# Lesson 12

Applications of Arithmetic with Powers of 10

Let's use powers of 10 to help us make calculations with large and small numbers.

### Problem 1

Which is larger: the number of meters across the Milky Way, or the number of cells in all humans? Explain or show your reasoning.

Some useful information:

- The Milky Way is about 100,000 light years across.
- There are about 37 trillion cells in a human body.
- One light year is about \(10^{16}\) meters.
- The world population is about 7 billion.

### Problem 2

Ecologists measure the body length and wingspan of 127 butterfly specimens caught in a single field.

- Draw a line that you think is a good fit for the data.
- Write an equation for the line.

- What does the slope of the line tell you about the wingspans and lengths of these butterflies?

### Problem 3

Diego was solving an equation, but when he checked his answer, he saw his solution was incorrect. He knows he made a mistake, but he can’t find it. Where is Diego’s mistake and what is the solution to the equation?

\(\displaystyle \begin{align} \text-4(7-2x)=3(x+4)\\ \text-28-8x=3x+12\\ \text-28=11x+12\\ \text-40=11x\\ \text{-}\frac {40}{11}=x\ \end{align}\)

### Problem 4

The two triangles are similar. Find \(x\).