Lesson 5Negative Exponents with Powers of 10
Learning Goal
Let’s see what happens when exponents are negative.
Learning Targets
I can use the exponent rules with negative exponents.
I know what it means if 10 is raised to a negative power.
Lesson Terms
- base (of an exponent)
Warm Up: Number Talk: What’s That Exponent?
Problem 1
Solve each equation mentally.
Activity 1: Negative Exponent Table
Problem 1
Complete the table to explore what negative exponents mean.
As you move toward the left, each number is being multiplied by 10. What is the multiplier as you move right?
How does a multiplier of 10 affect the placement of the decimal in the product? How does the other multiplier affect the placement of the decimal in the product?
Use the patterns you found in the table to write
as a fraction. Use the patterns you found in the table to write
as a decimal. Write
using a single exponent. Use the patterns in the table to write
as a fraction.
Activity 2: Follow the Exponent Rules
Problem 1
Match the expressions that describe repeated multiplication in the same way:
Write
as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Problem 2
Match the expressions that describe repeated multiplication in the same way:
Write
as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Problem 3
Match the expressions that describe repeated multiplication in the same way:
Write
as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Are you ready for more?
Problem 1
Priya, Jada, Han, and Diego stand in a circle and take turns playing a game.
Priya says, “SAFE.” Jada, standing to Priya’s left, says, “OUT” and leaves the circle. Han is next: he says, “SAFE.” Then Diego says, “OUT” and leaves the circle. At this point, only Priya and Han are left. They continue to alternate. Priya says, “SAFE.” Han says, “OUT” and leaves the circle. Priya is the only person left, so she is the winner.
Priya says, “I knew I’d be the only one left, since I went first.”
Record this game on paper a few times with different numbers of players. Does the person who starts always win?
Try to find as many numbers as you can where the person who starts always wins. What patterns do you notice?
Lesson Summary
When we multiply a positive power of 10 by
That means we can extend the rules to use negative exponents if we make
Here is an example of extending the rule
Here is an example of extending the rule