LESSON: Ordering Decimals

INTRODUCTION

READ: Compare Decimals

Compare Decimals

How can we compare decimals? When we compare decimals, we are trying to figure out which part of a whole is greater. To do this, we need to think about the number one.

1 is a whole. All decimals are part of one. The closer a decimal is to one, the larger the decimal is. How can we figure out how close a decimal is to one? This is a bit tricky, but if we look at the numbers and use place value we can figure it out.

Example

.45 ______ .67

Here we have two decimals that both have the same number of digits in them. When we compare our decimals need to have the same number of digits in them. Now we can look at the numbers without the decimal point. Is 45 or 67 greater?

67 is greater. We can say that sixty-seven hundredths is closer to one that forty-five hundredths.

Our answer is .45 < .67.

Steps for Comparing Decimals

1. Be sure that the decimals you are comparing have the same number of digits in them.
2. Think about the value of the number without the decimal point.
3. The larger the number, the closer it is to one.

What do we do if the decimals we are comparing don’t have the same number of digits?

Example

.567 ______ .64

Five hundred and sixty-seven thousandths seems greater. After all it is thousandths after all the tricky part is that thousandths are smaller than hundredths. Is this true? 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 .64 is larger than .567.

How can we compare without using a grid? Sometimes, we don’t have a grid to look at, what then? We can add zeros to make sure that digit numbers are equal. Then we can compare.

Example

.567 ______ .640

That made comparing very simple. 640 is larger than 567.

Our answer is that .567 < .640.

What about a decimal and a whole number? Sometimes, a decimal will have a whole number with it. If the whole number is the same, we just use the decimal part to compare.

Example

3.4 ______ 3.56

First, we add in our zeros.

3.40 ______ 3.56

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

Our answer is 3.4 < 3.56.

READ: Order Decimals

Order Decimals

Now that we know how to compare decimals, we can order them. Ordering means that we list a series of decimals according to size. We can write them from least to greatest or greatest to least. How can we order decimals? Ordering decimals involves comparing more than one decimal at a time. We need to compare them so that we can list them.

Example

.45, .32, .76

If we wanted to write these decimals in order from least to greatest, we can start by comparing them. The greater a decimal is the closer it is to one whole. The smaller a decimal is the further it is from one whole. Just like when we compared decimals, the first thing we need to look at is the digit number in each decimal. These each have two digits in them, so we can compare them right away. Next, we can look at each number without the decimal and write them in order from the smallest to the greatest.

.32, .45, .76

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

Our answer is .32, .45, .76

What about if we had decimals with different numbers of digits in them?

Example

Write these in order from greatest to least:

.45, .678, .23

Here we have two decimals with two digits and one decimal with three. We are going to need to create the same number of digits in all three decimals. We can do this by adding zeros.

.450, .678, .230

Now we can write them in order from greatest to least.

Our answer is .23, .45, .678

EXAMPLE 1

Ordering Decimals

EXAMPLE 2

CHECK Yourself! Compare and Order Decimals