About Exponential Numbers

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).

Laboratory:  Discovering an exponential relationship (Contributed by Enrica Giordano, University of Bicocca,  Milan, Italy)

 

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.