Introduction

Consider all the numbers you can think of—there are likely too many to count, let alone think of all at once. There are infinite numbers. When dealing with a concept like infinity, it is helpful to categorize the numbers.

There are three main categories of numbers: Whole Numbers, Integers, and Real Numbers. Throughout the Resource Center, references will be made to whole numbers and integers in regard to rounding. The numbers you will use throughout your life are real numbers.

Real World Application

To work in computer programming and with databases, it is important to understand the different classifications of numbers. Some programming languages use data types such as integers and real numbers as well as strings, null values, and other data types. Here is a piece of coding from the coding language Python that uses integers.

This video illustrates the lesson material below. Watching the video is optional.

• Whole Numbers, Integers, Real Numbers (05:36 mins) | Transcript

Whole Numbers

When you first learned to count, you learned by counting the numbers on your hand. You also learned the concept of 0. These are whole numbers.

Figure 1

Integers

Negative numbers and whole numbers are considered integers.

Figure 2

Real Numbers

There are an infinite number of numbers between each integer. These numbers, as well as all integers, are considered real numbers.

Fractions and decimals fall into this category.

Figure 3

Conclusion

Figure 4 can help you visualize the relationship between each category.

Everything within the biggest circle are real numbers. This includes numbers such as \(\large\frac{1}{3}\), -52, and 198.

Every number within the second biggest circle is considered an integer. This includes negative and positive numbers.

Everything within the smallest circle are whole numbers. This includes all positive integers.

Figure 4

To better understand how something can be a part of one set or multiple sets, consider this example of verses in the standard works of the Church.

Figure 5

A verse that is in the Bible is part of the Standard Works, but it isn’t part of the Pearl of Great Price or the Articles of Faith. In contrast, the 13th Article of Faith is a part of all three categories: the Articles of Faith, the Pearl of Great Price, and the Standard Works of the Church.

Things to Remember

• Whole numbers are positive countable numbers.
• Integers are all positive and negative complete numbers.
• Real numbers are all integers and every number (fraction and decimal) between.

Practice Problems

1. Which of the following numbers are whole numbers? (Indicate all that apply.) (
   Video Solution

   x

   Solution: c, d, and e.
   Details:
   

   
   (Whole Numbers, Integers, and Real Numbers #1 (01:19 mins) | Transcript)
   Transcript )
   
   1. -2
   2. -1.57
   3. 0
   4. 1
   5. 5
   6. 9.9999
2. Which of the following numbers are integers? (Indicate all that apply.) (
   Video Solution

   x

   Solution: a, c, d, and e.
   Details:
   

   
   (Whole Numbers, Integers, and Real Numbers #2 (01:27 mins) | Transcript)
   Transcript )
   
   1. -2
   2. -1.57
   3. 0
   4. 1
   5. 5
   6. 9.9999
3. Which of the following numbers are real numbers? (Indicate all that apply.) (
   Video Solution

   x

   Solution: a, b, c, d, e, and f.
   Details:
   

   
   (Whole Numbers, Integers, and Real Numbers #3 (01:57 mins) |Transcript)
   Transcript )
   
   1. -2
   2. -1.57
   3. 0
   4. 1
   5. 5
   6. 9.9999

Need More Help?

1. Study other Math Lessons in the Resource Center.
2. Visit the Online Tutoring Resources in the Resource Center.
3. Contact your Instructor.
4. If you still need help, Schedule a Tutor.