# Lesson 10: Representing Large Numbers on the Number Line

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

## 10.1: Labeling Tick Marks on a Number Line

Label the tick marks on the number line. Be prepared to explain your reasoning.

## 10.2: Comparing Large Numbers with a Number Line

1. Drag the points to their proper places on the number line. Be prepared to explain your reasoning.

GeoGebra Applet aWqR27Uy

1. Discuss with a partner how you decided where each point should go.

2. Which is larger, 4,000,000 or $75 \boldcdot 10^5$? Estimate how many times larger.

## 10.3: The Speeds of Light

The table shows how fast light waves or electricity can travel through different materials:

material speed of light (meters per second)
Row 1 space 300,000,000
Row 2 water $(2.25) \boldcdot 10^8$
Row 3 copper wire (electricity) 280,000,000
Row 4 diamond $124 \boldcdot 10^6$
Row 5 ice $(2.3) \boldcdot 10^8$
Row 6 olive oil 200,000,000
1. Which is faster, light through diamond or light through ice? How can you tell from the expressions for speed?

Let’s zoom in to highlight the values between $(2.0) \boldcdot 10^8$ and $(3.0) \boldcdot 10^8$.

GeoGebra Applet V7bWnzSb

1. Plot a point for each speed on both number lines, and label it with the corresponding material.

2. There is one speed that you cannot plot on the bottom number line. Which is it? Plot it on the top number line instead.

3. Which is faster, light through ice or light through diamond? How can you tell from the number line?

## Summary

There are many ways to compare two quantities. Suppose we want to compare the world population, about

7.4 billion

There are many ways to do this. We could write 7.4 billion as a decimal, 7,400,000,000, and then we can tell that there were more pennies made in 2015 than there are people in the world! Or we could use powers of 10 to write these numbers: $$7.4 \boldcdot 10^9$$ for people in the world and $$8.9 \boldcdot 10^9$$ for the number of pennies.
For a visual representation, we could plot these two numbers on a number line. We need to carefully choose our end points to make sure that the numbers can both be plotted. Since they both lie between $10^9$ and $10^{10}$, if we make a number line with tick marks that increase by one billion, or $10^9$, we start the number line with 0 and end it with $10 \boldcdot 10^{9}$, or $10^{10}$. Here is a number line with the number of pennies and world population plotted: