3
Use of Dimensions
When numbers are used to express results of measurements, the units of measurement should always be given. Too frequently these units, or dimensions,
are assumed but not shown.
In using dimensions in calculations, we follow a few simple rules.
1. Every number that represents a measurement is given with its
dimension—for example, 12 men, 16 feet, 5 miles.
2. Numbers that do not involve a measurement are written without a
dimension. Examples are 7r(the ratio of the circumference of a circle to
its diameter) and logarithms.
3. In addition and subtraction, all numbers must have the same dimensions. We can add 2 apples to 3 apples, but we cannot add 2 apples to 3
miles.
4. In multiplication and division, the dimensions of the numbers are multiplied and divided just as the numbers are, and the product or quotient
of the dimension appears in the final result. Thus the product (6 men)(2
days) = 12 man-days, and the product (5 £at)(4 Ibs/gat) = 20 Ibs. Note
that units common to both numerator and denominator cancel each
other, just as do factors common to both.
A term frequently used with numbers is per, which shows how many units of
one measurement correspond to one unit of another. A common method of
Use of Dimensions
When numbers are used to express results of measurements, the units of measurement should always be given. Too frequently these units, or dimensions,
are assumed but not shown.
In using dimensions in calculations, we follow a few simple rules.
1. Every number that represents a measurement is given with its
dimension—for example, 12 men, 16 feet, 5 miles.
2. Numbers that do not involve a measurement are written without a
dimension. Examples are 7r(the ratio of the circumference of a circle to
its diameter) and logarithms.
3. In addition and subtraction, all numbers must have the same dimensions. We can add 2 apples to 3 apples, but we cannot add 2 apples to 3
miles.
4. In multiplication and division, the dimensions of the numbers are multiplied and divided just as the numbers are, and the product or quotient
of the dimension appears in the final result. Thus the product (6 men)(2
days) = 12 man-days, and the product (5 £at)(4 Ibs/gat) = 20 Ibs. Note
that units common to both numerator and denominator cancel each
other, just as do factors common to both.
A term frequently used with numbers is per, which shows how many units of
one measurement correspond to one unit of another. A common method of