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.

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

  3. What does the slope of the line tell you about the wingspans and lengths of these butterflies?
Scatterplot, wingspan in millimeters, body length in millimeters. Please request assistance.
(From Unit 6, Lesson 5.)

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?

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


(From Unit 4, Lesson 5.)

Problem 4

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

Two triangles. The first has acute angles marked 46 degrees and x degrees. The second has an obtuse marked 106 degrees.
(From Unit 2, Lesson 7.)