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 \(4 \boldcdot 10^{\text-3}\):


\(4 \boldcdot (\frac{1}{10}) \boldcdot (\frac{1}{10}) \boldcdot (\frac{1}{10})\)


\(4 \boldcdot (\text{-}10) \boldcdot (\text{-}10) \boldcdot (\text{-}10)\)


\(4 \boldcdot 0.001\)


\(4 \boldcdot 0.0001\)





Problem 2

Write each expression as a multiple of a power of 10:

  1. 0.04
  2. 0.072
  3. 0.0000325
  4. Three thousandths
  5. 23 hundredths
  6. 729 thousandths
  7. 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.

  1. How fast are they traveling?
  2. Is the slope positive or negative? Explain how you know and why that fits the situation.
  3. 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.
(From Unit 5, Lesson 8.)

Problem 4

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

Two lines in an x y plane. 
(From Unit 5, Lesson 7.)

Problem 5

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

  1. What is the volume of the cylinder?
  2. What is the volume of the cylinder when its radius is tripled?
  3. What is the volume of the cylinder when its radius is halved?
(From Unit 6, Lesson 22.)