Unit 7 - Lesson 4 - Grade 8: Illustrative Mathematics

Complete the table to explore patterns in the exponents when dividing powers of 10. Use the “expanded” column to show why the given expression is equal to the single power of 10. You may skip a single box in the table, but if you do, be prepared to explain why you skipped it. If you chose to skip one entry in the table, which entry did you skip? Why?

It is predicted that by 2050, there will be 1010 people living on Earth. At that time, it is predicted there will be approximately 1012 trees. How many trees will there be for each person?

Write 1012 · 100 with a power of 10 with a single exponent using the appropriate exponent rule. Explain or show your reasoning.

Write the following with a single power of 10 using the appropriate exponent rule. Explain or show your reasoning.

What number could you divide 108 by to get this same answer?

If we want the exponent rules we found to work even when the exponent is 0, then what does the value of 100 have to be?

Noah says, “If I try to write 100 expanded, it should have zero factors that are 10, so it must be equal to 0.” Do you agree? Discuss with your partner.

Write as many expressions as you can that have the same value as 106. Focus on using exponents, multiplication, and division. What patterns do you notice with the exponents?

Why is the following equal? Explain or show your thinking?