📌 1. What are Significant Figures?
🔢 Significant figures are the meaningful digits in a number that show its accuracy and precision.
📘 They are very important when solving equations like:
ax² + bx + c = 0
📊 2. Rules of Significant Figures
🟢 Rule 1: Non-zero digits are always significant
245 → ⭐⭐⭐ (3 significant figures)
🟢 Rule 2: Zeros between digits are significant
2005 → ⭐⭐⭐⭐ (4 significant figures)
🔴 Rule 3: Leading zeros are NOT significant
0.0045 → ⭐⭐ (2 significant figures)
🟢 Rule 4: Zeros after decimal are significant
2.500 → ⭐⭐⭐⭐ (4 significant figures)
🔴 Rule 5: Trailing zeros (no decimal) are NOT significant
1500 → ⭐⭐ (2 significant figures)
🧠 3. Visual Understanding
Number: 0.04050
0 . 0 4 0 5 0
↑ ↑ ↑ ↑
✔ ✔ ✔ ✔
👉 Significant Figures = 4
🧮 4. Use in Quadratic Formula
📌 Formula:
x = (-b ± √(b² – 4ac)) / 2a
🎯 Where Significant Figures Apply
📥 Inputs:
a = 2.0 → 2 SF b = 5.25 → 3 SF c = 1.0 → 2 SF
📤 Output:
👉 Final answer must have 2 significant figures (because minimum = 2)
⚙️ 5. Calculation Flow
Step 1: Identify SF in a, b, c 📊
↓
Step 2: Apply quadratic formula 🧮
↓
Step 3: Keep full digits (no rounding) 🚫
↓
Step 4: Round final answer only 🎯
↓
Step 5: Match least SF ✔
✏️ 6. Example
Solve:
2.0x² + 5.25x + 1.0 = 0
📌 After solving:
x₁ = -0.234 x₂ = -2.167
🎯 Final Answer (2 SF):
x₁ = -0.23 x₂ = -2.2
🧪 Interactive: Round Off to Significant Figures
👉 Enter a number and choose how many significant figures to round to:
⚠️ 7. Common Mistakes
❌ Rounding too early
❌ Ignoring significant figures
❌ Writing too many digits
💡 8. Quick Tips
✔ Round only at the end
✔ Use calculator carefully
✔ Always check least SF
✔ Write answers neatly
🏁 Conclusion
✨ Significant figures ensure your answers are:
✔ Accurate
✔ Scientific
✔ Meaningful
