Lesson 6: Standard Form (Scientific Notation)

👨🏽‍🏫 Introduction

Have you ever seen numbers like 300,000,000 (the speed of light in m/s) or 0.000000056 (the width of a virus)? Writing these out every time is exhausting and error-prone. That’s why we use Standard Form, also called Scientific Notation! 🧪📏💡

It helps us express very large or very small numbers more conveniently using powers of 10.

In this lesson, you’ll learn to:

• Convert large numbers into standard form
• Convert small numbers into standard form
• Write standard form numbers back in ordinary form
• Compare, add, and multiply numbers in standard form

🧠 Key Concepts

📌 1. What Is Standard Form?

Standard Form (Scientific Notation) expresses a number as:

Where:

• a is a number between 1 and 10 (1 ≤ a < 10)
• n is an integer (positive for large numbers, negative for small)

🔢 2. Converting Large Numbers into Standard Form

Move the decimal to create a number between 1 and 10. Count how many places you moved — that becomes the power of 10.

Example:

We moved the decimal 6 places to the left.

🔽 3. Converting Small Numbers into Standard Form

For small numbers (less than 1), move the decimal to the right until you get a number between 1 and 10. The power of 10 will be negative.

Example:

🔁 4. Converting Standard Form to Ordinary Numbers

Move the decimal point based on the exponent of 10:

• Positive exponent: move right (makes big numbers)
• Negative exponent: move left (makes small numbers)

Examples:

⚙️ 5. Operations with Standard Form

✅ Multiplying Numbers in Standard Form:

Multiply the a values, and add the exponents.

Example:

✅ Dividing Numbers in Standard Form:

Divide the a values, subtract the exponents.

Example:

✅ Adding or Subtracting:

You must have the same exponent before adding/subtracting. If not, convert one to match.

Example:

Convert second term:

Now:

✍🏽 Sample Problem Walkthroughs

1. Convert 470000 to standard form:
   
2. Convert 0.000072 to standard form:
   
3. Convert 3.9 × 10³ to ordinary number:
   
4. Simplify:
   

🧪 Practice Exercises

✏️ A. Convert to Standard Form:

1. 920000
2. 0.0000095
3. 18300

✏️ B. Convert to Ordinary Numbers:

✏️ C. Calculate in Standard Form:

✅ Answers with Explanations

• A1:
• A2:
• A3:

• B1:
• B2:

• C1: Divide a-values: 2 ÷ 4 = 0.5 → subtract powers:
  
• C2: Multiply a-values: 5 × 6 = 30 →
  

📌 Recap

• ✅ Standard Form helps express very large or small numbers using powers of 10
• ✅ Positive exponents = large numbers, negative exponents = small numbers
• ✅ You can multiply/divide easily using index laws

💭 Reflection Prompt

Why might a scientist, engineer, or astronomer need to use scientific notation instead of ordinary numbers? Can you think of one extremely large and one extremely small number you’ve seen used in real life?