Lesson 11
Representing Small Numbers on the Number Line
Let’s visualize small numbers on the number line using powers of 10.
Problem 1
Select all the expressions that are equal to \(4 \boldcdot 10^{\text-3}\):
A:
\(4 \boldcdot (\frac{1}{10}) \boldcdot (\frac{1}{10}) \boldcdot (\frac{1}{10})\)
B:
\(4 \boldcdot (\text{-}10) \boldcdot (\text{-}10) \boldcdot (\text{-}10)\)
C:
\(4 \boldcdot 0.001\)
D:
\(4 \boldcdot 0.0001\)
E:
\(0.004\)
F:
\(0.0004\)
Problem 2
Write each expression as a multiple of a power of 10:
- 0.04
- 0.072
- 0.0000325
- Three thousandths
- 23 hundredths
- 729 thousandths
- 41 millionths
Problem 3
A family sets out on a road trip to visit their cousins. They travel at a steady rate. The graph shows the distance remaining to their cousins' house for each hour of the trip.
- How fast are they traveling?
- Is the slope positive or negative? Explain how you know and why that fits the situation.
- How far is the trip and how long did it take? Explain how you know.
![Coordinate plane, x, 0 to 8 by 1, y, 0 to 500 by 20. A line segment connects 0 comma 480 to 8 comma 0.](https://staging-cms-im.s3.amazonaws.com/yWXf8J3D3g9s8mAJNGrG2JPs?response-content-disposition=inline%3B%20filename%3D%228-8.3.C9.PP.graph2.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.C9.PP.graph2.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T155909Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7efd7d9d17dbe1f788ebcea3ed9c9513f4b50e7b6effa1ef5d61ae8d965f2ecb)