# What are Dimensions ?

For example, consider water in the beaker shown here:
Can be calculated or derived by multiplying or dividing fundamental dimensions.
Exampls: area, velocity, density and volume
2. Derived Dimensions -
Mass, Length, Time, Temperature, Moles and sometimes Force
Fundamental dimensions can be directly measured or are independently defined.
All other dimensions can be obtained from the fundamental dimensions.
1. Fundamental Dimensions -
There are two types of dimensions.
In science and engineering, numbers without units are not useful (unless they happen to be dimensionless).

Mass

Density

has derived dimensions made up of a combination of fundamental dimensions:
is a fundamental dimension.
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### Ch 1, Lesson B, Page 1 - What are Dimensions ?

• If I told you that I weighed 175, would you be worried that I might step on your foot ?
• I guess that depends on whether I weighed 175 pounds, 175 kg or 175 tons, doesn’t it ?
• Well, in science and engineering, a number without units like pounds or kg or ft/sec is just about meaningless.
• The exception is that some quantities are dimensionless, but we won’t run into many of them in this course.
• So, what is a dimension anyway ?
• A dimension is a TYPE of unit.
• Mass, length, time, temperature and sometimes force are fundamental dimensions.
• Mass might have units of pounds, kg or tons.
• Fundamental Dimensions cannot be reduced in terms of any combination of other fundamental dimensions.
• For example, no combination of length, time and temperature is equivalent to mass.
• Density is NOT a fundamental dimension because it is equivalent to mass over volume and volume is equivalent to length cubed.
• So, density has dimensions of mass per length cubed.  Because the dimensions of density can be written in terms of other fundamental dimensions, density is NOT a fundamental dimension.
• Now, lets take a closer look at UNITS.