# 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

Write each number in scientific notation.

1. 14,700
2. 0.00083
3. 760,000,000
4. 0.038
5. 0.38
6. 3.8
7. 3,800,000,000,000
8. 0.0000000009

### Problem 3

1. $$(2 \times 10^5) + (6 \times 10^5)$$

2. $$(4.1 \times 10^7) \boldcdot 2$$

3. $$(1.5 \times 10^{11}) \boldcdot 3$$

4. $$(3 \times 10^3)^2$$

5. $$(9 \times 10^6) \boldcdot (3 \times 10^6)$$

### Problem 4

Jada is making a scale model of the solar system. The distance from Earth to the Moon is about $$2.389 \times 10^5$$ miles. The distance from Earth to the Sun is about $$9.296 \times 10^7$$ miles. She decides to put Earth on one corner of her dresser and the Moon on another corner, about a foot away. Where should she put the sun?

• On a windowsill in the same room?
• In her kitchen, which is down the hallway?
• A city block away?

### Problem 5

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 13.)

### Problem 6

Here is the graph for one equation in a system of equations.

1. Write a second equation for the system so it has infinitely many solutions.
2. Write a second equation whose graph goes through $$(0,2)$$ so that the system has no solutions.
3. Write a second equation whose graph goes through $$(2,2)$$ so that the system has one solution at $$(4,3)$$.
(From Unit 5, Lesson 13.)