ORDERING RATIONAL NUMBERS ON A NUMBER LINE

In this section, we will learn how to compare rational numbers on a number line and list them from least to greatest.

Example 1 : 

Order the following rational numbers numbers on a number and list them from least to greatest.

-3, 2, 1/3, -1.5

Solution : 

Step 1 :

First, let's plot -3, 2, 1/3 and -1.5 on a number line.

Step 2 : 

On a number line, numbers to the left are less than numbers to the right.

Step 3 : 

On the number line above, read the numbers from left to right to place them in order from least to greatest.

The following numbers are ordered from least to greatest.

-3, -1.5, 1/3, 2

Example 2 : 

Order the following rational numbers numbers on a number and list them from least to greatest.

-9/2, -4.75, -5

Solution : 

Step 1 :

First convert the fraction -9/2 into decimal.

-9/2  =  -4.5

Step 2 :

First, let's plot -9/2 (or -4.5), -4.75 and -5 on a number line.

Step 3 : 

On a number line, numbers to the left are less than numbers to the right.

Step 4 : 

On the number line above, read the numbers from left to right to place them in order from least to greatest.

The following numbers are ordered from least to greatest.

-5, -4.75, -9/2

Example 3 : 

Order the following rational numbers numbers from least to greatest.

4 1/2, 4.7, 41/10

Solution : 

Step 1 :

Let us convert the mixed number 4 1/2 and fraction  41/10 into decimals. 

Because, if we convert them into decimals, they can be easily plotted on the number line. 

Step 2 :

First convert the mixed number 4 1/2 into decimal

4 1/2   =  4.5

Step 3 :

Now, convert the fraction 41/10 into decimal. 

41/10  =  4.1

Step 4 :

Plot 4 1/2 (or 4.5), 4.7, 41/10 (or 4.1) on a number line.

Step 5 :

On the number line above, read the numbers from left to right to place them in order from least to greatest.

The following numbers are ordered from least to greatest.

4.1, 4.5, 4.7

or 

41/10, 4 1/2, 4.7

Example 4 : 

Order the following rational numbers numbers from least to greatest.

-4 3/4, -7/2, -4.25

Solution : 

Step 1 :

Let us convert the mixed number -4 3/4 and fraction  -7/2 into decimals. 

Because, if we convert them into decimals, they can be easily plotted on the number line. 

Step 2 :

First convert the mixed number -4 3/4 into decimal

-4 3/4   =  -4.75

Step 3 :

Now, convert the fraction 41/10 into decimal. 

-7/2  =  -3.5

Step 4 :

Plot -4 3/4 (or -4.75), -7/2 (or -3.5) and -4.25 on a number line.

Step 5 :

On the number line above, read the numbers from left to right to place them in order from least to greatest.

The following numbers are ordered from least to greatest.

-4.75, -4.25, -3.5

or 

-4 3/4, -4.25, -7/2

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