# Classification of Numbers

## Numbers and Their Classifications

Why do we classify numbers? Why do we give them names, like integers, irrational numbers, or negative numbers? For the same reason, we classify anything. we want to make sure that everyone has an understanding of what specific numbers are called and what they mean. After all, there’s a difference between 25, and negative 32, and four to the sixth power.

In this Mometrix video, we’ll provide an overview of numbers and their classifications.

Numbers are our way of keeping order. We count the amount of money we have. We measure distance. We use percentages to indicate a sale. Numbers are an integral part of our everyday existence, whether they are whole numbers, rational numbers, or the first type of numbers we’re going to look at, real numbers.

**A real number** is any value of a continuous quantity that can represent distance on a number line. Essentially, it’s any number you can think of. Fifty (50) is a real number. One billion is a very large real number. Real numbers encompass three classifications of numbers, which we’ll talk about in a little bit. Whole numbers, rational numbers, and irrational numbers are all real numbers.

**Imaginary numbers** are not real numbers. They are complex numbers that are written as a real number multiplied by an imaginary unit (i). For instance, the square root of -1 calculates as the imaginary number “i” and the square root of -25 is 5i. Even though imaginary numbers aren’t “real numbers”, they do have value. Electricians use imaginary numbers when working with currents and voltage. Imaginary numbers are also used in complex calculus computations. So just because these numbers are called “imaginary” doesn’t mean they aren’t useful.

**Whole numbers** are the numbers we count with. One, two, three, four, and five are whole numbers. So are -17 and zero. Whole numbers do not have fractions or decimals.

All whole numbers are called **Integers**. Integers can be positive or negative whole numbers.

All integers and whole numbers are part of a bigger group called **rational numbers**. This group also includes fractions and decimals. That means ⅗ and 7.25 are rational numbers. Rational numbers can also be positive or negative.

Rational numbers have opposites, which are called **Irrational numbers**. These numbers can’t be written as a simple fraction. For example, 10 can be written as 52. That’s a simple fraction. Pi is the most famous irrational number. We have a close approximation of how to calculate Pi, but it’s just a close approximation. Pi is renowned for going on forever. That’s why it’s an irrational number. You can’t easily write it as a fraction.

**Natural numbers** are those that are positive integers, although there is some debate as to whether natural numbers start at zero or one. Negative numbers are, well, exactly that. They are the numbers below zero.

There are several other number classifications as well. Numbers are divided into **even** and **odd** numbers. If you can divide a number by two, that number is even. So, 24, 36, and 74 are all even numbers because if you divide them by two, you can 12, 18, and 37. Even numbers always end with 0, 2, 4, 6, or 8.

Odd numbers can’t be divided by two and leave a whole number. Any odd number divided by two will leave a fraction. So, 17 divided by two is 8.5. 23 divided by two is 11.5. All odd numbers will end in 1, 3, 5, 7, or 9.

Numerators and denominators form fractions, which are comprised of two integers. The number on top is the numerator; the number on the bottom is the denominator. The numerator, the top number, shows how many parts we have. The denominator, the bottom number, shows how many parts make a whole.

Let’s say you have six apples and three of the apples get eaten. The number of apples you have left over would be displayed as:

3/6

You would then divide 3, the top number, into 6, the bottom number, to determine the percentage of remaining apples. In this case, the number is 50 percent.

So that’s our look at numbers and their classifications. From whole numbers to irrational numbers, we need to know what to call numbers so we know what they mean.

I hope this overview was helpful.

See you guys next time!