The Real Number System
The Real Number System is a Grade 8 math topic in Saxon Math Course 3, Chapter 2, where students learn to classify all real numbers into subsets including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Understanding the hierarchy of the real number system helps students categorize any number and recognize relationships between number types.
Key Concepts
New Concept Mathematics is built upon a complete system of numbers, called the real numbers, which includes all rational and irrational values on the number line. What’s next Our journey begins by exploring the building blocks of this system. Next, you'll discover a fascinating type of number: the irrational numbers.
Common Questions
What are the subsets of the real number system?
The real number system includes natural numbers (counting numbers), whole numbers (natural plus zero), integers (positive and negative whole numbers and zero), rational numbers (fractions and repeating/terminating decimals), and irrational numbers (non-repeating non-terminating decimals).
What is the difference between rational and irrational numbers?
Rational numbers can be written as a fraction of two integers and produce terminating or repeating decimals. Irrational numbers cannot be expressed as fractions and have non-terminating non-repeating decimal expansions, such as pi and the square root of 2.
Are all integers rational numbers?
Yes. Every integer can be written as a fraction with denominator 1, so all integers are rational numbers. But not all rational numbers are integers.
How do you classify a number in the real number system?
Check if it is a counting number, then whether it is a whole number, then an integer, then rational, then irrational. Each category includes all the categories above it.
Where is the real number system taught in Grade 8?
It is covered in Saxon Math Course 3, Chapter 2: Number and Operations and Geometry.