Lesson 4: Dividing Powers of 10
Let’s explore patterns with exponents when we divide powers of 10.
Illustrative Math Unit 8.7, Lesson 4 (printable worksheets)
Lesson 4 Summary
The following examples explain and show how to use a rule for dividing powers of 10.
Lesson 4.1 A Surprising One
What is the value of the expression?
Lesson 4.2 Dividing Powers of Ten
- a. 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.
b. If you chose to skip one entry in the table, which entry did you skip? Why?
- Use the patterns you found in the table to rewrite 10m/10n as an equivalent expression of the form 10x.
- 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?
Are you ready for more?
104 ÷ 106 =
Lesson 4.3 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?
- Write 1012 · 100 with a power of 10 with a single exponent using the appropriate exponent rule. Explain or show your reasoning.
What number could you multiply 1012 by to get this same answer?
- Write 108 ÷ 100 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.
Lesson 4.4 Making Millions
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?
Lesson 4 Practice Problems
- Write each expression as a single power of 10.
- The Sun is roughly 102 times as wide as the Earth. The star KW Sagittarii is roughly 105 times as wide as the Earth. About how many times as wide as the Sun is KW Sagittarii? Explain how you know.
- Bananas cost $1.50 per pound, and guavas cost $3.00 per pound. Kiran spends $12 on fruit for a breakfast his family is hosting. Let b be the number of pounds of bananas Kiran buys and q be the number of pounds of guavas he buys.
a. Write an equation relating the two variables.
b. Rearrange the equation so b is the independent variable.
c. Rearrange the equation so g is the independent variable.
- Lin’s mom bikes at a constant speed of 12 miles per hour. Lin walks at a constant speed 1/3 of the speed her mom bikes. Sketch a graph of both of these relationships.
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