REAL NUMBERS
Definition Of Real Numbers
Real Numbers include all the rational and irrational numbers.
More About Real Numbers
Real numbers are denoted by the letter R.
Real numbers consist of the natural numbers, whole numbers, integers, rational, and irrational numbers. 
Examples of Real Numbers
Natural numbers, whole numbers, integers, decimal numbers, rational numbers, and irrational numbers are the examples of real numbers.
Natural Numbers = {1, 2, 3,...}
Whole Numbers = {0, 1, 2, 3,...}
Integers Z = {..., -2, -1, 0, 1, 2,...}
3/5, 10.3, 0.6, 12/5, 3/4, 3.46466466646666..., √ 2, √ 3 are few more examples.
Video Examples: What Are The Real Numbers?
Solved Example on Real Numbers
Ques: Name the subset(s) of the real numbers to which '- 25' belongs.
Choices:
A. integers, rational numbers, real numbers
B. whole numbers, integers, rational numbers, real numbers
C. natural numbers, whole numbers, integer numbers, rational numbers, real numbers
D. irrational numbers, real numbers
Correct Answer: A
Solution:
Step 1: - 25 is an integer.
Step 2: The set of integers is a subset of the rational numbers and the real numbers
Step 3: Therefore, the subsets to which - 25 belongs to are: integers, rational numbers, and the real numbers.
Quick Summary
- Real numbers are denoted by the letter R.
- Real numbers consist of natural numbers, whole numbers, integers, rational, and irrational numbers.
- Examples include natural numbers, whole numbers, integers, decimal numbers, rational numbers, and irrational numbers.
🍎 Teacher Insights
Use visual aids like number lines to demonstrate the density and continuous nature of real numbers. Emphasize the distinction between rational and irrational numbers with clear examples.🎓 Prerequisites
- Integers
- Rational Numbers
- Irrational Numbers
Check Your Knowledge
Q1: Which of the following is a real number?
Q2: Which set of numbers does -25 belong to?
Frequently Asked Questions
Q: Are all integers real numbers?
A: Yes, integers are a subset of real numbers.
Q: Are imaginary numbers real numbers?
A: No, imaginary numbers are not real numbers. Real numbers, when squared, result in a non-negative number.