5 Numbers Versus Quantities
When you ask how tall I am, you may get the answer: 5 feet and 10 inches or
1.75 meters. The answer in either of its forms involves both numbers and units.
A number times a unit of measurement gives you a quantity. Quantities can be
added together: 5 feet plus 10 inches is 5[5/6] feet.
To further understand the difference between numbers and quantities, you may
ask how many pennies (or cents) I have in my pocket. The answer could be the
number 10. For the same pocket, if you asked how much money I had in it, the
answer would be the quantity 10 cents or even 0.10 dollars, a tenth of a dollar.
Numbers are given by counts - whole numbers, proper and improper fractions,
decimal numbers. Quantities are given by a count (a whole number or fraction)
times a unit of measurement. Any object that can be counted can serve as a unit
of measurement. Examples of units of measurement are: meter, foot, $ or dollar,
square foot, square meter, second, hour, meters per second, kilometers per hour,
dollars per hour, miles per hour and so on.
Numbers include no units. You get a number when you ask how many units there
are, and you have specified the unit. You get a quantity when you ask how much
there is. Saying a length is given by the number 5 is meaningless, if no units
of measurement are given. Saying a length is 5 raises the question 5 what?
The number 5 may give the number of units of length in a distance. Writing
this number by itself does not say what the unit of length might be. Some
information, the unit, is missing. So I repeat, in answering questions demanding
how much, we need to give a unit of measurement as well as a number. People
should not have to guess your unit of measurement when you speak. A length may
be given by 5 miles (or 8 kilometers). Of course, if we are asked how many miles
(or kilometers) there are in the length concerned, the number 5 (or 8) is
expected because the unit was specified. When you are asked how many people
there are in a room, you may respond with a pure number like 7 or 10. The unit
of measurement can be worded or written as person or persons.
In measurement and counting, a single unit of measurement, a fraction of one
or several units, may appear. For instance, a length of time may involve 1 hour
or 12.5 hours. Notice the addition of the letter s to the unit hour here when
fractions or more than one unit appears. In mathematics, we choose to ignore the
difference in spelling between the singular and the plural. If we insisted on
using the singular form, we would have to write 12.5 hours = 12.5 ×1 hour.
The latter gives the exact meaning of 12.5 hours. In writing units in
calculations, we may and will change their spelling (or abbreviations) according
to the rules of grammar. The plural and singular forms of each unit are declared
to be equal or interchangeable. Each is allowed to replace the other. Which one
sounds the most appropriate will be written in our formulas and calculations.