Lesson 4Dividing Powers of 10
Learning Goal
Let’s explore patterns with exponents when we divide powers of 10.
Learning Targets
I can evaluate
and explain why it makes sense. I can explain and use a rule for dividing powers of 10.
Lesson Terms
- base (of an exponent)
Warm Up: A Surprising One
Problem 1
What is the value of the expression?
Activity 1: Dividing Powers of Ten
Problem 1
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.
expression
expanded
single power
If you chose to skip one entry in the table, which entry did you skip? Why?
Problem 2
Use the patterns you found in the table to rewrite
Problem 3
It is predicted that by 2050, there will be
Are you ready for more?
Problem 1
expression | expanded | single power |
---|---|---|
Activity 2: Zero Exponent
So far we have looked at powers of 10 with exponents greater than 0. What would happen to our patterns if we included 0 as a possible exponent?
Problem 1
Write
with a power of 10 with a single exponent using the appropriate exponent rule. Explain or show your reasoning. What number could you multiply
by to get this same answer?
Problem 2
Write
with a single power of 10 using the appropriate exponent rule. Explain or show your reasoning. What number could you divide
by to get this same answer?
Problem 3
If we want the exponent rules we found to work even when the exponent is 0, then what does the value of
Problem 4
Noah says, “If I try to write
Activity 3: Making Millions
Problem 1
Write as many expressions as you can that have the same value as
Lesson Summary
In an earlier lesson, we learned that when multiplying powers of 10, the exponents add together. For example,
This gives us a new exponent rule: