Whole Number

Definition

A whole number is a positive integer that is not a fraction or a decimal. Whole numbers are the most basic and fundamental set of numbers, forming the foundation for various mathematical operations and concepts.

5 Must Know Facts For Your Next Test

1. Whole numbers can be used to represent quantities, such as the number of objects in a set or the number of times an action is performed.
2. Whole numbers are essential in the context of adding and subtracting mixed numbers, as the whole number part is a crucial component of the operation.
3. When working with integer exponents, whole numbers are used as the base, and the exponent represents the number of times the base is multiplied by itself.
4. Whole numbers are often used in scientific notation to represent very large or very small quantities, where the exponent indicates the power of 10.
5. The set of whole numbers is denoted by the symbol $\mathbb{N}$ or $\mathbb{Z}^{+}$, and it includes the numbers 0, 1, 2, 3, and so on.

Review Questions

• Explain how whole numbers are used in the context of adding and subtracting mixed numbers.
  • When adding or subtracting mixed numbers, the whole number part is a crucial component of the operation. The whole number represents the number of complete units, while the fractional part represents the remaining portion. In order to perform these operations, the whole number parts must be combined first, and then the fractional parts can be added or subtracted accordingly. Understanding the role of whole numbers in mixed number operations is essential for accurately solving problems involving the addition and subtraction of mixed numbers.
• Describe the relationship between whole numbers and integer exponents.
  • Whole numbers are used as the base in integer exponent expressions. The exponent represents the number of times the base is multiplied by itself. For example, $2^3$ means 2 multiplied by itself 3 times, which equals 8. Whole numbers are the foundation for working with integer exponents, as they provide the numerical values that are raised to the specified power. Understanding the connection between whole numbers and integer exponents is crucial for manipulating and simplifying expressions involving exponents.
• Analyze the role of whole numbers in the context of scientific notation.
  • In scientific notation, whole numbers are used to represent the coefficient of a very large or very small quantity. The whole number is multiplied by a power of 10, which represents the magnitude of the number. For instance, the number 6,500 can be written in scientific notation as $6.5 \times 10^3$, where the whole number 6.5 is the coefficient, and the exponent 3 indicates that the number is multiplied by 1,000 (10 raised to the power of 3). Understanding the function of whole numbers in scientific notation is essential for accurately representing and manipulating extremely large or small quantities in various scientific and mathematical contexts.

Related terms

Integer: An integer is a whole number, including positive, negative, and zero.

Natural Number: Natural numbers are the set of positive whole numbers, starting from 1.

Counting Number: Counting numbers are the set of positive whole numbers, used for counting and ordering objects.