Multiplying Powers of Ten: IM 8.7.2
[url=https://im.kendallhunt.com/MS/teachers/3/7/2/preparation.html]“Multiplying Powers of Ten”[/url] from IM Grade 8 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 8.7.2
- IM 8.7.2 Lesson: Multiplying Powers of Ten
- Practice 8.7.2
- IM 8.7.2 Practice: Multiplying Powers of Ten
IM 8.7.2 Lesson: Multiplying Powers of Ten
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[/img][br][br]Clare said she sees 100.[br]Tyler says he sees 1.[br]Mai says she sees [math]\frac{1}{100}[/math].[br]Who do you agree with?
In the diagram, the medium rectangle is made up of 10 small squares. The large square is made up of 10 medium rectangles.
Explain your reasoning.
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?
Use your rule to write [math]10^4\cdot10^0[/math] with a single exponent. What does this tell you about the value of [math]10^0[/math]?
The state of Georgia has roughly [math]10^{^7}[/math] human residents. Each human has roughly [math]10^{^{13}}[/math] bacteria cells in his or her digestive tract. How many bacteria cells are there in the digestive tracts of all the humans in Georgia?
There are four ways to make by multiplying powers of 10 with smaller, positive exponents.
[math]10^1\cdot10^1\cdot10^1\cdot10^1[/math][br][math]10^1\cdot10^{^1}\cdot10^2[/math][br][math]10^1\cdot10^3[/math][br][math]10^2\cdot10^2[/math][br][br](This list is complete if you don't pay attention to the order you write them in. For example, we are only counting [math]10^1\cdot10^3[/math] and [math]10^{^3}\cdot10^1[/math] once.)[br][br]How many ways are there to make [math]10^6[/math] by multiplying smaller powers of 10 together?
How about [math]10^7[/math]?
How about [math]10^8[/math]?
IM 8.7.2 Practice: Multiplying Powers of Ten
Write each expression with a single exponent:
A large rectangular swimming pool is 1,000 feet long, 100 feet wide, and 10 feet deep. The pool is filled to the top with water.
What is the area of the surface of the water in the pool?
How much water does the pool hold?
Express your answers to the previous two questions as powers of 10.
[size=150]Here is triangle [math]ABC[/math]. Triangle [math]DEF[/math] is similar to triangle [math]ABC[/math], and the length of [math]EF[/math] is 5 cm. What are the lengths of sides [math]DE[/math] and [math]DF[/math], in centimeters?[br][/size][br][img]data:image/png;base64,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[/img]
Elena and Jada distribute flyers for different advertising companies. Elena gets paid 65 cents for every 10 flyers she distributes, and Jada gets paid 75 cents for every 12 flyers she distributes.[br][br]Draw graphs on the coordinate plane representing the total amount each of them earned, [math]y[/math], after distributing [math]x[/math] flyers. Use the graph to decide who got paid more after distributing 14 flyers.