Numerically it can be very cumbersome to describe extremely large
or small sizes. Our Milky Way Galaxy is about 100000000000000000000 meters
across while an atom is about 0.0000000001 meters across. These are too many
zeros to read; there is an easier way to represent large or small numbers -
exponential notation.
The diameter of our Milky Way galaxy (1 followed by 20 zeros can
be represented by the number 1 x 1020 or simply 1020 meters. The diameter of a
typical atom can be represented by 1 x 10-10 or simply 10-10 meters. If the
exponent is positive, then multiply by 10 the number of times described by the
exponent. If the exponent is negative, then divide by 10 the number of
times described by the exponent.
The difference between
multiplying by 10 or dividing by 10 is called an order of magnitude or a
"power of ten". For example, 100 (102) is one order of magnitude or
power of ten higher than 10 (101) and two orders of magnitude or powers of ten
higher than 1 (100). The number 1,000 (103) is three orders of magnitude or
powers of ten lower than 1,000,000 (106).
Your
students can derive an exponential relationship. Have students shine a light
through first one, then two, then up to 5 layers of ¼-1/2 inch plastic,
measuring with a lux meter the amount of light going in and exiting. These layers of plastic can be
purchased from a hardware store in a sheet, and then cut into squares.
Alternatively,
you can print on plastic overhead sheets matrices of dots that will allow the
different percentages of light to pass through.
Students
can put their results in a spreadsheet (e.g. Excel) and graph the results. In this process they will discover that
the results are not linear.