Scientific Notation Calculator

About Scientific Notation Calculator

Scientific notation (also called standard form or exponential notation) is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. In scientific notation, numbers are written as a base number between 1 and 10 multiplied by 10 raised to an exponent.

How Scientific Notation Works

The general form of a number in scientific notation is:

a × 10^b

Where:

• a is a number between 1 and 10 (1 ≤ |a| < 10)
• b is an integer (positive or negative)

Examples of Scientific Notation

Here are some examples of numbers written in decimal form and scientific notation:

• 300,000,000 = 3 × 10⁸
• 0.0000004 = 4 × 10^-7
• 7,245 = 7.245 × 10³
• 0.0078 = 7.8 × 10^-3

E-Notation

E-notation is a variant of scientific notation where the "× 10^b" is replaced by "e" or "E" followed by the exponent:

• 3 × 10⁸ = 3e8
• 4 × 10^-7 = 4e-7

When to Use Scientific Notation

Scientific notation is particularly useful when:

• Working with very large numbers (astronomical distances, national debts)
• Working with very small numbers (atomic sizes, microscopic measurements)
• Performing calculations where numbers have vastly different scales
• Expressing the precision of measurements (significant figures)

Operations with Scientific Notation

When performing calculations with numbers in scientific notation:

• Multiplication: Multiply the coefficients and add the exponents
• Division: Divide the coefficients and subtract the exponents
• Addition/Subtraction: First convert to the same exponent, then add/subtract coefficients