Identifying Rational Numbers

This page delves into the methods for identifying rational numbers and distinguishing them from irrational numbers.

Definition: How to identify rational numbers involves checking if they can be expressed as p/q where p and q are integers and q ≠ 0.

Example: 0.923076923076923... is a rational number because it has a recurring pattern of decimals (923076).

Highlight: √2 is an example of an irrational number as it produces a non-terminating, non-recurring decimal (1.414213562...).

Vocabulary: Irrational numbers are numbers that cannot be expressed as a simple fraction and have non-terminating, non-recurring decimal expansions.

Example: The process of identifying rational numbers includes:

1. Checking if it's an integer or fraction
2. Examining decimal patterns for termination or recurrence
3. Attempting to express it in p/q form

Understanding Rational Numbers

This page introduces the fundamental concept of rational numbers in maths. A comprehensive explanation reveals that rational numbers take the form p/q, where both p and q are integers and q cannot equal zero.

Definition: A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero.

Example: The following are all rational numbers:

• 56 $as 56/1$
• 0 $as 0/1$
• 1/2
• √16 (as 4)
• -3/4
• 0.3 $as 3/10$

Highlight: Rational numbers encompass several number types including natural numbers, whole numbers, integers, fractions of integers, and certain decimals.

Vocabulary: Terminating decimals (like 0.35) and recurring decimals (like 0.333...) are both types of rational numbers.