Identify rational and irrational numbers

Key Notes :

1️⃣ What are Numbers?

Numbers are symbols we use to count, measure, and label things.
They can be classified into Rational and Irrational numbers.

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2️⃣ Rational Numbers (✅)

A rational number is any number that can be written as a fraction p/q, where:

• p = integer
• q = non-zero integer (q ≠ 0)

🟢 Examples of Rational Numbers:

• Fractions: 1/2, -3/4
• Whole numbers: 5, 0, -7
• Decimals that terminate or repeat: 0.75, 0.333…

📝 Key Points:

• ✅ Can be written as fractions
• ✅ Decimal form terminates (stops) or repeats
• ✅ Can be positive or negative

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3️⃣ Irrational Numbers (❌)

An irrational number cannot be written as a fraction.
Its decimal form never ends and never repeats.

🔴 Examples of Irrational Numbers:

• √2, √3, √5
• π (Pi ≈ 3.14159…)
• e (Euler’s number ≈ 2.718…)

📝 Key Points:

• ❌ Cannot be written as a fraction
• ❌ Decimal form goes on forever
• ❌ Non-repeating decimals

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4️⃣ Quick Tips to Identify ✅ vs ❌

Clue	Rational	Irrational
Fraction form exists?	✅ Yes	❌ No
Decimal form?	✅ Terminates/Repeats	❌ Non-terminating/non-repeating
Examples	2, -3, 1/4, 0.666…	√2, π, √3

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5️⃣ Fun Emojis Trick to Remember

• ✅ Rational = “R for Regular” → neat fractions, repeats nicely ✨
• ❌ Irrational = “I for Infinite” → decimals never end 🌌

Learn with an example

Let’s practice!🖊️