Classifying Numbers

In the vast realm of mathematics, numbers take on different forms and possess distinct characteristics.

Understanding the classification of numbers is a crucial skill for Grade 7 students as they delve deeper into mathematical concepts. In this article, we will embark on a journey to explore the fascinating world of number classification

Table of Contents:

• How to Classify Numbers?
• Difference Between Rational and Irrational Numbers
• FAQs

How to Classify Numbers?

From natural numbers to irrational numbers, from integers to real numbers, we will unravel the properties and relationships between these different types of numbers.

Natural Numbers:

Natural numbers, denoted by the symbol “N,” are the counting numbers: 1, 2, 3, 4, 5, and so on.

They represent the quantities we use for counting and are always positive.

Whole Numbers:

Whole numbers, denoted by the symbol “W,” include all the natural numbers along with zero: 0, 1, 2, 3, 4, and so on.

Whole numbers encompass all the counting numbers and include zero as well.

Integers:

Integers, denoted by the symbol “Z,” are the set of whole numbers and their negatives, including zero: …, -3, -2, -1, 0, 1, 2, 3, …

Integers include both positive and negative numbers, along with zero.

Rational Numbers:

Rational numbers, denoted by the symbol “Q,” are numbers that can be expressed as a fraction, where the numerator and denominator are both integers.

Rational numbers can be either positive or negative, and they include integers and fractions, such as 1/2, -3/4, 2, -5, and so on.

Irrational Numbers:

Irrational numbers cannot be expressed as fractions or ratios of integers.

They include numbers such as the square root of 2 (√2) or pi (π).

Irrational numbers are non-repeating and non-terminating decimals.

Real Numbers:

Real numbers, denoted by the symbol “R,” represent the complete set of rational and irrational numbers.

Real numbers include all rational and irrational numbers, covering the entire number line.

Difference Between Rational and Irrational Numbers

Rational Numbers:

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. They can be positive or negative. For example, 1/2, -3/4, 5, and -7 are all rational numbers.

Rational numbers can also include integers since every integer can be expressed as a fraction with a denominator of 1. The defining characteristic of rational numbers is that they can be written in the form p/q, where p and q are integers and q is not equal to 0.

Example:

1/2: This is a positive rational number because it can be expressed as a fraction with integers as numerator and denominator.

-3/4: This is a negative rational number since it can be written as a fraction with integers as numerator and denominator.

5: This is a rational number because it can be expressed as 5/1, a fraction with integers as numerator and denominator.

-7: This is a rational number because it can be written as -7/1, a fraction with integers as numerator and denominator.

Irrational Numbers:

Irrational numbers, on the other hand, cannot be expressed as fractions or ratios of integers. They are non-repeating and non-terminating decimals.

Common examples of irrational numbers include the square root of 2 (√2), pi (π), and the golden ratio (φ). These numbers cannot be precisely represented by fractions or decimals with a finite number of digits after the decimal point.

Example:

√2 (square root of 2): This is an irrational number because it cannot be expressed as a fraction or ratio of integers. It is a non-repeating and non-terminating decimal.

π (pi): Pi is another example of an irrational number. Its decimal representation is non-repeating and non-terminating, making it impossible to express as a fraction of integers.

√3 (square root of 3): This is also an irrational number since it cannot be expressed as a fraction or ratio of integers.

Classifying Numbers FAQs

Grade 7 Science Worksheets

• Elements and Compounds
• Solar Energy
• Photosynthesis
• Electricity and Magnetism
• Law of conservation of energy
• Periodic table
• Properties of Matter
• Waves
• Energy Resources 
• Weather and Climate
• Immune, Circulatory and Digestive Systems
• Organs in Multi-cellular Organism
• Sedimentary, Igneous, and Metamorphic Rocks
• Structure of the Earth
• Law of Conservation of Mass
• Physical and Chemical Changes
• Scientific Method
• Human Digestive System
• Environmental Science
• Renewable and Non-renewable energy Resources
• Characteristics of Living Organisms
• Life Science
• Earth and Space Science
• Solar Eclipse
• Heat Technology
• Newton’s Laws of Motions
• Physical Science
• Tools, Measurement and SI Units
• Earth Atmosphere
• Interactions of Living things
• The Earth Ecosystem
• Organelles in Plant and Animal cells
• Layers of the Earth
• Cycles in Nature

Grade 7 Math Worksheets

• Fractions
• Linear equations word problems
• Statistics
• Properties of Parallel Line
• Finding slope from an equation
• Identifying Quadrilaterals
• Percent Change
• Properties of addition and multiplication
• Pythagorean Theorem
• Solving two step inequalities
• Symmetry
• Fractions to Decimals (New)
• Whole Number Exponents with Integer Bases (New)
• Adding and Subtracting Fractions (New)
• Integer Addition and Subtraction (New)
• Dividing Mixed Numbers (New)
• Basics of Coordinate Geometry (New)