Rounding Off Digits: Simple Rules with Examples | 9th Class PTCB Physics 2025

Rounding Off Digits: Simple Rules with Examples | 9th Class PTCB Physics 2025

1.13 Rounding Off the Digits 🔢 Introduction: Why Do We Round Off? 🤔

Imagine you measure something as 12.3456789 cm. Do you really need all those digits? 🤷

In science, we often need to simplify numbers while keeping them accurate. This is called rounding off! ✂️

Let's learn the simple rules! 📏✨

Basic Rule: Round to the Nearest Value 🎯

When rounding off numbers to a certain number of significant figures, round to the nearest value.

The Two Simple Rules: Rule 1: Last Digit 5 → Round UP ⬆️

If the last digit is MORE than 5, increase the retained digit by one.

Rule 2: Last Digit 5 → Keep Same ⏸️

If the last digit is LESS than 5, keep it as it is.

Examples: Basic Rounding 📝 Example 1: Round to 2 Significant Figures

Given: 2.512 × 10³ m

Step-by-step:

1. We want 2 significant figures (2 and 5)
2. Next digit is 1 (which is 5)
3. So keep 5 as it is ✅

Answer: 2.5 × 10³ m 🎯

Example 2: Round to 3 Significant Figures

Given: 3.4567 × 10⁴ kg

Step-by-step:

1. We want 3 significant figures (3, 4, and 5)
2. Next digit is 6 (which is 5)
3. So increase 5 to 6 ⬆️

Answer: 3.46 × 10⁴ kg 🎯

Real-World Examples 🌍 Example A: Your Height 📏

You measure: 172.348 cm Round to 3 sig figs: 172 cm (next digit is 3 5, keep as is)

Example B: Your Weight ⚖️

You measure: 65.789 kg Round to 3 sig figs: 65.8 kg (next digit is 8 5, round up)

Example C: Temperature 🌡️

Thermometer shows: 38.456°C Round to 2 sig figs: 38°C (next digit is 4 5, keep as is)

Special Rule: What About the Digit 5? 🤔

The digit 5 is tricky because it's exactly in the middle! Is it closer to 4 or 6? 🎲

Scientists have a special rule for this:

The "5 Rule" (Even-Odd Rule) ⚖️

Look at the digit BEFORE the 5:

If digit before 5 is EVEN → Keep it same ⏸️ If digit before 5 is ODD → Round up ⬆️

Why this rule? It prevents bias! Sometimes we round up, sometimes down. It balances out! ⚖️

Examples: Rounding with 5 🎲 Example 1: Even Number Before 5

Given: 4.45 × 10² m

Step-by-step:

1. We want 2 significant figures (4 and 4)
2. Next digit is 5
3. Digit before 5 is 4 (EVEN) ✅
4. So keep 4 as it is ⏸️

Answer: 4.4 × 10² m 🎯

Example 2: Odd Number Before 5

Given: 4.55 × 10² m

Step-by-step:

1. We want 2 significant figures (4 and 5)
2. Next digit is 5
3. Digit before 5 is 5 (ODD) ✅
4. So increase 5 to 6 ⬆️

Answer: 4.6 × 10² m 🎯

More Examples with 5 💡 Example A: 2.25 → Round to 2 sig figs

• Digit before 5 is 2 (EVEN)
• Keep as: 2.2 ✅

Example B: 2.35 → Round to 2 sig figs

• Digit before 5 is 3 (ODD)
• Round to: 2.4 ⬆️

Example C: 6.65 → Round to 2 sig figs

• Digit before 5 is 6 (EVEN)
• Keep as: 6.6 ✅

Example D: 7.75 → Round to 2 sig figs

• Digit before 5 is 7 (ODD)
• Round to: 7.8 ⬆️

Using Logic: The Smart Way 🧠

Sometimes we use logic instead of blindly following rules!

Example: 4.452 × 10² m (Round to 2 sig figs)

Method 1: Using the "5 rule"

• Look at 5, digit before is 4 (EVEN)
• Answer: 4.4 × 10² m

Method 2: Using Logic 💡

• 4.452 is closer to 4.5 than to 4.4
• Because 4.452 - 4.4 = 0.052
• But 4.5 - 4.452 = 0.048 (smaller!)
• So it makes more sense to round to 4.5 × 10² m ✅

Smart approach: When there are digits after 5, use logic! The number is closer to the higher value. 🎯

Practice Problems 📝

Try these yourself!

Problem 1:

Round 5.678 to 2 significant figures.

details summaryClick for answer/summary **Answer: 5.7** (next digit is 7 5, round up) /details

Problem 2:

Round 3.142 to 2 significant figures.

details summaryClick for answer/summary **Answer: 3.1** (next digit is 4 5, keep same) /details

Problem 3:

Round 2.65 to 2 significant figures.

details summaryClick for answer/summary **Answer: 2.6** (digit before 5 is 6, EVEN, keep same) /details

Problem 4:

Round 7.85 to 2 significant figures.

details summaryClick for answer/summary **Answer: 7.8** (digit before 5 is 8, EVEN, keep same) /details

Problem 5:

Round 9.752 × 10³ to 3 significant figures.

details summaryClick for answer/summary **Answer: 9.75 × 10³** (next digit is 2 5, keep same) /details

Real-Life Applications 🌟 In Daily Life 🏠

• Shopping: ₨299.99 rounds to ₨300 💰
• Cooking: 2.7 cups rounds to 3 cups 🍳
• Time: 2.4 hours rounds to 2 hours ⏰

In Science 🔬

• Lab Results: Precise measurements simplified
• Calculations: Making numbers manageable
• Reports: Presenting data clearly

In Engineering 🏗️

• Building Plans: Practical measurements
• Manufacturing: Tolerance levels
• Quality Control: Standard specifications

Summary Table: Rounding Rules 📊

Situation Rule Example Result

Last digit 5 Round UP ⬆️ 3.47 → 2 sig figs 3.5 Last digit 5 Keep SAME ⏸️ 3.42 → 2 sig figs 3.4 Last digit = 5 (before EVEN) Keep SAME ⏸️ 3.45 → 2 sig figs 3.4 Last digit = 5 (before ODD) Round UP ⬆️ 3.55 → 2 sig figs 3.6 Multiple digits after 5 Use LOGIC 🧠 3.452 → 2 sig figs 3.5

Key Takeaways 💡

✅ Rounding simplifies numbers while maintaining accuracy

✅ 5 → Round UP, 5 → Keep same

✅ = 5 rule: Check if digit before is EVEN or ODD

✅ EVEN before 5 → Keep same ⏸️

✅ ODD before 5 → Round up ⬆️

✅ Use logic when digits follow the 5

✅ Always specify how many significant figures you're rounding to!

Do You Know? 🤓

⏱️ Electronic timers can measure time intervals as short as 1/10,000 of a second!

That's 0.0001 seconds or 0.1 milliseconds! 🤯

Used in:

• Olympic timing 🏃
• Formula 1 racing 🏎️
• Scientific experiments 🔬
• High-speed photography 📸

Quick Tips for Success 🎯

💡 Tip 1: Always count from the LEFT to find significant figures

💡 Tip 2: Write your answer in scientific notation to avoid confusion

💡 Tip 3: When in doubt with 5, use the EVEN-ODD rule

💡 Tip 4: Double-check: Are you rounding to the correct number of sig figs?

💡 Tip 5: Practice makes perfect! Do lots of examples 📝

Remember! 🧠

"Rounding off is like packing a suitcase - keep what's important, leave what's extra. But always be honest about what you're keeping!" 🎒

Common Mistakes to Avoid ⚠️

❌ Mistake 1: Rounding multiple times

• Wrong: 3.456 → 3.46 → 3.5
• Right: 3.456 → 3.5 (in one step)

❌ Mistake 2: Forgetting the EVEN-ODD rule for 5

• Wrong: Always rounding up for 5
• Right: Check digit before 5

❌ Mistake 3: Not using scientific notation

• Wrong: 25000 (unclear sig figs)
• Right: 2.5 × 10⁴ (clear!)