Guide for the Use of the International System of Units (SI)

 
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Guide for the Use of the International System of Units (SI) 
 
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A derived quantity of dimension one, which is sometimes called a “dimensionless quantity,” is one 
for which all of the dimensional exponents are zero: dim Q = 1. It therefore follows that the derived unit for 
such a quantity is also the number one, symbol 1, which is sometimes called a “dimensionless derived 
unit.” 
Example: The mass fraction w
B
of a substance B in a mixture is given by w
B
= m
B 
/ m, where m
B 
is the 
mass of B and m is the mass of the mixture (see Sec. 8.6.10). The dimension of w
B
is dim 
w
B
= M
1
M
−1
= 1; all of the dimensional exponents of w
B
are zero, and its derived unit is 
kg
1
·kg
−1
= 1 also. 
8
Comments on Some Quantities and Their Units 
 
8.1 Time and rotational frequency 
 
The SI unit of time (actually time interval) is the second (s) and should be used in all technical 
calculations. When time relates to calendar cycles, the minute (min), hour (h), and day (d) might be 
necessary. For example, the kilometer per hour (km/h) is the usual unit for expressing vehicular speeds. 
Although there is no universally accepted symbol for the year, Ref. [4: ISO 80000-3] suggests the 
symbol a. 
The rotational frequency n of a rotating body is defined to be the number of revolutions it makes in a 
time interval divided by that time interval [4: ISO 80000-3]. The SI unit of this quantity is thus the 
reciprocal second (s
−1
). However, as pointed out in Ref. [4: ISO 80000-3], the designations “revolutions per 
second” (r/s) and “revolutions per minute” (r/min) are widely used as units for rotational frequency in 
specifications on rotating machinery.