<< Chapter < Page Chapter >> Page >
7 4 = 1 3 4 9 2 = −4 1 2 8 3 = 2 2 3

[link] shows the number line with all the points plotted.

There is a number line shown that runs from negative 6 to positive 6. From left to right, the numbers marked are negative 5, negative 9/2, negative 4/5, 1/5, 4/5, 8/3, and 3. The number negative 9/2 is halfway between negative 5 and negative 4. The number negative 4/5 is slightly to the right of negative 1. The number 1/5 is slightly to the right of 0. The number 4/5 is slightly to the left of 1. The number 8/3 is between 2 and 3, but a little closer to 3.

Locate and label the following on a number line: 4 , 3 4 , 1 4 , −3 , 6 5 , 5 2 , and 7 3 .

Locate and plot the integers, 4 , −3 .

Locate the proper fraction 3 4 first. The fraction 3 4 is between 0 and 1. Divide the distance between 0 and 1 into four equal parts then, we plot 3 4 . Similarly plot 1 4 .

Now locate the improper fractions 6 5 , 5 2 , 7 3 . It is easier to plot them if we convert them to mixed numbers and then plot them as described above: 6 5 = 1 1 5 , 5 2 = −2 1 2 , 7 3 = 2 1 3 .

There is a number line shown that runs from negative 6 to positive 6. From left to right, the numbers marked are negative 3, negative 5/2, negative 1/4, 3/4, 6/5, 7/3, and 4. The number negative 5/2 is halfway between negative 3 and negative 2. The number negative 1/4 is slightly to the left of 0. The number 3/4 is slightly to the left of 1. The number 6/5 is slightly to the right of 1. The number 7/3 is between 2 and 3, but a little closer to 2.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Locate and label the following on a number line: −1 , 1 3 , 6 5 , 7 4 , 9 2 , 5 , 8 3 .

There is a number line shown that runs from negative 4 to positive 5. From left to right, the numbers marked are negative 8/3, negative 7/4, negative 1, 1/3, 6/5, 9/2, and 5. The number negative 8/3 is between negative 3 and negative 2 but slightly closer to negative 3. The number negative 7/4 is slightly to the right of negative 2. The number 1/3 is slightly to the right of 0. The number 6/5 is slightly to the right of 1. The number 9/2 is halfway between 4 and 5.

Got questions? Get instant answers now!

Locate and label the following on a number line: −2 , 2 3 , 7 5 , 7 4 , 7 2 , 3 , 7 3 .

There is a number line shown that runs from negative 4 to positive 5. From left to right, the numbers marked are negative 7/3, negative 2, negative 7/4, 2/3, 7/5, 3, and 7/2. The number negative 7/3 is between negative 3 and negative 2 but slightly closer to negative 2. The number negative 7/4 is slightly to the right of negative 2. The number 2/3 is slightly to the left of 1. The number 7/5 is between 1 and 2, but closer to 1. The number 7/2 is halfway between 3 and 4.

Got questions? Get instant answers now!

In [link] , we’ll use the inequality symbols to order fractions. In previous chapters we used the number line to order numbers.

  • a<b a is less than b ” when a is to the left of b on the number line
  • a>b a is greater than b ” when a is to the right of b on the number line

As we move from left to right on a number line, the values increase.

Order each of the following pairs of numbers, using<or>. It may be helpful to refer [link] .

2 3 ___ −1 −3 1 2 ___ −3 3 4 ___ 1 4 −2 ___ 8 3

There is a number line shown that runs from negative 4 to positive 4. From left to right, the numbers marked are negative 3 and 1/2, negative 3, negative 8/3, negative 2, negative 1, negative 3/4, negative 2/3, and negative 1/4. The number negative 3 and 1/2 is between negative 4 and negative 3 The number negative 8/3 is between negative 3 and negative 2, but closer to negative 3. The numbers negative 3/4, negative 2/3, and negative 1/4 are all between negative 1 and 0.

Be careful when ordering negative numbers.


  1. 2 3 ___ −1 2 3 is to the right of −1 on the number line. 2 3 > −1


  2. −3 1 2 ___ −3 −3 1 2 is to the left of −3 on the number line. −3 1 2 < −3


  3. 3 4 ___ 1 4 3 4 is to the left of 1 4 on the number line. 3 4 < 1 4


  4. −2 ___ 8 3 −2 is to the right of 8 3 on the number line. −2 > 8 3
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Order each of the following pairs of numbers, using<or>:

1 3 ___ −1 −1 1 2 ___ −2 2 3 ___ 1 3 −3 ___ 7 3 .

> > < <

Got questions? Get instant answers now!

Order each of the following pairs of numbers, using<or>:

−1 ___ 2 3 −2 1 4 ___ −2 3 5 ___ 4 5 −4 ___ 10 3 .

< < > <

Got questions? Get instant answers now!

Locate decimals on the number line

Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.

Locate 0.4 on the number line.

A proper fraction has value less than one. The decimal number 0.4 is equivalent to 4 10 , a proper fraction, so 0.4 is located between 0 and 1. On a number line, divide the interval between 0 and 1 into 10 equal parts. Now label the parts 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0. We write 0 as 0.0 and 1 and 1.0, so that the numbers are consistently in tenths. Finally, mark 0.4 on the number line. See [link] .

There is a number line shown that runs from 0.0 to 1. The only point given is 0.4, which is between 0.3 and 0.5.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Locate on the number line: 0.6.

There is a number line shown that runs from 0.0 to 1. The only point given is 0.6, which is between 0.5 and 0.7.

Got questions? Get instant answers now!

Locate on the number line: 0.9.

There is a number line shown that runs from 0.0 to 1. The only point given is 0.9, which is between 0.8 and 1.

Got questions? Get instant answers now!

Locate −0.74 on the number line.

The decimal −0.74 is equivalent to 74 100 , so it is located between 0 and −1 . On a number line, mark off and label the hundredths in the interval between 0 and −1 . See [link] .

There is a number line shown that runs from negative 1.00 to 0.00. The only point given is negative 0.74, which is between negative 0.8 and negative 0.7.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Locate on the number line: −0.6 .

There is a number line shown that runs from negative 1.00 to 0.00. The only point given is negative 0.6, which is between negative 0.8 and negative 0.4.

Got questions? Get instant answers now!

Locate on the number line: −0.7 .

There is a number line shown that runs from negative 1.00 to 0.00. The only point given is negative 0.7, which is between negative 0.8 and negative 0.6.

Got questions? Get instant answers now!

Which is larger, 0.04 or 0.40? If you think of this as money, you know that $0.40 (forty cents) is greater than $0.04 (four cents). So,

0.40 > 0.04

Again, we can use the number line to order numbers.

  • a<b a is less than b ” when a is to the left of b on the number line
  • a>b a is greater than b ” when a is to the right of b on the number line

Where are 0.04 and 0.40 located on the number line? See [link] .

There is a number line shown that runs from negative 0.0 to 1.0. From left to right, there are points 0.04 and 0.4 marked. The point 0.04 is between 0.0 and 0.1. The point 0.4 is between 0.3 and 0.5.

We see that 0.40 is to the right of 0.04 on the number line. This is another way to demonstrate that 0.40>0.04.

How does 0.31 compare to 0.308? This doesn’t translate into money to make it easy to compare. But if we convert 0.31 and 0.308 into fractions, we can tell which is larger.

Practice Key Terms 6

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask