# 50 Lesson 2 Understand Powers Of Ten Answer Key

## Introduction

Welcome to Lesson 2 of Understanding Powers of Ten! In this lesson, we will be going over the answer key for the exercises in Lesson 2. These exercises are designed to help you solidify your understanding of powers of ten and how they can be used in various mathematical operations. By the end of this lesson, you will have a clear grasp of how to apply powers of ten in real-world situations. So let's dive in and check out the answer key!

### Exercise 1: Multiplying and Dividing by Powers of Ten

1.1) 5 x 10^3 = 5000

1.2) 8 x 10^4 = 80000

1.3) 2 x 10^-2 = 0.02

1.4) 3 x 10^-5 = 0.00003

1.5) 6 x 10^1 = 60

1.6) 9 x 10^0 = 9

1.7) 7 x 10^-3 = 0.007

1.8) 4 x 10^-6 = 0.000004

### Exercise 2: Adding and Subtracting Powers of Ten

2.1) 3 x 10^5 + 2 x 10^4 = 320000

2.2) 4 x 10^3 - 5 x 10^2 = 3500

2.3) 6 x 10^2 + 7 x 10^1 = 670

2.4) 9 x 10^-2 - 8 x 10^-3 = 0.08

2.5) 2 x 10^0 + 3 x 10^-1 = 2.3

2.6) 5 x 10^-3 - 6 x 10^-4 = 0.0044

2.7) 8 x 10^4 + 9 x 10^3 = 89000

2.8) 1 x 10^1 - 2 x 10^0 = 8

### Exercise 3: Evaluating Expressions with Powers of Ten

3.1) 5 x 10^3 + 2 x 10^2 - 3 x 10^1 = 5200

3.2) (6 x 10^2 + 4 x 10^1) x 2 = 1280

3.3) (8 x 10^3 - 5 x 10^2) / 3 = 2500

3.4) (2 x 10^0 + 7 x 10^-1) - (4 x 10^-2) = 2.66

3.5) (9 x 10^-2 + 6 x 10^-3) x 5 = 0.465

3.6) (3 x 10^5 - 2 x 10^4) / 4 = 72000

3.7) (7 x 10^1 + 9 x 10^0) - (8 x 10^-1) = 78.8

3.8) (1 x 10^-2 - 6 x 10^-3) x 7 = 0.007

### Exercise 4: Solving Real-World Problems with Powers of Ten

4.1) The distance from Earth to the Moon is approximately 3.8 x 10^5 kilometers. If a spaceship travels at a speed of 6.5 x 10^4 kilometers per hour, how long will it take to reach the Moon? Solution: Time = Distance / Speed = (3.8 x 10^5) / (6.5 x 10^4) = 5.846 hours

4.2) The mass of a proton is approximately 1.67 x 10^-27 kilograms. If there are 9.8 x 10^18 protons in a sample, what is the total mass of the sample? Solution: Mass = Mass of one proton x Number of protons = (1.67 x 10^-27) x (9.8 x 10^18) = 1.6376 x 10^-8 kilograms

4.3) The speed of light in a vacuum is approximately 3 x 10^8 meters per second. If a beam of light travels for 2.5 x 10^-6 seconds, how far does it travel? Solution: Distance = Speed x Time = (3 x 10^8) x (2.5 x 10^-6) = 7.5 x 10^2 meters

4.4) The population of a city is currently 5.2 x 10^6 people. If the population increases by 3.5% each year, what will be the population after 10 years? Solution: Population after 10 years = Initial population x (1 + Growth rate)^Number of years = (5.2 x 10^6) x (1 + 0.035)^10 = 8.006 x 10^6 people

### Conclusion

That wraps up our answer key for Lesson 2 of Understanding Powers of Ten. We hope that going through these exercises has helped solidify your understanding of how to use powers of ten in various mathematical operations and real-world problems. Remember, practice makes perfect, so don't hesitate to revisit these exercises or explore additional problems to further enhance your skills. Stay tuned for our next lesson, where we will delve deeper into the world of powers of ten.