RATIONAL NUMBERS
Definition Of Rational Numbers
A Rational Number is a real number written as a ratio of integers with a non-zero denominator.
More About Rational Numbers
Rational numbers are indicated by the symbol Q
Rational number is written in 
form, where p and q are integers and q is a non-zero denominator.
All the repeating or terminating decimal numbers are rational numbers.
Rational numbers are the subset of real numbers.
Examples of Rational Numbers
3/5,10.3,0.6,12/5,3/4 - All these are examples of rational numbers as they terminate.
Video Examples: Definition of Rational Numbers
Solved Example on Rational Numbers
Ques: Identify a number that is a rational number but not an integer.
Choices:
A. 
B. 10.3
C. - 3.523...
D. - 
Correct Answer: B
Solution:
Step 1: - 3.523... is a non-terminating and a non-repeating decimal number, so it is not a rational number.
Step 2: = - 5 is a rational number and also an integer.
Step 3: cannot be expressed as a quotient of two integers, so it is not a rational number.
Step 4: 10.3 = 103 / 10 is a rational number, but not an integer.
Quick Summary
- Rational numbers can be expressed as fractions.
- Rational numbers can be expressed as terminating or repeating decimals.
- Rational numbers are a subset of real numbers.
- The set of rational numbers is denoted by Q.
⚠️ Common Mistakes
- Confusing rational numbers with irrational numbers (e.g., square root of 2).
- Assuming all decimals are rational (non-repeating, non-terminating decimals are irrational).
- Forgetting that the denominator cannot be zero.
📋 Standards Alignment
CCSS.MATH. content.7.NS.A.2CCSS.MATH.content.8.NS.A.1
🍎 Teacher Insights
Use visual aids like number lines and pie charts to represent rational numbers. Emphasize the difference between rational and irrational numbers with examples. Relate rational numbers to real-world scenarios, such as sharing pizza or dividing quantities.🎓 Prerequisites
- Integers
- Fractions
- Decimals
- Division
Check Your Knowledge
Q1: Which of the following is a rational number but not an integer?
Q2: Which of the following numbers is NOT a rational number?
Frequently Asked Questions
Q: Is zero a rational number?
A: Yes, because it can be written as 0/1.
Q: Are all fractions rational numbers?
A: Yes, as long as the numerator and denominator are integers.
Q: Are all integers rational numbers?
A: Yes, because any integer 'n' can be written as n/1.