# Introduction to Decimals

## Objectives

After completing this unit, you should be able to:

• State the place value of each digit in a decimal.
• Given a decimal written in words, write the number in numerical form.
• Given a decimal written in numerical form, write the number in words.

## Understanding Place Values

Each place in a number has a different place value. This holds true both before and after the decimal. Below is a chart that shows the different place values in a number. As we look at this diagram, notice the spelling changes from the places to the left of the decimal point (which represent places for whole numbers) and the decimal places to the right of the decimal point.
 So, for the number 127.5369, there is a 1 in the hundreds place, a 2 in the tens place, a 7 in the ones place, a 5 in the tenths place, a 3 in the hundredths place, a 6 in the thousandths place, and a 9 in the ten thousandths place.

## Writing a Decimal in Words

When expressing decimals, it is important to use the correct language. When reading and writing decimals, there are two things you should keep in mind:

• A decimal point means and.
• Take note of the correct place of the last digit in the number.

Let's work through these steps of writing out in words a decimal given numerically.

 0.2 two tenths 1.2 one and two tenths

Note the use of the word and to signal where the decimal point is in this number. When you wish to read or write out a decimal, you should:

1. Look to see if there is a number to the left of the decimal; if so write it out. If there is no number to the left of the decimal, skip to step 3.
2. Write an and for the decimal point.
3. Write out the number to the right of the decimal. Do not yet include the place value.
4. Determine the place value of the last digit to the right of the decimal. Write the place value.

Let's try an example to illustrate these steps.

### Example

How would you write the following number: 12.25?

The answer is twelve and twenty-five hundredths

1. Look to see if there is a number to the left of the decimal, if so write it out. If there is no number to the left of the decimal, skip to step 3.

The number to the left of the decimal is 12, or twelve, so we start out with: twelve

2. Write an `and' for the decimal point.

After adding the and we have: twelve and

3. Write out the number to the right of the decimal. Do not yet include the place value.

The number to the right of the decimal is 25, or twenty-five. After this step we have: twelve and twenty-five

4. Determine the place value of the last digit to the right of the decimal. Write the place value.

The last digit, a 5, is two places right of the decimal, which is the hundredths place. We must add this on to the end of our answer. This gives us: twelve and twenty-five hundredths

Below are a few more examples of some decimals written out. Look through this list; then refer back to the steps above to be sure you understand how each is done. Remember, simply write the number as it appears, and add the appropriate ending to represent the place.

 0.004 The 4 is in the thousandths place, so is read as four thousandths. The zeros that we have added are called place holders. 0.003 three thousandths 0.03 three hundredths Note the difference between 0.003 and 0.03. This illustrates the use of zero as place holder. 0.123 This decimal is written as one hundred twenty-three thousandths 245.18 This decimal is written as two hundred forty-five and eighteen hundredths

Now let's look at writing decimals numerically.

## Writing a Decimal Numerically

In this section we will learn to take a decimal stated in words and write it out in its numerical form. To do this:

1. Look at the ending of the statement. The ending indicates the place value of the number the furthest to the right of the decimal. ( NOTE: For example, if the statement ends in tenths, hundredths, thousandths, etc., there will be a decimal). If there is no decimal, then it is a whole number. You can just write out the whole number, and you are done.
2. Look to see if there is an and in the statement. If there is an and, then there is a whole number to the left of the decimal, so write this number out and add a decimal on the end. If there is no and, move on to step 3.
3. Now note the ending, which represents the decimal place in which the decimal will end. Mark out some blanks for each place that will be filled to the right of the decimal. ( NOTE: You can always draw a chart like the one used in the first section of this unit.)
4. Looking at the number that appears after the decimal, write it out so that the last digit appears in the last place marked off in step 3.
5. If there are any spaces between the decimal and the number to the right of the decimal, add zeros as place holders.

If needed, you can use the chart shown in the first section of this unit to help you write out decimals. Let's work through an example using the steps above.

### Example

Write out the number thirteen and twenty-seven thousandths.

1. Look at the ending of the statement. See if it indicates there will be a decimal.

The ending here is thousandths, so there will be a decimal.

2. Look to see if there is an and in the statement. If there is an and, then there is a whole number to the left of the decimal. Write this number out and add a decimal on the end. If there is no and, move on to step 3.

The statement in front of the and is thirteen. This means the whole number in front of the decimal is 13, so we have:

13.

3. Now note the ending, which represents the decimal place in which the decimal will end. Mark out some blanks for each place that will be filled to the right of the decimal.
 Our ending is "thousandths," so the last digit is three places to the right of the decimal point.

4. Looking at the number that appears after the decimal, write it out so that the last digit appears in the last place marked off in step 3
 Twenty-seven, written 27, occupies two spaces so we place this number so that it occupies the last two spaces to the right of the decimal point.
5. If there are any spaces between the decimal and the number to the right of the decimal, add zeros as place holders.
 In the diagram above, we see that there is one space still open between the decimal and the number 27. This space is filled with a zero as a place holder.

The number thirteen and twenty-seven thousandths is written numerically as:

13.027

Now let's try practicing reading and writing decimals. This will help make sure you understand the last two sections of this unit.