 m -3 micrometer (µm) 10 mm -4 µm 10 cm -6 µm 10 m -5 µm in. -1 mm 10 cm cm in. -2 cm ft -2 cm 10 m m in. m ft m yd -3 m 10 km -4 m miles km miles -3 mils 10 in. -3 mils cm 3 in. 10 mils in cm ft cm rods yd miles 5280 ft miles 1760 yd miles km Issued 05/95

25 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Mass -3 mg 10 g -5 mg oz avdp -2 mg grains -2 g oz avdp -3 g 10 kg g dynes -3 g lb kg lb kg slugs 5 kg dynes 5 lb dynes lb g lb kg lb 16 oz avdp lb slugs -3 dynes g -6 dynes lb u (unified-- C scale) kg amu (physical-- 0 scale) kg oz g -2 oz lb NOTE: Mass to energy conversions under miscellaneous Issued 05/95

26 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Time days 86,400 sec days 1440 min days 24 hours 7 years sec years 525,960 min years 8766 hr years days Area barns 10 cm -7 2 circular mils in cm 10 barns 2 2 cm in cm ft cm 10 m 2 2 ft cm 2 2 ft 144 in ft m 2 2 in cm in ft in m 2 2 m 1550 in. 2 2 m ft 2 2 m yd 2-7 m sq mi Issued 05/95

27 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Volume 3 cm (cc) ml cm in cm 10 m 3-4 cm liters cm ft 3 3 m ft 3 2 m gal 3 2 m liters 3 3 in cm in ft 3-2 in liters 3-3 in gal ft m 3 ft gal 3 ft liters 3 3 ft 1728 in. gal (U.S.) in. 3 gal ft 3 liters fluid oz liters quarts liters gal gm moles (gas) 22.4 liters (s.t.p.) Issued 05/95

28 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Density cm /g ft /lb 3 3 ft /lb cm /g 3 3 g/cm lb/ft lb/ft g/cm 3 3 lb/in g/cm lb/gal g/cm 3 Radiological Units -11 becquerel curies 10 curies dis/sec 12 curies dis/min 3 curies 10 millicuries 6 curies 10 microcuries 12 curies 10 picocuries -3 curies 10 kilocuries 10 curies becquerel -10 dis/min millicuries -7 dis/min microcuries -8 dis/sec millicuries -5 dis/sec microcuries 3 kilocuries 10 curies 4 microcuries dis/sec 6 microcuries dis/min 7 millicuries dis/sec 9 millicuries dis/min Issued 05/95

29 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Radiological Units -11 becquerel curies 10 curies dis/sec Radiological Units (continued) -4 R C/kg of air 3 R 1 esu/cm of air (s.t.p.) R ion prs/cm of air (s.t.p.) 12 R ion prs/g of air R (33.7 ev/ion pr.) MeV/cm of air (s.t.p.) 7 R (33.7 ev/ion pr.) MeV/g of air R (33.7 ev/ion pr.) 86.9 ergs/g of air -6 R (33.7 ev/ion pr.) g-cal/g of air R (33.7 ev/ion pr.) 98 ergs/g of soft tissue rads 0.01 gray rads 0.01 J/kg rads 100 ergs/g rads MeV/cm or air (s.t.p.) 7 rads MeV/g -5 rads 10 watt-sec/g rads (33.7 ev/ion pr.) ion prs/cm of air (s.t.p.) gray 100 rad rem 0.01 sievert sievert 100 rem Issued 05/95

30 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Radiological Units -11 becquerel curies 10 curies dis/sec Radiological Units (continued) µci/ (µci/ml) dpm/m 3 9 µci/cm dpm/liter 3 3 dpm/m pci/m Energy 3 Btu joules (absolute) Btu kg-cal 10 Btu ergs -4 Btu kw-hr Btu/lb g-cal/g -12 ev ergs -19 ev joules (abs) -3 ev 10 kev -6 ev 10 MeV -7 ergs 10 joules (abs) 5 ergs MeV 11 ergs ev ergs 1.0 dyne-cm -11 ergs Btu -8 ergs ft-lb -8 ergs g-cal Issued 05/95

31 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Energy 3 Btu joules (absolute) Btu kg-cal Energy (continued) -3 ergs g-cm -3 gm-calories Btu 7 gm-calories ergs 7 joules (abs) 10 ergs joules (abs) ft-lb -4 joules (abs) Btu g-cal/g 1.8 Btu/lb kg-cal Btu 3 kg-cal ft-lb ft-lb joules (abs) -4 ft-lb kg-cal 19 kw-hr MeV 13 kw-hr ergs -6 MeV ergs NOTE: Energy to mass conversion under miscellaneous Issued 05/95

32 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Fission b Btu grams U fissioned Btu grams U destroyed b,c 13 Btu fissions 235 fission of 1 g U 1 megawatt-days -18 fissions kilowatt-hours b -4 fissions ergs kilowatt-hours U fission neutrons 235 kilowatts per kilogram U average thermal neutron flu in fuel b,d -4 e megawatt-days per ton U % U atoms fissioned megawatts per ton U 10 f /E average thermal neutron flu in fuel b 21 2 neutrons per kilobarn 1 10 neutrons/cm 10 watts fissions/sec b At 200 MeV/fission. c Thermal neutron spectrum ( = 0.193). d õ(fission = 500 barns). e At 200 MeV fission, in U- f 235 U mi ture of low U content. E = enrichment in grams U/gram total. No other fissionable isotope present Issued 05/95

33 CONVERSION FACTORS RCT STUDY GUIDE Multiply # of by to obtain # of to obtain # of by Divide # of Miscellaneous radians degrees -33 ev grams -9 ev u -21 erg grams proton masses MeV neutron masses MeV electron masses kev 12 u (amu on C scale) MeV Temperature C ( F 32) 1.8 C ( F 32) 5 9 F 1.8( C) 32 F K C ( C) 32 Wavelength to Energy Conversion kev = 12.40/Å ev = /m Issued 05/95

### 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

### 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,

### A physical quantity is any quantity that can be measured with a certain mathematical precision. Example: Force

1 Unit Systems Conversions Powers of Physical Quantities Dimensions Dimensional Analysis Scientific Notation Computer Notation Calculator Notation Significant Figures Math Using Significant Figures Order

### 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:

### 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

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

### 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

### 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,

### 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

### 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

### 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

### 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

### 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.

### 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

### = 800 kg/m 3 (note that old units cancel out) 4.184 J 1000 g = 4184 J/kg o C

Units and Dimensions Basic properties such as length, mass, time and temperature that can be measured are called dimensions. Any quantity that can be measured has a value and a unit associated with it.

### 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

### 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

### 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.

### Physics Notes Class 11 CHAPTER 2 UNITS AND MEASUREMENTS

1 P a g e Physics Notes Class 11 CHAPTER 2 UNITS AND MEASUREMENTS The comparison of any physical quantity with its standard unit is called measurement. Physical Quantities All the quantities in terms of

### 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

### 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

### 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

### 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,

### 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.

### CHAPTER 8 UNITS, PREFIXES AND ENGINEERING NOTATION

CHAPTER 8 UNITS, PREFIXES AND ENGINEERING NOTATION EXERCISE 34 Page 62 1. State the SI unit of volume. The SI unit of volume is cubic metres, m 3 2. State the SI unit of capacitance. The SI unit of capacitance

### 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

### 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

### 1Physical quantities and units

1Physical quantities and units By the end of this chapter you should be able to: explain what is meant by a in physics; state the five fundamental quantities recognised and used in physics; explain the

### Units and Dimensions in Physical Chemistry

Units and Dimensions in Physical Chemistry Units and dimensions tend to cause untold amounts of grief to many chemists throughout the course of their degree. My hope is that by having a dedicated tutorial

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Unit Conversions. Ben Logan 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.

### 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

### Chapter 7. Units and Measurements

Chapter 7. Units and Measurements The SI system (Système International d Unités) of reporting measurements is required in all ASA, CSSA, and SSSA publications. Other units may be reported parenthetically

### 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

### Conversions in the Metric System

The metric system is a system of measuring. It is used for three basic units of measure: metres (m), litres (L) and grams (g). Measure of Example Litres (L) Volume 1 L of juice Basic Units Grams (g) Mass

### Physical Quantities, Symbols and Units

Table 1 below indicates the physical quantities required for numerical calculations that are included in the Access 3 Physics units and the Intermediate 1 Physics units and course together with the SI

### 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:

### Welcome to the World of Chemistry

Welcome to the World of Chemistry The Language of Chemistry CHEMICAL ELEMENTS - pure substances that cannot be decomposed by ordinary means to other substances. Aluminum Bromine Sodium The Language of

### 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/,

### Preparation for BioScience Academy Math Assessment Test

Preparation for BioScience Academy Math Assessment Test Math is an essential component of laboratory science and solid math skills are required for a successful career in this field. To be eligible for

### Introduction to Reactor Physics

Introduction to Reactor Physics Vasily Arzhanov Reactor Physics, KTH Course Objectives Having finished the course, you will be able to: Derive and Solve Equations Describing Multiplying Media in Several

### 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

### 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

### 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

### 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,

### 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

### 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

### WEEK 1. Engineering Calculations Processes Process Variables

WEEK 1 Engineering Calculations Processes Process Variables 2.1 Units and Dimensions Units and dimensions are important in science and engineering A measured quantity has a numerical value and a unit (ex:

### 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

### 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

### 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

### Chapter 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

### 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

### 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

### Systems of Units and Conversion Factors

B Systems of Units and Conversion Factors B.1 SYSTEMS OF UNITS Measurement systems have been a necessity since people first began to build and barter, and every ancient culture developed some sort of measurement

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### How to Solve Drug Dosage Problems

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

### 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:

### Chapter 1. An Introduction to Chemistry By Mark Bishop

Chapter 1 An Introduction to Chemistry By Mark Bishop Chemistry The science that deals with the structure and behavior of matter Summary of Study Strategies The will to succeed is important, but what s

### 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

### More general mathematical solution: T half T half. = 0.25 This is the fraction left after 25 years.

Physics 07 Problem 2. O. A. Pringle Tritium has a half-life of 2.5 y against beta decay. What fraction of a sample will remain undecayed after 25 y? Simple solution: time (y) # of half-lives fraction left

### A=b h= 83 in. 45ft. ft. = ft.2

The Easiest Way to Convert Units in an Algebraic Equation Physics professors teach you to convert everything into standard SI units, solve the problem, and hope the units come out right. In Chemistry and

### 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.

### Appendix 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

### 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,

### hp calculators HP 35s Temperature Conversions Metric units and Imperial units Conversion keys

Metric units and Imperial units Conversion keys Practice working problems involving temperature conversions Conversion of temperatures and conversion of temperature differences Other temperature scales

### Chapter 2 Atoms and Elements. Electrons. Radioactivity. Electrons. Electrons. Atomic Structure and Subatomic Particles

Atomic Structure and Subatomic Particles John W. Moore Conrad L. Stanitski Peter C. Jurs http://academic.cengage.com/chemistry/moore Chapter 2 Atoms and Elements Stephen C. Foster Mississippi State University

### 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)

### 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

### Virginia Mathematics Checkpoint Assessment MATHEMATICS 5.8. Strand: Measurement

Virginia Mathematics Checkpoint Assessment MATHEMATICS 5.8 Strand: Measurement Standards of Learning Blueprint Summary Reporting Category Grade 5 SOL Number of Items Number & Number Sense 5.1, 5.2(a-b),

### Chapter 1: Energy, Work, and Power. 1. System of Units and Conversions

Chapter 1: Energy, Energy is a very important concept both in physics and in our world at large. Energy takes various forms. A massive truck traveling along the highway at a high speed has much kinetic

### Chemistry 1000 Lecture 2: Nuclear reactions and radiation. Marc R. Roussel

Chemistry 1000 Lecture 2: Nuclear reactions and radiation Marc R. Roussel Nuclear reactions Ordinary chemical reactions do not involve the nuclei, so we can balance these reactions by making sure that

### Lab Activity: Measuring with Metric. Introduction: Standard Metric Units. Names

Names Date Period Introduction: The purpose of this activity is to practice using the metric system. To conduct a scientific investigation, a researcher must be able to make accurate measurements. In today

### 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

### 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

### 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

### Units and Vectors: Tools for Physics

Chapter 1 Units and Vectors: Tools for Physics 1.1 The Important Stuff 1.1.1 The SI System Physics is based on measurement. Measurements are made by comparisons to well defined standards which define the

### Chapter 3 Process Variables. Mass and Volume

Chapter 3 Process Variables Process: to a chemical engineer, the set of tasks or operations that accomplish a chemical or material transformation to produce a product Feed or inputs: raw materials and

### College of the Canyons: Introduction to Biotechnology Custom Lab Exercises

College of the Canyons: Introduction to Biotechnology Custom Lab Exercises Metric System, Dimensional Analysis and Introduction to Solution Chemistry Version 04-06-12 The metric system is a decimal system

### .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

### 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

### 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

### 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

### Physical Quantities and Units

Physical Quantities and Units 1 Revision Objectives This chapter will explain the SI system of units used for measuring physical quantities and will distinguish between vector and scalar quantities. You

### 1 Introduction The Scientific Method (1 of 20) 1 Introduction Observations and Measurements Qualitative, Quantitative, Inferences (2 of 20)

The Scientific Method (1 of 20) This is an attempt to state how scientists do science. It is necessarily artificial. Here are MY five steps: Make observations the leaves on my plant are turning yellow

### APES Math Review. For each problem show every step of your work, and indicate the cancellation of all units No Calculators!!

APES Math Review For each problem show every step of your work, and indicate the cancellation of all units No Calculators!! Scientific Notation All APES students should be able to work comfortably with

### 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

### 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

### บทท 1 บทน า 1.1 ฟ ส กส ว ทยาศาสตร และเทคโนโลย

บทท 1 บทนา 1.1 ฟ ส กส ว ทยาศาสตร และเทคโนโลย ฟ ส กส (Physics) มาจากภาษากร ก ซ งหมายความว าธรรมชาต (nature) ค อว ทยาศาสตร ท ศ กษา เก ยวก บมวลสารและพล งงานเพ อนาไปอธ บายปรากฏการณ ทางธรรมชาต ท ส งเกตเห นหร

### 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

### 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