Lesson 4: Approximations and Significant Figures

👨🏽‍🏫 Introduction

Have you ever rounded up a price, estimated your age in years, or said a trip takes “about 30 minutes”? That’s approximation in action! 🎯

In real life, we often don’t need exact values — we just need reasonable estimates. In this lesson, you’ll learn how to approximate numbers by rounding them and how to identify and use significant figures.

By the end of this lesson, you’ll be able to:

• Round numbers to a given number of decimal places or significant figures
• Estimate values in calculations
• Distinguish between decimal places and significant figures
• Apply approximations in real-life contexts

🧠 Key Concepts

🔢 1. What Is Approximation?

Approximation is expressing a number close to its true value, often by rounding it. It helps us simplify calculations or give quick estimates.

🔹 Rounding to Decimal Places (DP)

Decimal Places count how many digits come after the decimal point.

Example: Round 7.2689 to:

• 1 DP → 7.3
• 2 DP → 7.27
• 3 DP → 7.269

Rule: Look at the next digit (the one after your target place):

• If it’s 5 or more → round up
• If it’s less than 5 → round down

🔸 Rounding to Whole Numbers

⭐ 2. Significant Figures (SF)

Significant Figures show how precise a number is, starting from the first non-zero digit.

Rules:

1. All non-zero digits are significant
2. Zeros between digits are significant
3. Leading zeros are NOT significant
4. Trailing zeros after the decimal are significant

Examples:

• 243.7 → 4 SF
• 0.00456 → 3 SF (ignore leading zeros)
• 50.0 → 3 SF (trailing zero counts)

🔹 Rounding to Significant Figures

Example: Round 0.0045678 to:

• 1 SF →
• 2 SF →
• 3 SF →

🧮 3. Estimation in Calculations

Estimation helps us do quick mental calculations.

Example:

✍🏽 Sample Problem Walkthroughs

1. Round 98.756 to:
   • 1 DP → 98.8
   • 2 SF → First 2 significant digits = 99
2. Round 0.006723 to:
   • 2 SF →
   • 3 SF →
3. Estimate:
   
4. Estimate:
   

🧪 Practice Exercises

✏️ A. Round the following numbers:

1. 76.489 to 1 decimal place
2. 0.007328 to 2 significant figures
3. 1459 to 2 significant figures

✏️ B. Estimate the following:

✅ Answers with Explanations

• A1: 76.5 (look at second decimal = 8, round up)
• A2: First 2 non-zero digits = 73 →
  
• A3: First 2 digits = 1 and 4 →
  

• B1: Estimate → 23 + 38 = 61
• B2: Estimate → 6.5 × 3 = 19.5
• B3: Estimate → 60 ÷ 5 = 12

📌 Recap

• ✅ Approximation is useful when exact answers aren’t necessary
• ✅ Decimal places count digits after the point
• ✅ Significant figures focus on precision and meaningful digits
• ✅ Estimations help in real-life quick calculations

💭 Reflection Prompt

Think about a time you estimated a cost, distance, or time. Why did you choose to estimate rather than be exact? Can you think of a situation where accuracy (more significant figures) would be very important?