Lesson 10
Representing Large Numbers on the Number Line
Let’s visualize large numbers on the number line using powers of 10.
Problem 1
Find three different ways to write the number 437,000 using powers of 10.
Problem 2
For each pair of numbers below, circle the number that is greater. Estimate how many times greater.
- \(17 \boldcdot 10^8\) or \(4 \boldcdot 10^8\)
- \(2 \boldcdot 10^6\) or \(7.839 \boldcdot 10^6\)
- \(42 \boldcdot 10^7\) or \(8.5 \boldcdot 10^8\)
Problem 3
What number is represented by point \(A\)? Explain or show how you know.
![A zoomed in number line. Top line, 0 on the first tick mark, 10 to the twelth power on the 11th tick mark. The eighth & ninth tick marks are zoomed out to show 11 tick marks, the fifth is labeled A.](https://staging-cms-im.s3.amazonaws.com/Kx4iwnVSBZkTkKCBLcBPrzg2?response-content-disposition=inline%3B%20filename%3D%228-8.7.C.PP.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%278-8.7.C.PP.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20241227%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20241227T193203Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6a7565872a65cad2f6a4de4551a0a9f1e983f7eee3d3fa4ccf1b03f863c9996b)
Problem 4
Here is a scatter plot that shows the number of points and assists by a set of hockey players. Select all the following that describe the association in the scatter plot:
![Scatterplot, horizontal, assists, 0 to 60 by 15, vertical, points, 0 to 80 by 20. A collection of points is clustered around a line through 7 comma 12 and 47 comma 72.](https://staging-cms-im.s3.amazonaws.com/N9BHQPQkCrgajPPuN7LN6EWf?response-content-disposition=inline%3B%20filename%3D%228-8.6.A2.PP.hockeypoints.png%22%3B%20filename%2A%3DUTF-8%27%278-8.6.A2.PP.hockeypoints.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20241227%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20241227T193203Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4871688718acbc0822f1c04055f11640ce31684ec74e88b582329b91d0346997)
Linear association
Non-linear association
Positive association
Negative association
No association
Problem 5
Here is the graph of days and the predicted number of hours of sunlight, \(h\), on the \(d\)-th day of the year.
![Coordinate plane, horizontal, d, 0 to 350 by 50, vertical, h, 0 to 20 by 5. A curve begins at 0 comma 8, increases to 180 comma 18, then decreases to 365 comma 8.](https://staging-cms-im.s3.amazonaws.com/Ls3VYnLuAQ42xQT1CH8Bq7Tu?response-content-disposition=inline%3B%20filename%3D%228-8.5.PP.B.Image.03.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.PP.B.Image.03.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20241227%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20241227T193203Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7bcdf1b4a9885c1760c06812cd51a604d696a24d530207a593c46def4b80208b)
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Is hours of sunlight a function of days of the year? Explain how you know.
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For what days of the year is the number of hours of sunlight increasing? For what days of the year is the number of hours of sunlight decreasing?
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Which day of the year has the greatest number of hours of sunlight?