Lesson 11Representing Small Numbers on the Number Line

Learning Goal

Let’s visualize small numbers on the number line using powers of 10.

Learning Targets

  • I can plot a multiple of a power of 10 on such a number line.

  • I can subdivide and label a number line between 0 and a power of 10 with a negative exponent into 10 equal intervals.

  • I can write a small number as a multiple of a power of 10.

Warm Up: Small Numbers on a Number Line

Problem 1

Kiran drew this number line.

A number line from 0 to 10 to the negative fifth

Andre said, “That doesn’t look right to me.”

Explain why Kiran is correct or explain how he can fix the number line.

Activity 1: Comparing Small Numbers on a Number Line

Problem 1

  1. Label the tick marks on the number line.

    A number line with endpoints 0 and 10 to the -5 and 9 tick marks in between.

  2. Plot the following numbers on the number line:

    A.

    B.

    C.

    D.

  3. Which is larger, or ? Estimate how many times larger.

  4. Which is larger, or ? Estimate how many times larger.

Activity 2: Atomic Scale

Problem 1

The radius of an electron is about 0.0000000000003 cm. Write this number as a multiple of a power of 10.

  1. Decide what power of 10 to put on the right side of this number line and label it.

  2. Label each tick mark as a multiple of a power of 10.

    A number line with eleven evenly spaced tick marks. The first tick is labeled 0, the last tick is labeled 10 to the blank power, and the remaining tick marks are blank.

  3. Plot the radius of the electron in centimeters on the number line.

Problem 2

The mass of a proton is about 0.0000000000000000000000017 grams.

  1. Write this number as a multiple of a power of 10.

  2. Decide what power of 10 to put on the right side of this number line and label it.

  3. Label each tick mark as a multiple of a power of 10.

    A number line with eleven evenly spaced tick marks. The first tick is labeled 0, the last tick is labeled 10 to the blank power, and the remaining tick marks are blank.

  4. Plot the mass of the proton in grams on the number line.

Problem 3

Point on the zoomed-in number line describes the wavelength of a certain X-ray in meters.

A zoomed in number line from 6 x 10 to the negative 12 that goes from 6 x 10 to the negative 12 to 7 x 10 to the negative 12 with 10 tick marks and tick 1 labeled A

  1. Write the wavelength of the X-ray as a multiple of a power of 10.

  2. Write the wavelength of the X-ray as a decimal.

Lesson Summary

The width of a bacterium cell is about meters. If we want to plot this on a number line, we need to find which two powers of 10 it lies between. We can see that is a multiple of . So our number line will be labeled with multiples of

A number line from 0 to 10 to the negative fifth and a point at 2 x 10 to the negative 6.

Note that the right side is labeled

The power of ten on the right side of the number line is always greater than the power on the left. This is true for positive or negative powers of ten.