Sections B.8 and B.9 give factors for converting values of quantities expressed in various units - predominantly units outside the SI that are unacceptable for use with it - to values expressed either in (a) SI units, (b) units that are accepted for use with the SI (especially units that better reflect the nature of the unconverted units), (c) units formed from such accepted units and SI units, or (d) decimal multiples or submultiples of the units of (a) to (c) that yield numerical values of convenient magnitudes.
An example of (d) is the following: the values of quantities expressed in ångströms, such as the wavelengths of visible laser radiations, are usually converted to values expressed in nanometers, not meters. More generally, if desired, one can eliminate powers of 10 that appear in converted values as a result of using the conversion factors (or simply factors for brevity) of Secs. B.8 and B.9 by selecting an appropriate SI prefix (see Sec. B.3).
The factors given in Secs. B.8 and B.9 are written as a number equal to or greater than 1 and less than 10, with 6 or fewer decimal places. The number is followed by the letter E, which stands for exponent, a plus (+) or minus (-) sign, and two digits which indicate the power of 10 by which the number is multiplied.
3.523 907 E-02 means 3.523 907 × 10-2 = 0.035 239 07
3.386 389 E+03 means 3.386 389 × 103 = 3386.389
A factor in boldface is exact. All other factors have been rounded to the significant digits given in accordance with accepted practice (see Sec. 7.9, B.7.2, and Refs. [4: ISO 31-0] and ). Where less than six digits after the decimal place are given, the unit does not warrant a greater number of digits in its conversion. However, for the convenience of the user, this practice is not followed for all such units, including the cord, cup, quad, and teaspoon.
|To convert from||to||Multiply by|
|atmosphere, standard (atm)||pascal (Pa)||1.013 25 E+05|
|cubic foot per second (ft3/s)||cubic meter per second (m3/s)||2.831 685 E-02|
|means||1 atm = 101 325 Pa (exactly)|
|1 ft3/s = 0.028 316 85 m3/s|
Thus to express, for example, the pressure p = 11.8 standard atmospheres (atm) in pascals (Pa), write
p = 11.8 atm × 101 325 Pa/atm
and obtain the converted numerical value 11.8 × 101 325 = 1 195 635 and the converted value p = 1.20 MPa.
1. Guidance on rounding converted numerical values of quantities is given in Sec. B.7.2.
2. If the value of a quantity is expressed in a unit of the center column of Secs. B.8 or B.9 and it is necessary to express it in the corresponding unit of the first column, divide by the factor.
|Examples:||To find the factor for converting values in lb · ft/s to values in kg · m/s, obtain from Sec. B.8 or B.9|
|1 lb = 4.535 924 E-01 kg|
1 ft = 3.048 E-01 m
and substitute these values into the unit lb · ft/s to obtain
|1 lb · ft/s||= 0.453 592 4 kg × 0.3048 m/s|
|= 0.138 255 0 kg · m/s|
and the factor is 1.382 550 E-01.
1 oz = 2.834 952 E-02 kg
1 in2 = 6.4516 E-04 m2
and substitute these values into the unit oz · in2 to obtain
|1 oz · in2||= 0.028 349 52 kg × 0.000 645 16 m2|
|= 0.000 018 289 98 kg · m2|
and the factor is 1.828 998 E-05.
In Sec. B.8 the units for which factors are given are listed alphabetically, while in Sec. B.9 the same units are listed alphabetically within the following alphabetized list of kinds of quantities and fields of science:
AND SECOND MOMENT OF AREA
CAPACITY (see VOLUME)
DENSITY (that is, MASS DENSITY)
(see MASS DIVIDED BY VOLUME)
ELECTRICITY and MAGNETISM
ENERGY (includes WORK)
ENERGY DIVIDED BY AREA TIME
FLOW (see MASS DIVIDED BY TIME
or VOLUME DIVIDED BY TIME)
FORCE DIVIDED BY AREA
FORCE DIVIDED BY LENGTH
Coefficient of Heat Transfer
Density of Heat
Density of Heat Flow Rate
Heat Capacity and Entropy
Heat Flow Rate
Specific Heat Capacity and
MASS and MOMENT OF INERTIA
MASS DENSITY (see MASS DIVIDED BY VOLUME)
MASS DIVIDED BY AREA
MASS DIVIDED BY CAPACITY
(see MASS DIVIDED BY VOLUME)
MASS DIVIDED BY LENGTH
MASS DIVIDED BY TIME (includes FLOW)
MASS DIVIDED BY VOLUME
(includes MASS DENSITY
and MASS CONCENTRATION)
MOMENT OF FORCE or TORQUE
MOMENT OF FORCE or TORQUE,
DIVIDED BY LENGTH
PRESSURE or STRESS (FORCE DIVIDED BY AREA)
SPEED (see VELOCITY)
STRESS (see PRESSURE)
TORQUE (see MOMENT OF FORCE)
VELOCITY (includes SPEED)
VOLUME (includes CAPACITY)
VOLUME DIVIDED BY TIME (includes FLOW)
WORK (see ENERGY)
In Secs. B.8 and B.9, the units in the left-hand columns are written as they are often used customarily; the rules and style conventions recommended in this Guide are not necessarily observed. Further, many are obsolete and some are not consistent with good technical practice. The corresponding units in the center columns are, however, written in accordance with the rules and style conventions recommended in this Guide.
The efficiency of motor vehicles in the United States is commonly expressed in miles per U.S. gallon, while in most other countries it is expressed in liters per one hundred kilometers. To convert fuel economy stated in miles per U.S. gallon to fuel consumption expressed in L/(100 km), divide 235.215 by the numerical value of the stated fuel economy. Thus 24 miles per gallon corresponds to 9.8 L/(100 km).
The U.S. Metric Law of 1866 gave the relationship 1 m = 39.37 in (in is the unit symbol for the inch). From 1893 until 1959, the yard was defined as being exactly equal to (3600/3937) m, and thus the foot was defined as being exactly equal to (1200/3937) m.
In 1959 the definition of the yard was changed to bring the U.S. yard and the yard used in other countries into agreement; see Ref. [7: FR 1959]. Since then the yard has been defined as exactly equal to 0.9144 m, and thus the foot has been defined as exactly equal to 0.3048 m. At the same time it was decided that any data expressed in feet derived from geodetic surveys within the United States would continue to bear the relationship as defined in 1893, namely, 1 ft = (1200/3937) m (ft is the unit symbol for the foot). The name of this foot is "U.S. survey foot," while the name of the new foot defined in 1959 is "international foot." The two are related to each other through the expression 1 international foot = 0.999 998 U.S. survey foot exactly.
In Secs. B.8 and B.9, the factors given are based on the international foot unless otherwise indicated. Users of this Guide may also find the following summary of exact relationships helpful, where for convenience in this section, the symbols ft and mi, that is, ft and mi in italic type, indicate that it is the U.S. survey foot or U.S. survey mile that is meant rather than the international foot (ft) or international mile (mi), and where rd is the unit symbol for the rod and fur is the unit symbol for the furlong.
1 ft = (1200/3937) m
1 ft = 0.3048 m
1 ft = 0.999 998 ft
1 rd, pole, or perch = 16½ ft
40 rd = 1 fur = 660 ft
8 fur = 1 U.S. survey mile (also called "statute mile") = 1 mi = 5280 ft
1 fathom = 6 ft
1 international mile = 1 mi = 5280 ft
272¼ ft2 = 1 rd2
160 rd2 = 1 acre = 43 560ft2
640 acre = 1 mi2
Rules for rounding numbers are discussed in Refs. [4: ISO 31-0] and ; the latter reference also gives rules for rounding the converted numerical values of quantities whose values expressed in units that are not accepted for use with the SI (primarily customary or inch-pound units) are converted to values expressed in acceptable units. This Guide gives the principal rules for rounding numbers in Sec. B.7.1, and the basic principle for rounding converted numerical values of quantities in Sec. B.7.2. The cited references should be consulted for additional details.
To replace a number having a given number of digits with a number (called the rounded number) having a smaller number of digits, one may follow these rules:
1. If the digits to be discarded begin with a digit less than 5, the digit preceding the 5 is not changed.
Example: 6.974 951 5 rounded to 3 digits is 6.97
2. If the digits to be discarded begin with a 5 and at least one of the following digits is greater than 0, the digit preceding the 5 is increased by 1.
|Examples:||6.974 951 5 rounded to 2 digits is 7.0|
|6.974 951 5 rounded to 5 digits is 6.9750|
3. If the digits to be discarded begin with a 5 and all of the following digits are 0, the digit preceding the 5 is unchanged if it is even and increased by 1 if it is odd. (Note that this means that the final digit is always even.)
|Examples:||6.974 951 5 rounded to 7 digits is 6.974 952|
|6.974 950 5 rounded to 7 digits is 6.974 950.|
The use of the factors given in Secs. B.8 and B.9 to convert values of quantities was demonstrated in Sec. B.3. In most cases the product of the unconverted numerical value and the factor will be a numerical value with a number of digits that exceeds the number of significant digits (see Sec. 7.9) of the unconverted numerical value. Proper conversion procedure requires rounding this converted numerical value to the number of significant digits that is consistent with the maximum possible rounding error of the unconverted numerical value.
The final result, l = 11.0 m, is based on the following reasoning: The numerical value "36" has two significant digits, and thus a relative maximum possible rounding error (abbreviated RE in this Guide for simplicity) of ± 0.5/36 = ± 1.4 % because it could have resulted from rounding the number 35.5, 36.5, or any number between 35.5 and 36.5. To be consistent with this RE, the converted numerical value "10.9728" is rounded to 11.0 or three significant digits because the number 11.0 has an RE of ± 0.05/11.0 = ± 0.45 %. Although this ± 0.45 % RE is one-third of the ± 1.4 % RE of the unconverted numerical value "36," if the converted numerical value "10.9728" had been rounded to 11 or two significant digits, information contained in the unconverted numerical value "36" would have been lost. This is because the RE of the numerical value "11" is ± 0.5/11 = ± 4.5 %, which is three times the ± 1.4 % RE of the unconverted numerical value "36." This example therefore shows that when selecting the number of digits to retain in the numerical value of a converted quantity, one must often choose between discarding information or providing unwarranted information. Consideration of the end use of the converted value can often help one decide which choice to make.
Note: Consider that one had been told initially that the value l = 36 ft had been rounded to the nearest inch. Then in this case, since l is known to within ± 1 in, the RE of the numerical value "36" is ± 1 in/(36 ft × 12 in/ft) = ± 0.23 %. Although this is less than the ± 0.45 % RE of the number 11.0, it is comparable to it. Therefore, the result l = 11.0 m is still given as the converted value. (Note that the numerical value "10.97" would give excessive unwarranted information because it has an RE that is one-fifth of ± 0.23 %.)