Approximation & Estimation

🎯 Learning Objective

Round smartly to eliminate options without exact calculation.

💡 Concept

• Round each number to a friendly value: 398 → 400, 24.8% → 25%
• Keep track of rounding direction (up/down) to know if your estimate is high or low
• % shortcuts: 10% = ÷10, 5% = half of 10%, 1% = ÷100
• In options far apart → approximate boldly; close options → calculate carefully

🧮 Key Formulas

10% = ÷10 | 1% = ÷100 | 25% = ÷4 | 12.5% = ÷8

✏️ Easy Example

Q. Approximate: 39.97% of 649.8

1. Treat as 40% of 650
2. 40% = 4 × (10% of 650) = 4 × 65

Answer: ≈ 260

🇮🇳 Real-Life Example

At a sale showing '39.9% off on ₹649', your brain should instantly say 'about ₹260 off'. That's exam-grade estimation.

📝 Exam-Level Example

Q. √6398 ≈ ?

1. 80² = 6400
2. 6398 is just below 6400

Answer: ≈ 80

🪄 Memory Trick

Anchor on perfect squares/cubes: 6398→80², 1730→12³ (1728). Options do the rest.

⚠️ Common Mistakes

• ❌ Rounding both numbers the same direction and drifting too far
• ❌ Approximating when options differ by less than 2–3%

🏆 Exam Tips

• ✅ Squares till 30, cubes till 15 — non-negotiable
• ✅ Practice 10 approximation questions daily for speed

📌 Summary

• Round to friendly numbers
• Track rounding direction
• Far options → estimate; close options → compute