# Lesson 13

Definition of Scientific Notation

Let’s use scientific notation to describe large and small numbers.

### Problem 1

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 2

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 3

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?

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 $$(4,3)$$.