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:
Now, why are 2 and 0 examples of such numbers?
It is because 2 and 0 can be written as
x can be any number since 0 divided by any number is zero
Decimal expansion:
We can also write rational numbers as a decimals.
We do this by performing a quick division that is dividing the numerator by the denominator
For instance,
or
Notice that you can continue division to keep getting zeros for the decimal places after 4
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
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
Test your understanding of this lesson with the rational numbers quiz below.

Jul 20, 17 10:41 PM
A water tank is emptied at a constant rate. Initially, 36,000 gallons of water were in the tank. A the end of five hours, 16,000 gallons remained. How
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.