When converting from one unit system to another, always be sure you’re talking about the same quantity or phenomenon. For example, you cannot convert meters squared to centimeters cubed or candela to meters per second. You must keep in mind what you’re trying to express and be sure that you are not, in effect, trying to change an apple into an orange.
The particular thing that a unit quantifies is called the dimensionof the quantity or phenomenon. Thus meters per second, feet per hour, and furlongs per fortnight represent expressions of the speed dimension; seconds, minutes, hours, and days are expressions of the time dimension. Units are always associated with dimensions. So are most constants, although there are a few constants that stand by themselves (and eare two well-known examples).
PROBLEM 6-4
You step on a scale, and it tells you that you mass 63 kilograms. How many pounds does this represent?
SOLUTION 6-4
Assume that you are on the planet Earth, so your mass-to-weight conversion can be defined in a meaningful way. (Remember, mass is not the same thing
Table 6-3 Conversions for Base Units in the International System (SI) to Units in Other Systems (When no coefficient is given, it is exactly equal to 1.)
C o n v e r s e l y ,
To convert: To: Multiply by: multiply by:
meters (m) Angstroms 1010 1010
meters (m) nanometers (nm) 109 109
meters (m) microns (µ) 106 106
meters (m) millimeters (mm) 103 103
meters (m) centimeters (cm) 102 102
meters (m) inches (in) 39.37 0.02540
meters (m) feet (ft) 3.281 0.3048
meters (m) yards (yd) 1.094 0.9144
meters (m) kilometers (km) 103 103
meters (m) statute miles (mi) 6.214 104 1.609 103 meters (m) nautical miles 5.397 104 1.853 103 meters (m) light-seconds 3.336 109 2.998 108 meters (m) astronomical units (AU) 6.685 1012 1.496 1011 meters (m) light-years 1.057 1016 9.461 1015 meters (m) parsecs (pc) 3.241 1017 3.085 1016 kilograms (kg) atomic mass units (amu) 6.022 1026 1.661 1027
kilograms (kg) nanograms (ng) 1012 1012
kilograms (kg) micrograms (g) 109 109
kilograms (kg) milligrams (mg) 106 106
kilograms (kg) grams (g) 103 103
kilograms (kg) ounces (oz) 35.28 0.02834
kilograms (kg) pounds (lb) 2.2050.4535
kilograms (kg) English tons 1.103 103 907.0
seconds (s) minutes (min) 0.01667 60.00
seconds (s) hours (h) 2.778 104 3.600 103
seconds (s) days (dy) 1.157 105 8.640 104
seconds (s) years (yr) 3.169 108 3.156 107
seconds (s) centuries 3.169 1010 3.156 109
seconds (s) millennia 3.169 1011 3.156 1010
degrees Kelvin (K) degrees Celsius (°C) Subtract 273 Add 273
degrees Kelvin (K) degrees Fahrenheit Multiply by 1.80, Multiply by 0.556,
(°F) then subtract 459 then add 255
degrees Kelvin (K) degrees Rankine (°R) 1.80 0.556 amperes (A) carriers per second 6.24 1018 1.60 1019 amperes (A) statamperes (statA) 2.998 109 3.336 1010
as weight.) Use Table 6-3. Multiply 63 by 2.205 to get 139 pounds. Because you are given your mass to only two significant figures, you must round this off to 140 pounds to be purely scientific.
PROBLEM 6-5
You are driving in Europe and you see that the posted speed limit is 90 kilo- meters per hour (km/h). How many miles per hour (mi/h) is this?
SOLUTION 6-5
In this case, you only need to worry about miles versus kilometers; the “per hour” part doesn’t change. Thus you convert kilometers to miles. First remember that 1 km 1,000 m; then 90 km 90,000 m 9.0 104m. The conversion
of meters to statute miles (these are the miles used on land) requires that you multiply by 6.214 104. Therefore, you multiply 9.0 104by 6.214 104
to get 55.926. This must be rounded off to 56, or two significant figures, because the posted speed limit quantity, 90, only goes that far.
PROBLEM 6-6
How many feet per second is the speed limit in Problem 6-5? SOLUTION 6-6
This is a two-step problem. You’re given the speed in kilometers per hour. You must convert kilometers to feet, and you also must convert hours to seconds. These two steps should be done separately. It does not matter in which order you do them, but you must do both conversions independently if you want to avoid getting confused. (Some of the Web-based calculator programs will do it all for you in a flash, but here, all we have is Table 6-3.)
Table 6-3 Conversions for Base Units in the International System (SI) to Units in Other Systems (When no coefficient is given, it is exactly equal to 1.) (Continued)
C o n v e r s e l y ,
To convert: To: Multiply by: multiply by:
amperes (A) nanoamperes (nA) 109 109
amperes (A) microamperes (A) 106 106
amperes (A) abamperes (abA) 0.10000 10.000
amperes (A) milliamperes (mA) 103 103
candela (cd) microwatts per 1.464 103 6.831 104 steradian (W/sr)
candela (cd) milliwatts per 1.464 0.6831
steradian (mW/sr)
candela (cd) lumens per steradian Identical; no Identical; no
(lum/sr) conversion conversion
candela (cd) watts per steradian 1.464 103 683.1 (W/sr)
Let’s convert kilometers per hour to kilometers per second first. This requires division by 3,600, the number of seconds in an hour. Thus 90 km/h 90/3600 km/s 0.025 km/s. Now convert kilometers to meters; multiply by 1,000 to obtain 25 m/s as the posted speed limit. Finally, convert meters to feet; multiply 25 by 3.281 to get 82.025. This must be rounded off to 82 ft/s, again because the posted speed limit is expressed to only two significant figures.
Quiz
Refer to the text in this chapter if necessary. A good score is eight correct. Answers are in the back of the book.
1. The mole is a unit that expresses the (a) number of electrons in an ampere. (b) number of particles in a sample. (c) distance from the Sun to a planet.
(d) time required for an electron to orbit an atomic nucleus. 2. A joule is the equivalent of a
(a) foot-pound. (b) meter per second. (c) kilogram per meter. (d) watt-second.
3. A direct current of 3 A flows through a coil whose inductance is 1 H. The magnetic flux caused by this current is
(a) 3 Wb. (b) 3 H. (c) 3 T.
(d) impossible to determine from this information.
4. A light source generates the equivalent of 4.392 mW/sr of energy at the peak visible wavelength. This is approximately equal to
(a) 6.4 106cd. (b) 3.0 cd. (c) 6.4 cd. (d) 3.0 106cd.
5. A temperature of 0 K represents
(a) the freezing point of pure water at sea level. (b) the boiling point of pure water at sea level. (c) the absence of all heat.
6. A newton is equivalent to a (a) kilogram-meter.
(b) kilogram-meter per second. (c) kilogram-meter per second squared. (d) kilogram-meter per second cubed.
7. Kilograms can be converted to pounds only if you also know the (a) temperature.
(b) mass of the object in question. (c) gravitational-field intensity. (d) material quantity.
8. The SI system is an expanded form of the (a) English system.
(b) metric system. (c) European system. (d) American system. 9. The radian is a unit of
(a) visible-light intensity. (b) temperature.
(c) solid angular measure. (d) plane angular measure. 10. The pound is a unit of
(a) mass. (b) substance. (c) material quantity. (d) none of the above.