# 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.

### Problem 4

These two lines are parallel. Write an equation for each.

### Problem 5

A cylinder has a radius of 4 cm and a height of 5 cm.

- What is the volume of the cylinder?
- What is the volume of the cylinder when its radius is tripled?
- What is the volume of the cylinder when its radius is halved?