Unit 35: Exponents and Roots

Day 11 of 30

Scientific notation: large numbers

6-8Mathematics

Content is AI-assisted and continuously improved through educator review

Learning Objective

Students will explore scientific notation and large numbers through guided practice and application.

Today's Lesson

In this lesson, we'll explore scientific notation: large numbers. Mathematical thinking develops logical reasoning and problem-solving abilities.

Scientific notation writes very large or very small numbers compactly as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. Large numbers: positive exponent (3,000,000 = 3 × 10⁶). Small numbers: negative exponent (0.00004 = 4 × 10⁻⁵). To multiply: multiply the a parts, add exponents. To divide: divide a parts, subtract exponents. Scientific notation is essential in science for distances (light-years), sizes (atoms), and measurements. It makes calculations with extreme numbers manageable!

As you work through today's material, pay attention to the examples and try to identify the patterns or strategies being used. This will help you apply these concepts to new problems.

Take notes on key points and make connections to what you've already learned in previous lessons.

Key Terms
Problem

A mathematical question requiring analysis and solution

Solution

The result obtained by solving a problem

Activities
Instructions
1. Review the example problems for scientific notation: large numbers. 2. Identify the steps and strategies used. 3. Work through practice problems independently. 4. Compare solutions with a partner.
Materials Needed
  • Notebook
  • Calculator (if needed)
  • Graph paper
Practice Problems
1

Write 4,500,000 in scientific notation

Hint: Move decimal left until 1 ≤ a < 10. Count moves.
2

Write 0.00032 in scientific notation

Hint: Move decimal right. Negative exponent for small numbers.
3

What is (2 × 10³) × (3 × 10²)?

Hint: Multiply coefficients, add exponents.

Teaching Tip

For advanced learners: Encourage deeper analysis and real-world connections. Consider extension activities that allow students to apply scientific notation: large numbers to novel situations.

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