Scientific Notation

Scientific Notation

Scientific notation is a convenient way to represent extremely large or small numbers using powers of 10. Instead of writing out long strings of digits, scientific notation shortens the number into a compact form.

For example:
100,000,000 = 1 × 10⁸
0.0000001 = 1 × 10⁻⁷

This makes it easier to read, compare, and compute values especially in science, astronomy, and engineering.

 

Table of Contents

• What is Scientific Notation?
• Scientific Notation Formula
• 5 Rules of Scientific Notation
• Positive and Negative Exponents
• Scientific Notation Examples
• Conversion Problems with Solutions
• Practice Problems
• FAQs on Scientific Notation

 

What is Scientific Notation?

Scientific notation is a way of writing numbers as the product of a single-digit number and a power of 10. It is typically used when dealing with very large or very small values.

General Form:
a × 10^b
Where:

• 1 ≤ a < 10

• b is an integer (positive or negative)
  
  

This notation simplifies calculations, avoids large strings of zeros, and improves readability.

 Insert image here: Diagram showing standard vs. scientific notation (e.g., 0.000001 → 1 × 10⁻⁶, 500000 → 5 × 10⁵)

 

Scientific Notation Formula

The general formula is:
a × 10^b, where:

• a is the coefficient (1 ≤ a < 10)

• 10 is the base

• b is the exponent (positive for large numbers, negative for small)
  
  

 

5 Rules of Scientific Notation

1. The base is always 10.

2. The exponent must be a non-zero integer (positive or negative).

3. The absolute value of the coefficient must be ≥1 and <10.

4. Coefficients may be positive or negative decimals or whole numbers.

5. The mantissa holds the remaining significant digits.
   
   

Positive and Negative Exponents

• Positive exponent: When the number is greater than 1
  Example:
  20000 = 2 × 10⁴
  
  

• Negative exponent: When the number is less than 1
  Example:
  0.0002 = 2 × 10⁻⁴
  
  

Scientific Notation Examples

• 490000000 = 4.9 × 10⁸

• 1230000000 = 1.23 × 10⁹

• 50500000 = 5.05 × 10⁷

• 0.000000097 = 9.7 × 10⁻⁸

• 0.0000212 = 2.12 × 10⁻⁵
  
  

 

Conversion Problems with Solutions

Example 1: Convert 0.00000046 to scientific notation
Move decimal 7 places to the right:
= 4.6 × 10⁻⁷

 

Example 2: Convert 301000000 into scientific notation
Move decimal 8 places to the left:
= 3.01 × 10⁸

 

Example 3: Convert 1.36 × 10⁷ to standard form
Move decimal 7 places to the right:
= 13,600,000

 

Practice Problems

Problem 1: Convert into scientific notation
a) 28100000
b) 7890000000
c) 0.00000542

Problem 2: Convert into standard form
a) 3.5 × 10⁵
b) 2.89 × 10⁻⁶
c) 9.8 × 10⁻²

 

Frequently Asked Questions on Scientific Notation

Q1. How do you write 0.00001 in scientific notation?

 0.00001 = 1 × 10⁻⁵

Q2. What are the 5 rules of scientific notation?

1. Base must be 10

2. Exponent is a non-zero integer

3. Coefficient is between 1 and 10

4. Coefficient can be positive or negative

5. Mantissa carries remaining significant digits
   
   

Q3. What are the 3 parts of scientific notation?

Coefficient, base (10), and exponent

Q4. What is the scientific notation of 75?

75 = 7.5 × 10¹

Q5. How do you convert from scientific notation to standard form?

Move the decimal point left if exponent is negative, right if positive - by the number of positions equal to the exponent.

 

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