Clare, Tyler, and Mai are looking at the diagram.

• Clare said she sees 100.
• Tyler says he sees 1.
• Mai says she sees .

Whom do you agree with? Be prepared to explain your reasoning.

In the diagram, the medium rectangle is made up of 10 small squares. The large square is made up of 10 medium rectangles.

1. How could the large square be represented as a power of 10? Explain your reasoning.
2. If each small square represents , then what does the medium rectangle represent? The large square?
3. If the medium rectangle represents , then what does the large square represent? The small square?
4. If the large square represents , then what does the medium rectangle represent? The small square?

1. 1. Complete the table to explore patterns in the exponents when multiplying powers of 10. You may skip a single box in the table, but if you do, be prepared to explain why you skipped it.

      expression	expanded	single power of 10

   2. If you chose to skip one entry in the table, which entry did you skip? Why?
2. 1. Use the patterns you found in the table to rewrite  as an equivalent expression with a single exponent, like .
   2. Use your rule to write with a single exponent.  What does this tell you about the value of ?
3. The state of Georgia has roughly human residents. Each human has roughly bacteria cells in his or her digestive tract. How many bacteria cells are there in the digestive tracts of all the humans in Georgia?