DOE-HDBK-1122-99 Module 1.02, Fundamental Academic Training Instructor's Guide Phase I; Module 1.02, Unit Analysis and Conversion

DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-1 Course Title: Radiological Control Technician Module Title: Unit Analysis & Conversion Module Number: 1.02 Objectives: 1.02.01 Identify the commonly used unit systems of measurement and the base units for mass, length, and time in each system. 1.02.02 Identify the values and abbreviations for SI prefixes. 1.02.03 Given a measurement and the appropriate conversion factor(s) or conversion factor table, convert the measurement to the specified units. 1.02.04 Using the formula provided, convert a given temperature measurement to specified units. INTRODUCTION A working knowledge of the unit analysis and conversion process is necessary 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 International System of Units (SI), the prefixes used with SI units, and the unit analysis and conversion process. Many calculations accomplished in radiological control are actually unit conversions, not complex calculations involving formulas that must be memorized. REFERENCES: 1. "Health Physics and Radiological Health Handbook"; Scinta, Inc; 1989. 2. DOE-HDBK-1010-92 (June 1992) "Classical Physics" DOE Fundamental Handbook; US Department of Energy. 3. "Nuclides and Isotopes"; Fourteenth Edition, General Electric Company; 1989. 4. "Chemistry: An Investigative Approach"; Houghton Mifflin Co., Boston; 1976. 5. "Introduction to Chemistry: sixth ed.; Dickson, T. R.; John Wiley & Sons, Inc.; 1991. 6. "Physics"; 2nd ed.; Giancoli, Douglas C.; Prentice Hall, Inc.; 1985. 7. "Modern Physics"; Holt, Rinehart and Winston, Publishers; 1976. 8. NIST Special Publication 330; "The International System of Units"' National Institute of Standards and Technology; 1991. DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-2 L e n g t h T i m eM a s s Figure 1. Fundamental Units 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. 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 (L) • Mass (M) (not the same as weight) • Time (T) Derived Quantities Other quantities are derived from the fundamental quantities. These 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 L2. • Volume is area times length, which is length times length times length, or L3. • Velocity is expressed in length per unit time, or L/T. • Density is expressed in mass per unit volume, or M/L3. DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-3 1.02.01 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. The base units for length, mass, and time in the English system are the foot, pound, and second, respectively. 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 Quantity Unit Abbr. Length: foot ft. Mass: pound lb. Time: second sec. DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-4 1.02.02 Identify the values and abbreviations for SI prefixes. 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. SI Prefixes The SI 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 equals 1000 cm3. 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, 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 unit 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.

DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-5 Table 2. SI Prefixes PREFIX FACTOR SYMBOL PREFIX FACTOR SYMBOL yotta 1024 Y deci 10-1 d zetta 1021 Z centi 10-2 c exa 1018 E milli 10-3 m peta 1015 P micro 10-6 µ tera 1012 T nano 10-9 n giga 109 G pico 10-12 p mega 106 M femto 10-15 f kilo 103 k atto 10-18 a hecto 102 h zepto 10-21 z deka 101 da yocto 10-24 y Prior to the adoption of the SI system, two groups of units were commonly used for the quantities length, mass, and time: MKS (for meter-kilogram-second) and CGS (for centimeter-gram-second). Table 3. Metric Subsystems Physical Quantity CGS MKS Length: centimeter meter Mass: gram kilogram Time: second second SI Units There are seven fundamental physical quantities in the SI system . These are length, mass, time, temperature, electric charge, luminous intensity, and molecular quantity (or amount of substance). In the SI system there is one SI unit for each physical quantity. The SI system base units are those in the metric MKS system. Table 4 lists the 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 are derived. For most applications the RCT will only be concerned with the first four quantities as well as the quantities derived from them. DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-6 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 equivalence is the sievert, which has the units of joule per kilogram. These quantities and their applications will be discussed in detail in Lesson 1.06. 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. DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-7 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 meter m3 m3 Force: newton N kg�m/s2 Work/Energy: joule J N�m Power: watt W J/s Pressure: pascal Pa N/m2 Electric charge: coulomb C A�s Electric potential: volt V J/C Electric resistance: ohm Ω 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 DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-8 1.02.03 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 measurement units are subject to the same algebraic rules as the values. Some examples are provided below. (cm) × (cm) � cm 2 ft 3 ft � ft 2 1 yr � yr �1 As a result, measurements can 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, when the measurements are in different units, and cannot be multiplied directly. 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. Then we can then calculate the area as 12 inches × 18 inches, which equals 216 in2, which is a valid measurement. Steps for Unit Analysis and Conversion 1) Determine given unit(s) and desired unit(s). 2) Build (or obtain) conversion factor(s) -- see Conversion Tables at end of lesson 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 a conversion factor equals 1, it does not matter which value is placed in the numerator or denominator of the fraction. DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-9 1E�2m 1cm � 1m 100cm Examples of conversion factors are: 365 days 1 year 12 inches 1 foot 1 foot 3 2.832E4 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: m (milli-) = 10-3 or 1E-3 1E�3 g 1 mg Also remember that algebraic manipulation can be used when working with metric prefixes and bases. For example, 1 centimeter = 10-2 meters. This means that 1 meter = 1/10-2 centimeters, or 100 cm. Therefore, the two conversion factors below are equal: 3) Set up an equation by multiplying the given units by the conversion factor(s) to obtain desired unit(s). DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-10 3 years� 365.25 days� 1 year� 24 hours� 1 day� 60 minutes� 1 hour� 60 seconds 1 minute� � 94,672,800 sec. When a measurement is multiplied by a conversion factor, the unit(s) (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 unit(s). By properly arranging the numerator and denominator of the conversion factor(s), 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: EXAMPLE 1. Convert 3 years to seconds. Step 1 - Determine given and desired unit(s):

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 = 365.25 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds Step 3 - Analyze and cancel given and intermediate units. Perform multiplication and division of numbers: DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-11 2000 dpm� gal� 4.5E�7 µCi 1 dpm� 0.26418 gal� 1 �� 1 �� 1,000 ml � 2.38E�7 µCi ml EXAMPLE 2. What is the activity of a solution in if it has 2000 ? µCi ml dpm gallon Step 1 - Determine given and desired unit(s): Given units: dpm gallon Desired units: µCi ml Step 2 - Build conversion factor(s): 1 liter = 0.26418 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. Practical exercises and their solutions are provided at the end of this lesson. DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-12 1.02.04 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 the Fahrenheit scale was adopted, 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 re-named it the Celsius scale 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 273.15°C below zero, or -273.15°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 Kelvin (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 = 273.15 K by definition.

DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-13 Kelvin Celsius Fahrenheit Water boils 373 K 100� C 212� F Human body temp. Room temp. Water freezes K �C �F 37.0� C 20.0� C 0� C -17.8� C -40� C 310 K 293 K 273 K 255 K 233 K 98.6� F 68.0� F 32.0� F 0� F -40� F Absolute zero -273� C0 K -460� F -150� C123 K -238� FLiquid nitrogen Figure 2. Comparison of Kelvin, Celsius and Fahrenheit scales. To convert from one unit system to another, the following formulas are used: Table 5. Equations for Temperature Conversions °F to °C or�C � (�F�32) 1.8 �C � (�F�32) 5 9 °C to °F or�F � 1.8(�C) � 32 �F � 9 5 (�C) � 32 °C to K K � �C � 273.15 DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-14 �C � (65�F� 32) 1.8 �C � 33 1.8 �C � 18.3�C EXAMPLE 3. Convert 65° Fahrenheit to Celsius. DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-15 PRACTICAL EXERCISES: Convert the following measurements: 1. 67 mm = __________ feet. 2. 1843 ounces = __________ kg. 3. 3500 microsieverts (µSv) = __________ millirem (mrem). 4. 0.007 years = __________ minutes. 5. 5000 disintegrations per minute (dpm) = __________ millicuries (mCi). DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-16 6. 2350 micrometer (µm) = __________ inches. 7. 2.5E-4 ergs = __________ keV. 8. 205 �F = __________ K. 9. 2E-3 rad = __________ milligray (mGy). 10. �25 �C = __________ �F. DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-17 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 and analyzed the sample reads 7685 disintegrations per minute (dpm). What is the concentration of the sample in microcuries/cm3? DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-18 PRACTICAL EXERCISE SOLUTIONS: 1. 67 mm = __________ feet. 67 mm 1 1 m 1E3 mm 3.2808 ft 1 m � 0.22 ft 2. 1843 ounces = __________ kg. 1843 oz 1 28.35 g 1 oz 1 kg 1E3 g � 52.25 kg 3. 3500 microsieverts (µSv) = __________ millirem (mrem). 3.5E3 µSv 1 1 Sv 1E6 µSv 1E2 rem 1 Sv 1E3 mrem 1 rem � 3.5E2 mrem � 350 mrem 4. 0.007 years = __________ minutes. 0.007 year 1 365.25 days 1 year 24 hours 1 day 60 minutes 1 hour � 3681.72 minutes 5. 5000 dis./min. = __________ millicuries (mCi). 5E3 dis min 1 Ci 2.22E12 dis min 1E3 mCi 1 ci � 2.25E�6 mCi DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-19 6. 2350 micrometer (µm) = __________ inch. 2350 µ 1 3.937E�5 inches 1 µ � 0.0925 inches � 9.25E�2 inch 7. 2.5E-4 ergs = __________ keV. 2.5E�4 ergs 1 6.2148E11 ev 1 erg 1 keV 1E3 eV � 1.55E5 keV 8. 205 �F = __________ K. �C � (205 �F � 32) 1.8 � 96.1 �C K � 96.1 �C � 273.16 � 369.27 K 9. 2E-3 rad = __________ milligray (mGy). 2E�3 rad 1 0.01 Gy 1 rad 1E3 mGys 1 Gy � 2E�2 mGy � 0.02 mGy 10. �25 �C = __________ �F. �F � (�25 �C)1.8 � 32 � �13 �F DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-20 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 � 1153.85 dollars pay period 13. An air sampler has run for 18 hours, 15 minutes at 60 liters per minute. When collected and analyzed the sample reads 7685 dis./min. What is the concentration of the sample in microcuries/cm3? 15 minutes 1 1 hour 60 minutes � 0.25 hour 18 hours � 0.25 hours � 18.25 hours 18.25 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 0.99997 ml 1 cc � 5.26E�11 µCi cc DOE-HDBK-1122-99 Module 1.02 Unit Analysis & Conversion Study Guide 1.02-21 INSTRUCTIONS FOR USING CONVERSION FACTOR TABLES The tables that follow include conversion factors that are useful to the RCT. They are useful in making a single conversion from one unit to another by using the guide arrows at the top of the page in accordance with the direction of the conversion. However, when using the tables to develop equivalent fractions for use in unit analysis equations, a better understanding of how to read the conversion factors given in the table is required. The conversions in the table have been arranged by section in the order of fundamental units, followed by derived units: Length Mass Time Area Volume Density Radiological Energy Fission Miscellaneous (Temperature, etc.) The easiest way to read a conversion from the table is done as follows. Reading left to right, "one (1) of the units in the left column is equal to the number in the center column of the unit in the right column." For example, look at the first conversion listed under Length. This conversion would be read from left to right as "1 angstrom is equal to E-8 centimeters," or 1� � 10�8 centimeters � 1 � 10�8 centimeters Another conversion would be read from left to right as "1 millimeter (mm) is equal to 1E-1 centimeters," or 1 mm = 0.1 cm. This method can be applied to any of the conversions listed in these tables when reading left to right. If reading right to left, the conversion should be read as "one (1) of the unit in the right column is equal to the inverse of (1 over) the number in the center column of the unit in the left column." For example, using the conversion shown previously, the conversion reading right to left would be "1 inch is equal to the inverse of 3.937E-5 (1/3.937E-5) micrometers," or 1 inch � 1 3.937E�5 µm � 2.54E4 µm Project Number TRNG-0003 Conversion Factors Study Guide Multiply # of �������������������� by �������������������� to obtain # of to obtain # of �������������������� by �������������������� Divide # of 1.02-22 Length angstroms (Å) 10-8 cm Å 10-10 m micrometer (µm) 10-3 mm µm 10-4 cm µm 10-6 m µm 3.937 × 10-5 in. mm 10-1 cm cm 0.3937 in. cm 3.2808 × 10-2 ft cm 10-2 m m 39.370 in. m 3.2808 ft m 1.0936 yd m 10-3 km m 6.2137 × 10-4 miles km 0.62137 miles mils 10-3 in. mils 2.540 × 10-3 cm in. 103 mils in. 2.5400 cm ft 30.480 cm rods 5.500 yd miles 5280 ft miles 1760 yd miles 1.6094 km Project Number TRNG-0003 Conversion Factors Study Guide Multiply # of �������������������� by �������������������� to obtain # of

to obtain # of �������������������� by �������������������� Divide # of 1.02-23 Mass mg 10-3 g mg 3.527 × 10-5 oz avdp mg 1.543 × 10-2 grains g 3.527 × 10-2 oz avdp g 10-3 kg g 980.7 dynes g 2.205 × 10-3 lb kg 2.205 lb kg 0.0685 slugs kg 9.807 × 105 dynes lb 4.448 × 105 dynes lb 453.592 g lb 0.4536 kg lb 16 oz avdp lb 0.0311 slugs dynes 1.020 × 10-3 g dynes 2.248 × 10-6 lb u (unified--12C scale) 1.66043 × 10-27 kg amu (physical--160 scale) 1.65980 × 10-27 kg oz 28.35 g oz 6.25 × 10-2 lb NOTE: Mass to energy conversions under miscellaneous. Project Number TRNG-0003 Conversion Factors Study Guide Multiply # of �������������������� by �������������������� to obtain # of to obtain # of �������������������� by �������������������� Divide # of 1.02-24 Time days 86,400 sec days 1440 min days 24 hours years 3.15576 × 107 sec years 525,960 min years 8766 hr years 365.25 days Area barns 10-24 cm2 circular mils 7.854 × 10-7 in.2 cm2 1024 barns cm2 0.1550 in.2 cm2 1.076 × 10-3 ft2 cm2 10-4 m2 ft2 929.0 cm2 ft2 144 in2 ft2 9.290 × 10-2 m2 in.2 6.452 cm2 in.2 6.944 × 10-3 ft2 in.2 6.452 × 10-4 m2 m2 1550 in.2 m2 10.76 ft2 m2 1.196 yd2 m2 3.861 × 10-7 sq mi Project Number TRNG-0003 Conversion Factors Study Guide Multiply # of �������������������� by �������������������� to obtain # of to obtain # of �������������������� by �������������������� Divide # of 1.02-25 Volume cm3 (cc) 0.99997 ml cm3 6.1023 × 10-2 in.3 cm3 10-6 m3 cm3 9.9997 × 10-4 liters cm3 3.5314 × 10-5 ft3 m3 35.314 ft3 m3 2.642 × 102 gal m3 9.9997 × 102 liters in.3 16.387 cm3 in.3 5.787 × 10-4 ft3 in.3 1.639 × 10-2 liters in.3 4.329 × 10-3 gal ft3 2.832 × 10-2 m3 ft3 7.481 gal ft3 28.32 liters ft3 1728 in.3 gal (U.S.) 231.0 in.3 gal 0.13368 ft3 liters 33.8147 fluid oz liters 1.05671 quarts liters 0.26418 gal gm moles (gas) 22.4 liters (s.t.p.) Project Number TRNG-0003 Conversion Factors Study Guide Multiply # of �������������������� by �������������������� to obtain # of to obtain # of �������������������� by �������������������� Divide # of 1.02-26 Density cm3/g 1.602 × 10-2 ft3/lb ft3/lb 62.43 cm3/g g/cm3 62.43 lb/ft3 lb/ft3 1.602 × 10-2 g/cm3 lb/in.3 27.68 g/cm3 lb/gal 0.1198 g/cm3 Radiological Units becquerel 2.703 × 10-11 curies curies 3.700 × 1010 dis/sec curies 2.220 × 1012 dis/min curies 103 millicuries curies 106 microcuries curies 1012 picocuries curies 10-3 kilocuries curies 3.700 × 1010 becquerel dis/min 4.505 × 10-10 millicuries dis/min 4.505 × 10-7 microcuries dis/sec 2.703 × 10-8 millicuries dis/sec 2.703 × 10-5 microcuries kilocuries 103 curies microcuries 3.700 × 104 dis/sec microcuries 2.220 × 106 dis/min millicuries 3.700 × 107 dis/sec millicuries 2.220 × 109 dis/min R 2.58 × 10-4 C/kg of air R 1 esu/cm3 of air (s.t.p.) R 2.082 × 109 ion prs/cm3 of air (s.t.p.) Project Number TRNG-0003 Conversion Factors Study Guide Multiply # of �������������������� by �������������������� to obtain # of to obtain # of �������������������� by �������������������� Divide # of 1.02-27 Radiological Units (continued) R 1.610 × 1012 ion prs/g of air R (33.7 eV/ion pr.) 7.02 × 104 MeV/cm3 of air (s.t.p.) R (33.7 eV/ion pr.) 5.43 × 107 MeV/g of air R (33.7 eV/ion pr.) 86.9 ergs/g of air R (33.7 eV/ion pr.) 2.08 × 10-6 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 8.071 × 104 MeV/cm3 or air (s.t.p.)

rads 6.242 × 107 MeV/g rads 10-5 watt-sec/g rads (33.7 eV/ion pr.) 2.39 × 109 ion prs/cm3 of air (s.t.p.) gray 100 rad rem 0.01 sievert sievert 100 rem µCi/3 (µCi/ml) 2.22 × 1012 dpm/m3 µCi/cm3 2.22 × 109 dpm/liter dpm/m3 0.4505 pCi/m3 Energy Btu 1.0548 × 103 joules (absolute) Btu 0.25198 kg-cal Btu 1.0548 × 1010 ergs Btu 2.930 × 10-4 kW-hr Btu/lb 0.556 g-cal/g eV 1.6021 × 10-12 ergs Project Number TRNG-0003 Conversion Factors Study Guide Multiply # of �������������������� by �������������������� to obtain # of to obtain # of �������������������� by �������������������� Divide # of 1.02-28 Energy (continued) eV 1.6021 × 10-19 joules (abs) eV 10-3 keV eV 10-6 MeV ergs 10-7 joules (abs) ergs 6.2418 × 105 MeV ergs 6.2418 × 1011 eV ergs 1.0 dyne-cm ergs 9.480 × 10-11 Btu ergs 7.375 × 10-8 ft-lb ergs 2.390 × 10-8 g-cal ergs 1.020 × 10-3 g-cm gm-calories 3.968 × 10-3 Btu gm-calories 4.186 × 107 ergs joules (abs) 107 ergs joules (abs) 0.7376 ft-lb joules (abs) 9.480 × 10-4 Btu g-cal/g 1.8 Btu/lb kg-cal 3.968 Btu kg-cal 3.087 × 103 ft-lb ft-lb 1.356 joules (abs) ft-lb 3.239 × 10-4 kg-cal kW-hr 2.247 × 1019 MeV kW-hr 3.60 × 1013 ergs MeV 1.6021 × 10-6 ergs NOTE: Energy to mass conversion under miscellaneous Project Number TRNG-0003 Conversion Factors Study Guide Multiply # of �������������������� by �������������������� to obtain # of to obtain # of �������������������� by �������������������� Divide # of 1.02-29 Fission Btu 1.28 × 10-8 grams 235U fissionedb Btu 1.53 × 10-8 grams 235U destroyedb,c Btu 3.29 × 1013 fissions fission of 1 g 235U 1 megawatt-days fissions 8.9058 × 10-18 kilowatt-hours fissionsb 3.204 × 10-4 ergs kilowatt-hours 2.7865 × 1017 235U fission neutrons kilowatts per kilogram 235U 2.43 × 1010 average thermal neutron flu× in fuelb,d megawatt-days per ton U 1.174 × 10-4 % U atoms fissionede megawatts per ton U 2.68 × 1010/Ef average thermal neutron flu× in fuelb neutrons per kilobarn 1 × 1021 neutrons/cm2 watts 3.121 × 1010 fissions/sec ______________________ b At 200 MeV/fission. c Thermal neutron spectrum (α = 0.193). d õ(fission = 500 barns). e At 200 MeV fission, in 235U-238U mi×ture of low 235U content. f E = enrichment in grams 235U/gram total. No other fissionable isotope present. Project Number TRNG-0003 Conversion Factors Study Guide Multiply # of �������������������� by �������������������� to obtain # of to obtain # of �������������������� by �������������������� Divide # of 1.02-30 Miscellaneous radians 57.296 degrees eV 1.78258 × 10-33 grams eV 1.07356 × 10-9 u erg 1.11265 × 10-21 grams proton masses 938.256 MeV neutron masses 939.550 MeV electron masses 511.006 keV u (amu on 12C scale) 931.478 MeV Temperature �C � (�F�32) 1.8 �C � (�F�32) 5 9 �F � 1.8(�C) � 32 �F � 9 5 (�C) � 32 �K � �C � 273.16 Wavelength to Energy Conversion keV = 12.40/Å eV = 1.240 × 10-6/m Module Number: 1.02