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?
![Scatterplot, wingspan in millimeters, body length in millimeters. Please request assistance.](https://staging-cms-im.s3.amazonaws.com/1qwT2Gh5DaqpAMgxcZP33uZi?response-content-disposition=inline%3B%20filename%3D%228-8.6.PP.B.Image.20.png%22%3B%20filename%2A%3DUTF-8%27%278-8.6.PP.B.Image.20.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141938Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=cdf44931d1de2d02d6ce837bb5dae736a56b7f0188662c2122ece75532e510e6)
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 \(x\).
![Two triangles. The first has acute angles marked 46 degrees and x degrees. The second has an obtuse marked 106 degrees.](https://staging-cms-im.s3.amazonaws.com/idy2ZBdpMfi5f4Pq7iq5T8Y9?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.08.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.08.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141938Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1c3a3ca6d4d20a3032e36e78f84f8559682fbc5056ff754db81072be2cfddbe4)