The Different Types of Numbers, Explained

When taking the SAT or ACT, or when navigating your way through a math course, chances are you’ll be required to know the definitions of different types of numbers. You wouldn’t believe how many students aren’t sure what tests and teachers mean when they use words like “real numbers,” “rational numbers,” or “complex numbers.” And many students are shaky on what an integer is! Is 0 an integer? We’ll see. Today, our goal is to look at the different classifications of numbers and learn what types of numbers those classifications include. By the end of this blog article, you’ll be an expert on the different types of numbers! And once you are, you’ll be primed for success on the math section of the SAT or ACT, or even a difficult math exam! Ready to go?

Natural Numbers

The first type of number we’ll take a look at is natural numbers. Natural numbers are traditionally known as the “counting numbers,” and they include 1, 2, 3, 4, and so on. However, some definitions of natural numbers also include 0. So, for our purpose, we can define the natural numbers as all non-negative integers.

What are some examples of a natural number? 513. 72. 1,000,034. But not 3/5. Not -7. Not the square root of 2.

Whole Numbers

Whole numbers include 0, 1, 2, 3, 4… and so on. Negative numbers are not normally classified as whole numbers. If negative numbers were classified as whole numbers, whole numbers would be the same thing as integers. As it stands, though, whole numbers are the same as natural numbers, if your definition of natural numbers includes 0.

What are some examples of whole numbers? 74. 904,984. But not -3. Not 1.7.

Integers

Let’s learn once and for all what an integer is. An integer is a positive or negative whole number, including 0.

What are some examples of integers? -72. 55. 2,000,384. But not 1.4. Not -11.4.

Rational Numbers

Rational numbers are numbers that can be expressed as the ratio of an integer to a non-zero integer. All integers are rational numbers, but not all rational numbers are integers! What are some rational numbers? 5. 11. 22. 3/4. -1/7. And so on. Anything you can express as a fraction is a rational number.

Real Numbers

Real numbers are numbers that can be represented as a decimal that have either a finite or an infinite number of digits after the decimal point. Real numbers can be positive, negative, or 0. All rational numbers are real numbers, but not all real numbers are rational numbers.

Irrational Numbers

Irrational numbers are real numbers that are NOT rational. That means they can’t be expressed as the ratio of one integer to a non-zero integer. All square roots of natural numbers that are NOT perfect squares are irrational. Pi is another example of an irrational number. The square root of 71 is another example.

Imaginary Numbers

Imaginary numbers can be expressed as the product of a real number and i, where is the square root of -1. As -1 is a negative number, it is not possible for a negative number to have a square root in the “real” world. Hence, the concept of “imaginary number” depends on the imaginary concept of taking the square root of a negative number. Fun fact: the number 0 can be classified as both a real and an imaginary number.

Complex Numbers

Complex numbers include real numbers, imaginary numbers, and the sums and differences of real and imaginary numbers. Complex numbers are numbers that can be expressed in the format a+bi, where a and b can be anything, and i is the square root of -1.

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That’s it! For more math articles, as well as a plethora of SAT and ACT prep tips, check out the rest of our blog. Looking for 1-on-1 ACT or SAT prep tutoring to help you with the college application process? Want to join an SAT or ACT group class? Contact us today!  We’re perfect-scoring tutors with years of experience helping students achieve the SAT and ACT scores they need to make their dreams a reality!

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