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Illustrative Math
Grade 8
Lesson 5: Negative Exponents with Powers of 10
Let’s see what happens when exponents are negative.
Illustrative Math Unit 8.7, Lesson 5 (printable worksheets)
Lesson 5 Summary
The following examples explain what it means if 10 is raised to a negative power and how to use the exponent rules with negative exponents.
Lesson 5.1 Number Talk: What’s That Exponent?
Solve each equation mentally.
Lesson 5.2 Negative Exponent Table
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 each of these multipliers affect the placement of the decimal?
 Use the patterns you found in the table to write 10^{7} as a fraction.
 Use the patterns you found in the table to write 10^{5} as a decimal.
 Write 1/1,000,000 using a single exponent.
 Use the patterns in the table to write 10^{n} as a fraction.
Lesson 5.3 Follow the Exponent Rules
 a. Match the expressions that describe repeated multiplication in the same way:
b. Write (10^{2})^{3} as a power of 10 with a single exponent. Be prepared to explain your reasoning.
 a. Match the expressions that describe repeated multiplication in the same way:
b. Write 10^{2}/10^{5} as a power of 10 with a single exponent. Be prepared to explain your reasoning.
 a. Match the expressions that describe repeated multiplication in the same way:
b. Write 10^{4} · 10^{3} as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Are you ready for more?
Priya, Jada, Han, and Diego are playing a game. They stand in a circle in this order 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?

Show Answer
The person who starts win when there are even number of players.
Lesson 5 Practice Problems
 Write with a single exponent:
 Write each expression as a single power of 10.
 Select all of the following that are equivalent to 1/10,000
 Match each equation to the situation it describes. Explain what the constant of proportionality means in each equation.
 a. Explain why triangle ABC is similar to EDC.
b. Find the missing side lengths.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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