Math Flashcards: Real, Rational, Integers

Study Notes

Types of Numbers

Whole numbers and integers are synonymous; both encompass all positive and negative whole numbers.
Rational numbers include integers and can be expressed as fractions (a/b) where a and b are integers, with b not equal to zero.
All rational numbers may have terminating or repeating decimal representations.

Rational Numbers Characteristics

Can be represented as fractions.
Terminating decimals (e.g., 0.5) and repeating decimals (e.g., 0.333...) are rational forms.

Irrational Numbers

Defined as numbers that cannot be expressed as simple fractions.
Exhibit non-terminating, non-repeating decimal patterns, such as π (pi) or √2.

Integer Definition

Comprised of positive whole numbers, negative whole numbers, and zero.

Examples of Number Types

Whole numbers include 0, 47, and 279; they can also include fractions like 24/8 and whole numerators like 56/1.
Examples of irrational numbers include repeating decimals, roots of non-perfect squares (e.g., √6), and π.
Integer examples comprise -4, -12, and -√100, demonstrating they can be negative or zero.
Rational number examples involve decimals or fractions like 2.45, -0.6, and 24 1/2.

True or False Statements

Every number is a real number if it is not imaginary. (True)
All integers qualify as rational numbers. (True)
Not all negative numbers are classified as integers. (False)
3.87655 is considered a rational number due to its decimal form. (True)
√7 is categorized as a real number because it is not imaginary. (True)
Not all fractions can be classified as integers; they are often rational. (False)

Description

Explore the definitions and relationships between whole numbers, integers, and rational numbers with these informative flashcards. Gain a clearer understanding of how these mathematical concepts intersect and their classifications in mathematics.