Scientific Notation Lesson: Definition, Conversion, Rules and Examples

Lesson Overview

• What Is Scientific Notation?
• Rules for Writing Scientific Notations
• Positive and Negative Exponent
• Scientific Notation to Standard Form​
• Scientific Notation Examples
• Scientific Notation Assessment

In this Scientific Notation Lesson, you will learn what scientific notation is, how to convert numbers into this form, and the rules for using it. 

What Is Scientific Notation?

Scientific notation is a way to write very large or very small numbers in a simpler format. It makes numbers easier to work with and compare.

In scientific notation, a number is written as a product of two parts:

1. A number between 1 and 10.
2. A power of 10.

For example: 

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The Scientific Notation Practice Quiz- I

Rules for Writing Scientific Notations

To determine the exponent of 10, it is important to apply the following guideline

How to Write Numbers in Scientific Notation

When you wonder how do I convert to scientific notation, the process is simple and follows these steps:

1. Move the Decimal Point:
   Move the decimal point to the right or left until you have a number between 1 and 10.
2. Count the Places You Moved the Decimal Point:
   The number of places you move the decimal point becomes the exponent of 10.
3. Write the Number as a Product:
   The number you get from step 1 is multiplied by 10 raised to the power of the number you counted in step 2.

Example: Write 5,000 in Scientific Notation

To convert 5,000 into scientific notation, follow these steps:

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Scientific Notation Quiz questions

Positive and Negative Exponent

Positive Exponent:

• Decimal moves right for large numbers, exponent is positive.
• Example: 50,000 = 5 × 10⁴

Negative Exponent:

• Decimal moves left for small numbers, the exponent is negative.
• Example: 0.00005 = 5 × 10⁻⁵

Take this Quiz: The Scientific Notation Practice Quiz- II (157846)

Scientific Notation to Standard Form​

To convert a number from scientific notation to standard form, follow these steps:

1. Identify the exponent of 10: The exponent tells you how many places to move the decimal point.
   
2. Move the decimal point:
   • If the exponent is positive, move the decimal point to the right.
   • If the exponent is negative, move the decimal point to the left.
     
3. Write the number in standard form: After moving the decimal point, you will have the number in its standard form.

Example 1:

Scientific Notation: 4.2 × 10³

Steps: Move the decimal point 3 places to the right.

Standard Form: 4,200

Example 2:

Scientific Notation: 5.6 × 10⁻²

Steps: Move the decimal point 2 places to the left.

Standard Form: 0.056

Scientific Notation Examples

1. 45,000,000 - 4.5 × 10⁷
2. 0.0000067 - 6.7 × 10⁻⁶
3. 0.000000089 - 8.9 × 10⁻⁸
4. 12,300 - 1.23 × 10⁴
5. 0.000053 - 5.3 × 10⁻⁵

These examples show how to express both large and small numbers in scientific notation. Large numbers like 45,000,000 are written with a positive exponent, such as 4.5 × 10⁷, while small numbers like 0.0000067 are written with a negative exponent, like 6.7 × 10⁻⁶. The key is moving the decimal point and adjusting the exponent based on how many places it moves.

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convert a number to scientific notation Quiz

Scientific Notation Assessment

Example 1: Convert 0.00000084 into scientific notation.

Solution:

• Move the decimal point to the right of 0.000000084 up to 8 places.
• The decimal point was moved 8 places to the right to form the number 8.4.
• Since the number is less than 10 and the decimal moved to the right, we use a negative exponent.
  ⇒ 0.000000084 = 8.4 × 10⁻⁸
  Answer: 0.000000084 = 8.4 × 10⁻⁸

Example 2: Convert 5000 into scientific notation.

Solution:

Move the decimal point 3 places to the left in 5000 to get 5.0.

Since the decimal moved to the left, the exponent is positive.
⇒ 5000 = 5.0 × 10³
Answer: 5000 = 5 × 10³

Example 3: Convert 0.0045 into scientific notation.

Solution:

Move the decimal point 3 places to the right in 0.0045 to get 4.5.

Since the decimal moved to the right, we use a negative exponent.
⇒ 0.0045 = 4.5 × 10⁻³
Answer: 0.0045 = 4.5 × 10⁻³

Example 4: Convert 123000000 into scientific notation.

Solution

Move the decimal point 8 places to the left in 123000000 to get 1.23.

Since the decimal moved to the left, we use a positive exponent.
⇒ 123000000 = 1.23 × 10⁸
Answer: 123000000 = 1.23 × 10⁸

Example 5: Convert 0.00056 into scientific notation.

Solution:

• Move the decimal point 4 places to the right in 0.00056 to get 5.6.
• Since the decimal moved to the right, we use a negative exponent.
  ⇒ 0.00056 = 5.6 × 10⁻⁴
  Answer: 0.00056 = 5.6 × 10⁻⁴