Unit 4: Decimals
In this unit, we study decimals, which are simply another way to write fractions. For example, think about American currency. One dollar is 100 cents and a quarter is 25 cents, or $0.25 when written as a decimal. We can explain a quarter as being 25/100 of a dollar. This reduces to 1/4, which we read as one-quarter. Decimals are everywhere, just like fractions. We use them in money, in measuring lengths, and in amounts. In this unit, we study how to add, subtract, multiply, and divide decimals, and how to convert between fractions and decimals.
Completing this unit should take you approximately 8 hours.
Upon successful completion of this unit, you will be able to:
- recognize the place value of decimals;
- apply rounding and estimation concepts with decimals;
- convert between fractions and decimals;
- perform operations with decimals; and
- solve real-world and mathematical problems with decimals.
4.1: Decimal Place Value
Before we can perform any calculations with decimals, we need to understand the way decimals are written.
After you watch the video, take this quiz and check your answers.
4.2: Rounding Decimals
We often need to round decimals to a certain point. One example is when we are dealing with money.
For example, we might calculate the cost of something to be 0.557 dollars. However, we know that there are only 100 cents in a dollar, meaning we need to round our decimal to the hundredths place, which means that we would round this dollar amount to $0.56, or 56 cents.
Watch this video for examples of how we can round decimals to specific decimal places.
Read this section up to to Sample Set A. This section gives a set of rules for determining how to round a decimal and some step-by-step directions for rounding numbers.
4.3: Converting Between Decimals and Fractions
Decimals give us the same information as fractions. Therefore, we can write the same number as a decimal or a fraction. For example, 0.25 equals 25/100, which can be reduced to ¼. Because decimals and fractions give us the same information, we need to be comfortable converting between them.
Begin by watching this video, which shows examples of converting decimals to fractions.
Read up to "Repeating Fractions". Do examples 5.28 and 5.29 and check your answers. For more practice, do Try It exercises 5.55–5.58.
Complete this quiz and check your answers. If you need more practice, you can do problem sets 2 and 3.
4.4: Converting Repeating Decimals to Fractions
The examples in the last section involved decimals that ended. For example, we saw that 0.25 equals ¼. However, some decimals are repeating, meaning that they go on infinitely. These repeating decimals are still equal to fractions.
Watch these two videos for worked examples of how to handle repeating decimals.
Read the "Repeating Decimals" section. Pay attention to the notation for the repeating portion of the decimal, which is to write a line above the numbers that repeat. Do examples 5.30 and 5.31 and check your answers. If you need more practice, do Try It exercises 5.59 and 5.60.
4.5: Adding and Subtracting Decimals
When adding and subtracting decimals, we need to pay attention to the placement of the decimal point.
Watch this video for an example of doing an addition problem with decimal numbers. Pay attention to how the decimal point must be lined up when completing an addition problem.
Watch these videos for examples of doing a subtraction problem with decimal numbers.
For more examples, read the "Add and Subtract Decimals" section. Do examples 5.11–5.14 and check your answers.
4.6: Multiplying Decimals
When multiplying decimals, we also need to keep track of the decimal point.
Read the "Multiply Fractions" section up to the header "Multiply by Powers of Ten". Pay attention to the overview of the steps for multiplying two fractions. Do examples 5.15–5.17 and check your answers. If you need more practice, do Try It exercises 5.29–5.34.
4.7: Dividing Decimals
The last basic mathematical operation we need to perform with decimals is division. Division with decimals works in a similar manner to multiplication with decimals.
Read the "Divide Decimals" section, and pay attention to the step-by-step summaries of how to divide decimals. Do examples 5.19–5.23 and check your answers. If you need more practice, do Try It exercises 5.37–5.46.
4.8: Word Problems Using Decimals
Decimals appear in many places in the real world, especially in problems involving money.
Watch this video to see how to solve word problems that use decimals.
After you watch the video, complete this assignment. The solutions to the problems are at the end of the document.
