Candace uses a ruler to cut three different sized ribbons. One is 6.5 inches long. One is 6.25 inches long and the other is 6.75 inches long. She decides to order the ribbons from smallest to largest. Without seeing her ribbons, the only way to determine the order is to arrange the measurements from least to greatest. What is the order of the ribbons?

In this concept, you will learn how to compare decimals.

### Comparing Decimals

When you **compare decimals**, you are trying to figure out which part of a whole is greater. To do this, you need to think about the number 1.

1 is a whole. All decimals are part of 1.

The closer a decimal is to 1, the larger the decimal is.

Let's use place value to figure out which number is closer to one then compare the values.

0.45 ______ 0.67

You have two decimals that both have the same number of digits in them. It is easy to compare decimals that have the same number of digits. Look at the numbers without the decimal point and determine which number is greater. 67 is greater. You can say that sixty-seven hundredths is closer to one than forty-five hundredths.

The answer is 0.45 < 0.67.

When comparing decimals, use the following steps:

- If the decimals you are comparing have the same number of digits in them, think about the value of the number without the decimal point.
- The larger the number, the closer it is to one.

Now, let's compare decimals that don’t have the same number of digits.

0.567 ______ 0.63

Five hundred sixty-seven thousandths seems greater. However, thousandths are smaller than hundredths.

To test this statement let’s look at a hundreds grid and a thousands grid.

Now it is easier to compare. You can see that 0.63 is larger than 0.567.

You can also compare without using a grid.

Add zeros to make sure that the digit numbers are equal.

0.567 ______ 0.630

Then compare the numbers without the decimal point to determine which is greater. 640 is greater than 567.

The answer is that 0.567 < 0.640.

The same technique is used when whole numbers are involved.

3.4 ______ 3.56

First, add in a zero.

3.40 ______ 3.56

The whole number, 3 is the same, so look at the decimal. Notice that 40 is less than 56 so you can use symbols to compare.

The answer is 3.4 < 3.56.

Now that you know how to compare decimals, you can **order** them. **Ordering** means that you list a series of decimals according to size. Write them from least to greatest or greatest to least.

0.45, 0.32, 0.76

To write these decimals in order **from least to greatest**, start by comparing them. The greater a decimal is, the closer it is to one whole. The smaller a decimal is the farther it is from one whole. The first thing you need to look at is the digit number in each decimal. These each have two digits in them, so you can compare them right away. Next, look at each number without the decimal and write them in order from the smallest to the greatest.

0.32, 0.45, 0.76

32 is smaller than 45, 45 is greater than 32 but smaller than 76, 76 is the largest number

The answer is 0.32, 0.45, 0.76.

### Examples

#### Example 1

Earlier, you were given a problem about Candace and her ribbons.

If the ribbons are 6.5 inches, 6.25 inches and 6.75 inches long, how can they be arranged from least to greatest?

First, add zeros to make the digit numbers equal.

6.50, 6.25, 6.75

Next, compare the numbers without a decimal to determine which is greater.

675 is greater than 650 and 650 is greater than 625

Then, list the numbers in order from least to greatest.

6.25, 6.5, 6.75

The answer is 6.25, 6.5, 6.75.

Candace's ribbons are arranged with the 6.25 inch ribbon first then the 6.5 inch ribbon and the 6.75 inch ribbon.

#### Example 2

Compare the two decimals.

0.256 _____ 0.17

First, add zeros to make the digit numbers equal.

0.256 ______ 0.170

Next, compare the numbers without a decimal to determine which is greater.

256 is greater than 170

Then, make the comparison between the decimals.

0.256 > 0.17

The answer is that 0.256 is greater than 0.17.

#### Example 3

Compare the two decimals.

0.0987 ______ 0.987

First, add zeros to make the digit numbers equal.

0.0987 ______ 0.9870

Next, compare the numbers without a decimal to determine which is greater.

9870 is greater than 987

Then, make the comparison between the decimals.

0.0987 < 0.987

The answer is that 0.0987 is less than 0.987.

#### Example 4

Compare the two decimals.

0.453 ______ 0.045

First, notice that the decimals have the same number of digits. This means that you can go directly to comparing the numbers without a decimal to determine which is greater.

453 is greater than 45

Then, make the comparison between the decimals.

0.453 > 0.045

The answer is that 0.453 is greater than 0.045.

#### Example 5

Order the decimals from least to greatest.

0.34, 0.745, 0.281

First, add zeros to make the digit numbers equal.

0.340, 0.745, 0.281

Next, compare the numbers without a decimal to determine which is greater.

0.745 is greater than 0.34 and 0.34 is greater than 0.281

Then, list the numbers in order from least to greatest.

0.281, 0.34, 0.745

The answer is 0.281, 0.34, 0.745.

### Review

Compare the following decimals using <, >, or =

- .4 ______ .2
- .67 ______ .75
- .90 ______ .9
- .234 ______ .54
- .123 ______ .87
- .954 ______ .876
- .32 ______ .032
- .8310 ______ .0009
- .9876 ______ .0129
- .8761 ______ .9992

Order the following decimals from least to greatest.

- .8, .9. .2,. 4
- .02, .03, .07, .05, .04
- .34, .21, .05, .55
- .07, .7, .007, .0007
- .87, 1.0, .43, .032, .5
- .067, .055, .023, .011, .042
- .55, .22, .022, .033, .055
- .327, .222, .0222, .321, .4
- .65, .6, .67, .678, .69
- .45, .045, 4.5, .0045, .00045

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.10.