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Unit 7 - Lesson 2 - Grade 8: Illustrative Mathematics

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11 Questions
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Grade 8 Unit 7
Lesson 2: Multiplying Powers of Ten
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 7
Lesson 2: Multiplying Powers of Ten
CC BY 2021 Illustrative Mathematics®
Lesson: Multiplying Powers of Ten

100, 1, or 1/100? (Warm Up)


Clare said she sees 100.
Tyler says he sees 1.
Mai says she sees 1/100.
1.

Who do you agree with?

Picture a Power of 10

In the diagram, the medium rectangle is made up of 10 small squares. The large square is made up of 10 medium rectangles.

2.

How could you represent the large square as a power of 10?

3.

If each small square represents 102, then what does the medium rectangle represent? The large square?


4.

If the medium rectangle represents 105, then what does the large square represent? The small square?


5.

If the large square represents 10100, then what does the medium rectangle represent? The small square?


Multiplying Powers of Ten

6.

  • 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.
  • If you chose to skip one entry in the table, which entry did you skip? Why?


7.

Use the patterns you found in the table to rewrite 10n · 10m as an equivalent expression with a single exponent, like 10▢.

8.

Use your rule to write 104 · 100 with a single exponent. What does this tell you about the value of 100?

9.

The state of Georgia has roughly 107 human residents. Each human has roughly 1013 bacteria cells in his or her digestive tract. How many bacteria cells are there in the digestive tracts of all the humans in Georgia?

Cool Down: That's a Lot of Dough, Though!

That's a Lot of Dough, Though!

10.

Rewrite 1032 · 106 using a single exponent.

11.

Each year, roughly 106 computer programmers each make about $105 . How much money is this all together? Express your answer both as a power of 10 and as a dollar amount.