Lesson 2Multiplying Powers of Ten
Learning Goal
Let’s explore patterns with exponents when we multiply powers of 10.
Learning Targets
I can explain and use a rule for multiplying powers of 10.
Warm Up: 100, 1, or ?
Problem 1
Clare said she sees 100.
Tyler says he sees 1.
Mai says she sees
.
Who do you agree with?
Activity 1: Picture a Power of 10
Problem 1
In the diagram, the medium rectangle is made up of 10 small squares. The large square is made up of 10 medium rectangles.
How could you represent the large square as a power of 10?
If each small square represents
, then what does the medium rectangle represent? The large square? If the medium rectangle represents
, then what does the large square represent? The small square? If the large square represents
, then what does the medium rectangle represent? The small square?
Print Version
In the diagram, the medium rectangle is made up of 10 small squares. The large square is made up of 10 medium rectangles.
How could you represent the large square as a power of 10?
If each small square represents
, then what does the medium rectangle represent? The large square? If the medium rectangle represents
, then what does the large square represent? The small square? If the large square represents
, then what does the medium rectangle represent? The small square?
Activity 2: Multiplying Powers of Ten
Problem 1
Complete the table to explore patterns in the exponents when multiplying powers 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 of 10
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
as an equivalent expression with a single exponent, like . Use your rule to write
with a single exponent. What does this tell you about the value of ?
Problem 3
The state of Georgia has roughly
Are you ready for more?
Problem 1
There are four ways to make
(This list is complete if you don’t pay attention to the order you write them in. For example, we are only counting
How many ways are there to make
by multiplying smaller powers of 10 together? How many ways are there to make
in the same way? ?
Lesson Summary
In this lesson, we developed a rule for multiplying powers of 10: multiplying powers of 10 corresponds to adding the exponents together. To see this, multiply
This rule makes it easier to understand and work with expressions that have exponents.