Length Scales in PhysicsPhysicists try to figure out understand how the universe works. This requires them to understand processes that are larger than galaxies as well as ones that are smaller than atoms. To describe how exactly how big or small things are we use measurement units. You are probably familiar with some measurement units, such as feet, inches, yards, and miles. Or perhaps you are familiar with the metric system and units like centimeters, meters and kilometers. Because it is easy to change from using one metric unit to another (you'll see how this is done), and because people all over the world use the metric system, scientists find it the easiest system to use.
The basic metric unit of length is the meter. Originally, a meter was defined as 1/10,000,000 of the distance between the equator and the north pole. Today it is accurately defined in terms of the length of light waves. (If you are curious, a meter is 1,650,763.73 times the wavelength of a red-orange light emitted by krypton-86 gas when electricity is run though it.)
Its not a coincidence that the basic metric unit of length is about right for measuring a person. We must, however be able to describe the size of things that are much smaller and much larger than a meter. To avoid having to say or write long numbers like 0.0000000001 , people use two different shourcuts. These are the metric prefixes and scientific notation. Before we look at this, use the applet below to see the range of length scales we use in physics.
In our discussion of how physicists study membranes and surfaces we mention membranes and surfaces of vastly different sizes. Most that we discuss are smaller than a meter. Use the applet to get a feel for the sizes involved and see how we use scientific notation and metric prefixes.
Scientific notation is a short way to write very large or very small numbers.
The trick is simple. We write numbers as a number between one and ten
multiplied by 10 with some exponent. So instead of writing 127,000,000,
we would notice that
Since there are 8 factors of 10 we write, in scientific notation,
If we wanted to use the number 0.00000075, we'd notice that
Because we are dividing by 10 seven times, the scientific notation is
If the number refers to metric units, often we can replace the factor of ten to an exponent with a prefix. Some of these are so familiar that we don't even think about them - the centimeter for example, it means one hundredth of a meter and the symbol cm is a combination of the prefix c meaning 1/100 and m for meter. Here's how this and other prefixes work: