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.
4.1: Decimal Place Value
Before we can perform any calculations with decimals, we need to understand the way decimals are written.
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.
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.
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.
4.5: Adding and Subtracting Decimals
When adding and subtracting decimals, we need to pay attention to the placement of the decimal point.
4.6: Multiplying Decimals
When multiplying decimals, we also need to keep track of the decimal point.
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.
4.8: Word Problems Using Decimals
Decimals appear in many places in the real world, especially in problems involving money.