Rational Numbers

Rational numbers are any numbers that can be written as a fraction. In other words, you can rewrite the number so it will have a numerator and a denominator.
They have the form  
a / b
 in which a and b are integers and b not equal to zero.

Notice that we said b cannot be zero. It is because any number divided by 0 has no answer.

Examples of numbers that are rational are:

 
2 / 3
, 
5 / 2
, 
1 / 4
,  2, 
-8 / 2
,  and 0  
 
2 / 3
, 
5 / 2
, 
1 / 4
,  2, 
-8 / 2
,  and 0  

Now, why are 2 and 0 examples of such numbers?

It is because 2 and 0 can be written as

 
2 / 1
  and  
0 / x
 
2 / 1
  and  
0 / x

Decimal expansion of rational numbers


x can be any number since 0 divided by any number is zero.

We can also write rational numbers as decimals.

We do this by performing a quick division that is dividing the numerator by the denominator.

For instance,

2 / 5
= 0.4
or

2 / 5
= 0.400000000

Notice that you can continue division to keep getting zeros for the decimal places after 4.

Terminating decimal

The bar on top of 0 means that if we continue to perform long division, we will keep getting an infinite number of zeros.

Another way to convert  
2 / 5
 into a decimal is to notice that we can multiply 5 by 20 and 2 by 20


We will get  
40 / 100


And  
40 / 100
= 0.40


Diving by 100 or any other power of 10 is a straightforward process.

If you are dividing by 10, just move the decimal point one place to the left.

If you are dividing by 100, just move the decimal point 2 places to the left.

and so forth...

For  
40 / 100
, the decimal point is after 0 for 40.


Moving that two places to the left bring the decimal point right before the 4.

A rational number can have either repeating decimal expansion or terminating decimal expansion.

Repeating decimal expansion:

A decimal expansion in which the numbers repeat in exactly the same order.

For example, 0.251251251251 is a repeating decimal expansion because 251 keeps repeating in the same order.

Terminating decimal expansion:

A decimal expansion that ends in all zeros.

For example, 0.150 is a terminating decimal expansion.

Figure summarizing rational numbers

Rational numbers

Test your understanding of this lesson with the rational numbers quiz below.

Recent Articles

RSS

  1. Write a Polynomial from Standard Form to Factored Form

    Oct 14, 21 05:41 AM

    Learn how to write a polynomial from standard form to factored form

    Read More

Check out some of our top basic mathematics lessons.

Formula for percentage

Types of angles

Area of ​​irregular shapes

Math problem solver

Math skills assessment

Compatible numbers

Surface area of ​​a cube

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.