### Unit 4: Decimals

In this unit, you will turn your attention to the "fraternal twin" of fractions: decimals. Yes, decimals are really just fractions in disguise! Who knew? For example, look at (American) money. A dollar is 100 cents; a quarter is 25 cents, or in decimal form, $0.25. The fraction 25/100 reduces to 1/4, which is read as "one-quarter." Decimals are fractions, and fractions are decimals. It's all in how you write them.

Decimals are everywhere, just like fractions. You cannot go shopping without encountering decimals. Whether you are adding up totals on your shopping list, calculating your change, or even just measuring the length of something, you will use decimals. If you add up all your purchases, find that your total comes to $17.31, and you hand the cashier $20, you need to know how to determine your change to make sure the cashier gives you back the correct amount of money. If you are measuring the length of your wall in order to fit a couch there, you might find that the wall's length is in between two lengths, measuring at, say, 11.5 ft. You have to know how to deal with decimals to approximate distances.

In this unit, you will learn how to add/subtract/multiply/divide decimals as well as how to convert between fraction and decimal form.

**Completing this unit should take you approximately 26 hours.**

Upon successful completion of this unit, the student will be able to:

- recognize the place value of decimals;
- apply rounding and estimation concepts with decimals;
- convert between fraction and decimals;
- perform operations with multi-digit whole numbers and with decimals; and
- solve real-world and mathematical problems involving the four operations with decimals.

### 4.1: Decimal Basics

### 4.1.1: Decimal Place Value

Take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to understand place value. Watch the second presentation carefully two or three times until you are able to write decimals in word form.

Study the "Introduction to Decimals," "Decimal Notation," and "Pronouncing Decimal Numbers" sections on pages 342-346 of the textbook, stopping at "Decimals to Fractions." The material may also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1-6 on pages 344-346. This material contains examples of decimal notation and pronouncing decimal numbers.

Complete the odd-numbered exercises for 1-39 on pages 353 and 354 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to identify decimal places and writing out decimals numbers in expanded form and words. The solutions to these problems are located in the "Answers" section on page 356 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, "Answers").

### 4.1.2: Rounding Decimals

Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to round decimals.

Read the "Rounding Decimal Numbers" section through "Sample Set A." Then, complete "Practice Set A," exercises 1-7. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to round decimals to various positions. Then, complete the even-numbered problems for 8-22. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will help you practice rounding decimals to various positions.

### 4.1.3: Comparing Decimals

Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to compare decimals accurately.

Study the "Comparing Decimals" section on pages 350-352 of the textbook. The material may also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, "Comparing Decimals"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 11 and 12 on pages 351 and 352. This material contains examples of comparing decimal numbers. Then, complete the odd-numbered exercises for 81-91 on page 355 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to identify decimal places and write out decimals numbers in expanded form and words. The solutions to these problems are located in the "Answers" section on page 356 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, "Answers").

### 4.1.4: Conversion

### 4.1.4.1: Converting Decimals to Fractions

Take notes as you watch these videos. Watch these presentations carefully two or three times until you are able to convert fractions to decimals.

Read the "Converting a Fraction to a Decimal" section, stopping at "Sample Set A," Example 5. Then, complete "Practice Set A," exercises 1-4. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to convert fractions into decimals. Then, complete the odd-numbered problems for 7-31 and 37-53. The solutions to the problems can be revealed by the "Show Solution" link under each problem. These problems will allow you to convert fractions into decimals.

Complete the assignment that tests your knowledge of converting fractions to decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.1.4.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

### 4.1.4.2: Converting Decimals to Fractions

Take notes as you watch these videos. View these presentations carefully two or three times until you are able to convert decimals to fractions.

Read the "Converting an Ordinary Decimal to a Fraction" section through "Sample Set A," and complete "Practice Set A," exercises 1-4. The solutions to the problems are shown directly below each problem. These problems will allow you to convert decimals into fractions. Then, complete the odd-numbered problems for 9-27. The solutions to the problems are shown directly below each problem. These problems will allow you to convert decimals into fractions.

Complete the assignments that test your knowledge of converting decimals to fractions. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.1.4.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

Complete the assignments that test your knowledge of converting decimals to fractions. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.1.4.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

### 4.1.4.3: Converting Repeating Decimals to Fractions

Take notes as you watch these videos. View these presentations carefully two or three times until you are able to convert repeating decimals to fractions.

### 4.2: Decimal Operations

### 4.2.1: Adding and Subtracting

### 4.2.1.1: Adding Decimals

Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to add decimals.

Study the "Adding Decimals" section on pages 359-361 of the textbook, stopping at "Subtracting Decimals." The material may also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Adding Decimals"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1-4 on pages 359-361. This material contains examples of adding decimal numbers. Then, complete the odd-numbered exercises for 1-11 on page 366 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to adding decimal numbers. The solutions to these problems are located in the "Answers" section on page 368 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Answers").

Complete the assignment that tests your knowledge of adding decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2.1.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

Complete the assignment that tests your knowledge of adding decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2.1.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

### 4.2.1.2: Subtracting Decimals

Take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to subtract decimals. Watch the second presentation carefully two or three times until you are able to add and subtract decimals in application.

Study the "Subtracting Decimals" section on pages 361 and 362 of the textbook, stopping at "Adding and Subtracting Signed Decimal Numbers." The material may also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Subtracting Decimals"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 5 and 6 on pages 361 and 362. This material contains examples of subtracting decimal numbers. Then, complete the odd-numbered exercises for 13-23 and 81-87 on page 366 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply the addition and subtraction of decimals. The solutions to these problems are located in the "Answers" section on page 368 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Answers").

Complete the assignment that tests your knowledge of subtracting decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2.1.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

Complete the assignment that tests your knowledge of subtracting decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2.1.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

### 4.2.1.3: Adding and Subtracting Signed Decimal Numbers

Study the "Adding and Subtracting Signed Decimal Numbers" section on pages 362-364 of the textbook. The material may also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Adding and Subtracting Signed Decimal Numbers"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 7-10 on pages 362-364. This material contains examples of adding and subtracting signed decimal numbers. Then, complete the odd-numbered exercises for 25-63 on page 366 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to add and subtract signed decimals numbers. The solutions to these problems are located in the "Answers" section on page 368 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, "Answers").

### 4.2.2: Multiplying and Dividing

### 4.2.2.1: Multiplying Decimals

Take notes as you watch this video. Watch the presentation carefully two or three times until you are able to multiply decimals.

Study the "Multiplying Decimals" section on pages 370-373 of the textbook, stopping at "Multiplying Signed Decimal Numbers." Then, read "The Circle" section on pages 376-380. The material may also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals) and (5 Decimals, 5.3 Multiplying Decimals, "The Circle"), which will take you directly to the readings. After reading and studying these sections, complete the "You Try It" problems beside Examples 1-3 on pages 370-373 and Examples 9 and 10 on pages 378-380. This material contains examples of multiplying decimal numbers and its applications. Then, complete the odd-numbered exercises for 1-27 and 89-105 on page 381 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to multiply decimals numbers and study applications of multiplying decimals, which include finding the total cost of items. The solutions to these problems are located in the "Answers" section on page 384 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Answers").

### 4.2.2.2: Multiplying Signed Decimal Numbers

Study the "Multiplying Signed Decimal Numbers" section on pages 373 and 374 of the textbook, stopping at "Order of Operations." The material may also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Multiplying Signed Decimal Numbers"), which will take you directly to the material. After reading and studying this section, complete the "You Try It" problems beside Examples 4 and 5 on pages 373 and 374. This reading contains examples of multiplying signed decimal numbers. Then, complete the odd-numbered exercises for 29-55 on page 381 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to multiply signed decimals numbers. The solutions to these problems are located in the "Answers" section on page 385 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Answers").

Complete this assignment that tests your knowledge of operations with decimals. This assignment incorporates concepts on multiplying decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2.2.1, and 4.2.2.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

### 4.2.2.3: Dividing Decimals

Take notes as you watch these videos. Watch each presentation carefully two or three times until you are able to divide decimals.

Study the "Dividing Decimals" on pages 386-390 of the textbook, stopping at "Dividing Signed Decimal Numbers." The material may also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Examples 1-3 on pages 387-390. This reading contains examples and applications of dividing decimal numbers. Then, complete the odd-numbered exercises for 1-39 and 107-113 on page 395 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, "Exercises"), which will take you directly to the material. These exercises will provide you with the opportunity to divide decimals numbers and study applications of dividing decimals, which include finding averages for a project. The solutions to these problems are located in the "Answers" section on page 399 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, "Answers").

### 4.2.2.4: Dividing Signed Decimal Numbers

Study the "Dividing Signed Decimal Numbers" section on pages 390 and 391 of the textbook, stopping at "Rounding." The material may also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, "Dividing Signed Decimal Numbers"), which will take you directly to the reading. After reading and studying this section, complete the "You Try It" problems beside Example 4 on page 390. This reading contains examples of dividing signed decimal numbers. Then, complete the odd-numbered exercises for 41-63 on page 395 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, "Exercises"), which will take you directly to the assignment. These exercises will provide you with the opportunity to divide signed decimals numbers. The solutions to these problems are located in the "Answers" section on page 399 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, "Answers").

Complete this assignment that tests your knowledge of operations with decimals. This assignment incorporates concepts on dividing decimals. You can review the concepts associated with the questions with the Khan videos in sub-subunit 4.2.3.1, and 4.2.3.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on "Check Answer" to see if you were correct or if you need to try again.

### 4.3: Order of Operations

Study the "Order of Operations" section on pages 374 and 375 of the textbook, stopping at "Powers of Ten." Then, read "Order of Operations" through Example 8 on pages 393 and 394. The material may also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Order of Operations")and (5 Decimals, 5.4 Dividing Decimals, "Order of Operations"), which will take you directly to the readings. Review only the processes involved with each problem and do not worry about substituting into the expression. This material contains examples of order of operations. Then, complete the odd-numbered exercises for 69-79 on page 382 and 89-99 on page 397 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Exercises") and (5 Decimals, 5.4 Dividing Decimals, "Exercises"), which will take you directly to the assignments. These exercises will provide you with the opportunity to apply order of operations to decimal numbers. The solutions to these problems are located in the "Answers" section on page 384 and page 399 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, "Answers") and (5 Decimals, 5.4 Dividing Decimals, "Answers").