ORDERING REAL NUMBERS ON A NUMBER LINE

We can compare and order real numbers on a number line and list them from least to greatest.

Example 1 : 

Order √22, π + 1 and 4 1/2 on a number line. Then list them in the order from least to greatest. 

Solution : 

Step 1 :

First approximate √22.

√22 is between 4 and 5. Since we don’t know where it falls between 4 and 5, we need to find a better estimate for √22. 

So that we can compare it to 4 1/2.

Since 22 is closer to 25 than 16, use squares of numbers between 4.5 and 5 to find a better estimate of √22. 

4.5²  =  20.25

4.6²  =  21.16

4.7²  =  22.09

4.8²  =  23.04

Since 4.7²  =  22.09, an approximate value for  √22 is 4.7.

That is, 

 √22  ≈  4.7 -----(1)

Step 2 :

An approximate value of π is 3.14. So an approximate value of π + 1 is 4.14.

That is, 

 π + 1  ≈  4.14 -----(2)

Step 3 :

The value of 4 1/2 is 4.5. 

That is, 

 4 1/2  =  4.5 -----(3)

Step 4 :

Plot  √22, π + 1 and 4 1/2 on a number line. 

Step 5 :

Read the numbers from left to right to list them in order from least to greatest..

π + 1, 4 1/2, √22

Example 2 : 

Order π², 10 and √75 on a number line. Then list them in the order from least to greatest. 

Solution : 

Step 1 :

An approximate value of π is 3.14. So an approximate value of π² is 9.86.

That is, 

π²  ≈  9.86 -----(2)

Step 2 :

First approximate √75.

√75 is between 8 and 9. 

Since we do not know the exact value of √75, we have to mark √75 on a number line at somewhere between 8 and 9. 

Step 3 :

Now, plot π², 10 and √75 on a number line

Step 4 :

Read the numbers from left to right to list them in order from least to greatest..

√75,  π², 10

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