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.



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.







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...



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.