# Lesson 11

Representing Small Numbers on the Number Line

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

### 11.1: Small Numbers on a Number Line

Kiran drew this number line.

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

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

### 11.2: Comparing Small Numbers on a Number Line

1. Label the tick marks on the number line.

2. Plot the following numbers on the number line:

A. $$6 \boldcdot 10^{\text -6}$$

B. $$6 \boldcdot 10^{\text -7}$$

C. $$29 \boldcdot 10^{\text -7}$$

D. $$(0.7) \boldcdot 10^{\text -5}$$

3. Which is larger, $$29 \boldcdot 10^{\text -7}$$ or $$6 \boldcdot 10^{\text -6}$$? Estimate how many times larger.
4. Which is larger, $$7 \boldcdot 10^{\text -8}$$ or $$3 \boldcdot 10^{\text -9}$$? Estimate how many times larger.

### 11.3: Atomic Scale

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.

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

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.

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

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

### Summary

The width of a bacterium cell is about $$\displaystyle 2 \boldcdot 10^{\text -6}$$ 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 $$2 \boldcdot 10^{\text -6}$$ is a multiple of $$10^{\text -6}$$. So our number line will be labeled with multiples of $$\displaystyle 10^{\text -6}$$

Note that the right side is labeled $$\displaystyle 10 \boldcdot 10^{\text -6} =10^{\text -5}$$