Lesson 72: Converting Between Standard Form and Scientific Notation

• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

Scientific notation is used to write very large and very small numbers in a compact form. In this lesson, you will learn how to convert numbers from standard form to scientific notation and from scientific notation back to standard form by correctly moving the decimal and applying powers of ten.

Learning Objectives

• Convert large numbers from standard form to scientific notation.
• Convert small decimal numbers from standard form to scientific notation.
• Convert numbers from scientific notation back to standard form.

Topics Covered

• Moving the decimal point
• Positive and negative exponents
• Writing numbers in proper scientific notation form

Key Terms

• Scientific Notation: A way of writing numbers as a number between 1 and 10 multiplied by a power of 10.
• Exponent: A number that tells how many times a base is multiplied by itself.
• Standard Form: A number written in regular decimal form.

Lesson Examples

Example 1: Standard Form to Scientific Notation (Large Number)

1. Start with 45,000.
2. Move the decimal 4 places left to get 4.5.
3. Write as 4.5 × 10⁴.

Example 2: Scientific Notation to Standard Form (Small Number)

1. Start with 3.2 × 10⁻³.
2. A negative exponent means move the decimal 3 places left.
3. The answer is 0.0032.

Practice Problems

1. Convert 72,000 to scientific notation.
2. Convert 0.00056 to scientific notation.
3. Convert 6.1 × 10⁵ to standard form.
4. Convert 9.3 × 10⁻⁴ to standard form.

Tips & Common Mistakes

• Always make sure the first number is between 1 and 10.
• Moving left gives a positive exponent; moving right gives a negative exponent.
• Count decimal moves carefully to avoid exponent errors.

Summary

Converting between standard form and scientific notation requires careful movement of the decimal point and correct use of exponents. Large numbers produce positive exponents, and small decimals produce negative exponents. Always ensure your final scientific notation number is between 1 and 10.

Challenge Problems

1. Convert 0.00000089 to scientific notation.
2. Convert 1.2 × 10⁷ to standard form.
3. Write 305,000,000 in scientific notation.