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

7.10.4 Roman numerals 
 
It is unacceptable to use Roman numerals to express the values of quantities. In particular, one 
should not use C, M, and MM as substitutes for 10
2
, 10
3
, and 10
6
, respectively. 
7.11 Quantity equations and numerical-value equations 
 
A quantity equation expresses a relation among quantities. An example is l = υt, where l is the 
distance a particle in uniform motion with velocity υ travels in the time t. 
Because a quantity equation such as l = υt is independent of the units used to express the values of 
the quantities that compose the equation, and because l, υ, and t represent quantities and not numerical 
values of quantities, it is incorrect to associate the equation with a statement such as “where l is in meters, υ 
is in meters per second, and t is in seconds.” 
On the other hand, a numerical value equation expresses a relation among numerical values of 
quantities and therefore does depend on the units used to express the values of the quantities. For example, 
{l}
m
= 3.6
−1
{υ}
km/h 
{t}
s
expresses the relation among the numerical values of l, υ, and t only when the 
values of l, υ, and t are expressed in the units meter, kilometer per hour, and second, respectively. (Here 
{A}
X
is the numerical value of quantity A when its value is expressed in the unit X—see Sec. 7.1, note 2.) 
An alternative way of writing the above numerical value equation, and one that is preferred because 
of its simplicity and generality, is l/m = 3.6
−1
[υ/(km/h)](t / s). NIST authors should consider using this 
preferred form instead of the more traditional form “l = 3.6
−1
υt, where l is in meters, υ is in kilometers per 
hour, and t is in seconds.” In fact, this form is still ambiguous because no clear distinction is made between 
a quantity and its numerical value. The correct statement is, for example, “l* = 3.6
−1
υ* t *, where l* is the 
numerical value of the distance l traveled by a particle in uniform motion when l is expressed in meters, υ* 
is the numerical value of the velocity υ of the particle when υ is expressed in kilometers per hour, and t* is 
the numerical value of the time of travel t of the particle when t is expressed in seconds.” Clearly, as is 
done here, it is important to use different symbols for quantities and their numerical values to avoid 
confusion.
It is the strong recommendation of this Guide that because of their universality, quantity equations 
should be used in preference to numerical-value equations. Further, if a numerical-value equation is used, it 
should be written in the preferred form given in the above paragraph, and if at all feasible the quantity 
equation from which it was obtained should be given. 
Notes: 
1. Two other examples of numerical-value equations written in the preferred form are as follows, 
where E
g
is the gap energy of a compound semiconductor and k is the conductivity of an 
electrolytic solution: 

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