### APPLICATION OF EXPONENTS

#### S. Kastberg

Sometimes it seems as though mathematical notation is just that, notation. So why have exponents? Are they just more notation without meaning or is there a reason for using them?

Do you remember scientific notation? Your calculator does. Try entering 1,000,000,000,000. You should get something like 1 E 12 which means . What is the 12 telling you?

Can you write 10 in scientific notation? How about 0.01?

Make a table like the one below. You may use your calculator, a spreadsheet, or a paper and pencil to record your data.

 Exponents Scientific Notation Expanded Notation -2 -1 0 1 2 3 4 5 100,000

Fill in the table.

Consider the entries in the table. How are the entries in the exponent column related as you go up/down the column? What operation would you use to go up/down?

How are the entries in the scientific notation column related as you go up/down the column? What operation would you use to go up/down?

How are the entries in the expanded notation column related as you go up/down the column? What operation would you use to go up/down?

Do you see any other patterns.

Suppose n is a positive integer. How would the number in expanded notation corresponding to n in the exponent column be similar/different from the entry corresponding to -n?

Write the radius of each of the circles in the following GSP file in scientific notation and organize the radi from least to greatest.

Use a table like the one below to record the results from your GSP investigation.

Fill in the remaining columns by answering the following questions.

1. A circle whose radius is one-tenth the measure of circle B has a radius of what measure?

2. A circle whose radius is is how much more than the radius of circle A?

3. A circle whose radius is 100 times that of circle D has a radius of what measure?

Reflecting on patterns

Explain what you think the exponents explored in this activity mean?

Explain what the number 10 had to do with this activity?

Using the measure of radii, is it ever possible to get 0 measure? If so how, if not how close can you get?

If you were trying to get 0 radius, how might you do it?