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Whole Numbers, Integers, and Real Numbers
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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

This is a screenshot of some computer coding. There are five lines of text. They have the following text. CREATE TABLE people ( id INTEGER, name TEXT, age INTEGER )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

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.

An image of a hand with each finger numbered from 1 to 5. 

Figure 1

Integers

Negative numbers and whole numbers are considered integers.

A number line with zero in the middle and positive numbers 1 through 5 to the right and negative numbers 1 through 5 to the left. 

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.

This image shows the infinite number of numbers between each integer, which means these numbers are considered real numbers. There are three number lines, the first showing -5 through 0 through 5; the second line highlights what is between 1 and 2 which shows 1.1 through 1.9; and the third line highlights what is between 1.5 and 1.6 which shows 1.51 through 1.59. 

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.

A figure that shows the relationship between whole numbers, integers, and real numbers. Whole numbers are a subset of integers, and integers are a subset of real numbers. 

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.

A figure that shows the relationship between the Articles of Faith, the Pearl of Great Price, and the standard works. The Articles of Faith are contained within the Pearl of Great Price, and the Pearl of Great Price is contained within the standard works. 

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
    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
    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
    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.
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