Types of Numbers & Place Value

🎯 Learning Objective

Identify natural, whole, integer, rational and prime numbers, and find the place value of any digit.

💡 Concept

• Natural numbers: 1, 2, 3, … (counting numbers)
• Whole numbers: 0, 1, 2, 3, … (natural + zero)
• Integers: …, −2, −1, 0, 1, 2, … (negatives included)
• Prime number: exactly 2 factors — 1 and itself (2, 3, 5, 7, 11…). 2 is the only even prime.
• Composite number: more than 2 factors (4, 6, 8, 9…). 1 is neither prime nor composite.
• Place value of a digit = digit × position value (…, 1000, 100, 10, 1)

🧮 Key Formulas

Place value = digit × 10^(position from right − 1)

>

1 is neither prime nor composite

✏️ Easy Example

Q. What is the place value of 7 in 3,745?

1. 7 is at the hundreds position
2. Place value = 7 × 100

Answer: 700

🇮🇳 Real-Life Example

Your railway ticket PNR is a 10-digit number — each digit's position gives it meaning, exactly like place value.

📝 Exam-Level Example

Q. How many prime numbers are there between 1 and 50?

1. List them: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
2. Count them = 15

Answer: 15

🪄 Memory Trick

Primes till 50 count: 15. Till 100: 25. Remember '15–25'.

⚠️ Common Mistakes

• ❌ Treating 1 as a prime number
• ❌ Confusing place value (700) with face value (7)
• ❌ Forgetting 0 is a whole number but not a natural number

🏆 Exam Tips

• ✅ Learn primes up to 100 by heart — direct questions come every year
• ✅ Face value is always the digit itself

📌 Summary

• Natural → Whole (add 0) → Integers (add negatives)
• Prime = exactly 2 factors; 2 is the only even prime
• Place value = digit × position; face value = digit itself
• Primes: 15 till 50, 25 till 100