Rational & Irrational Numbers — Simple Definitions, Examples & Quick Quiz (Class 8) | Math with Raabi

 

🌟 Rational & Irrational Numbers — Simple Definitions, Examples & Quick Quiz (Class 8)

Asslam o Alaikum learners! In this lesson we’ll learn what rational and irrational numbers are, see clear examples, and practice with a short 5-question quiz at the end.

You’ve already learned about Natural, Whole, and Integers. Now it’s time to explore how these numbers extend further. Let’s understand what makes a number rational or irrational — and how both together build the complete number system! 🌟

What are Rational Numbers?

Rational numbers are numbers that can be written in the form p/q, where p and q are integers and q ≠ 0. This group includes whole numbers, integers, fractions, terminating decimals, and repeating decimals.

Quick note: If a decimal terminates (for example 0.6 = 3/5) or repeats (for example 0.333… = 1/3), the number is rational.

What are Irrational Numbers?

Irrational numbers cannot be expressed as p/q with integers p and q. Their decimal forms neither terminate nor repeat. Famous irrational numbers include π and √2.

Examples (easy):

• Rational: 7, -3, 4/5, 0.125 ( = 1/8 ), 0.666… ( = 2/3 )
• Irrational: π ≈ 3.14159265…, √2 ≈ 1.41421356… , √3 , (these decimals never terminate or repeat)

🌸 Difference Between Rational & Irrational Numbers

Rational Numbers	Irrational Numbers
Can be written as p/q	Cannot be written as p/q
Have terminating or repeating decimals	Have non-terminating, non-repeating decimals
Examples: 1/2, 3.75, -4	Examples: √3, π, √7

Real Numbers — Putting Them Together

The set of real numbers is the collection of all rational and all irrational numbers. In short: every real number is either rational or irrational — and nothing else.

Concept Summary

Rational: can be written as p/q (q ≠ 0).

Irrational: cannot be written as p/q.

Real Numbers: include both Rational ∪ Irrational.

Rational vs Irrational

Rational	Irrational
5/9, -2, 0.75	√2, π

Both together make the set of Real Numbers 🌸

Worked Example — Identify the Set

Example: For each number below, say whether it is Rational or Irrational and give a short reason.

1. 5/22
2. √121
3. √56
4. -36/4
5. 0.272727…

Solutions (short):

1. 5/22 = 0.227272… (digits ‘27’ repeat) → Rational (can be written p/q).
2. √121 = 11 → Rational (an integer).
3. √56 ≈ 7.48… (non-terminating, non-repeating) → Irrational.
4. -36/4 = -9 → Rational (integer).
5. 0.272727… = 3/11 (repeating) → Rational.

Tip: Try to express the number as a fraction p/q. If you succeed, it’s rational. If the decimal neither terminates nor repeats and you can’t write it as p/q, it’s likely irrational.

Quick Practice (Write short answers)

1. Explain why 0 is a rational number in one line.
2. Is √9 rational or irrational? Give a short reason.
3. Give one example of a repeating decimal and write it as a fraction.

🎯 Quick Quiz — Rational & Irrational Numbers (Class 8)

Answer the short questions below. Click Show Answer to check your response. 🌸

Q1: Define a rational number in one sentence.

✅ A rational number can be written as p/q where p and q are integers and q ≠ 0.

Q2: Give two examples of irrational numbers.

✅ Examples: π (pi), √2 (square root of 2).

Q3: Is 0.75 rational or irrational? Explain briefly.

✅ Rational — 0.75 = 3/4 (terminating decimal → rational).

Q4: Which set does the number -9 belong to? (one-word answer)

✅ Integer (also Rational).

Q5: Explain in one line why √56 is irrational.

✅ √56 is not a ratio of two integers and its decimal expansion is non-terminating & non-repeating, so it is irrational.

📚 Previous Topics — Keep Learning!

• Understanding Sets in Mathematics (Class 8)
• Venn Diagrams for Class 8 — Types of Sets
• Real Numbers — Decimal & Fractions

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© Math with Raabi — Class 8 Mathematics Notes | Rational & Irrational Numbers explained with examples and practice for students.