What is Scientific Notation?

Scientific notation is a way of expressing very large or very small numbers in a compact form. It is widely used in science, engineering, and mathematics.

The Format

A number in scientific notation is written as: a × 10ⁿ

• a (coefficient): A number where 1 ≤ |a| < 10
• n (exponent): An integer indicating the power of 10

Converting to Scientific Notation

For large numbers:

1. Move the decimal point left until you have a number between 1 and 10
2. Count how many places you moved (this is your positive exponent)
3. Write: coefficient × 10^(number of places)

Example: 6,500,000 = 6.5 × 10⁶

For small numbers:

1. Move the decimal point right until you have a number between 1 and 10
2. Count how many places you moved (this is your negative exponent)
3. Write: coefficient × 10^(-number of places)

Example: 0.00045 = 4.5 × 10⁻⁴

E-Notation

Computers often use E-notation (or exponential notation) as an alternative:

• 6.5 × 10⁶ is written as 6.5e6 or 6.5E6
• 4.5 × 10⁻⁴ is written as 4.5e-4 or 4.5E-4

Arithmetic Operations

Multiplication

Multiply coefficients and add exponents:

(a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10⁽ᵐ⁺ⁿ⁾

Division

Divide coefficients and subtract exponents:

(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10⁽ᵐ⁻ⁿ⁾

Addition & Subtraction

First align the exponents, then add or subtract the coefficients:

(a × 10ⁿ) + (b × 10ⁿ) = (a + b) × 10ⁿ

Common Examples