Scientific Notation and Operations

Multiplying Numbers in Scientific Notation

Scientific notation is a way to express very large or very small numbers using powers of ten. It is commonly used in science and mathematics to simplify calculations and clearly indicate the magnitude of a number.

• Scientific Notation Format: A number is written as a × 10n, where 1 ≤ a < 10 and n is an integer.

• Multiplication Rule: To multiply numbers in scientific notation, multiply the coefficients and add the exponents.

General Formula:

Example Problem

Multiply the following numbers and express the answer in scientific notation:

• Step 1: Multiply the coefficients:

• Step 2: Add the exponents:

• Step 3: Combine the results:

• Step 4: Adjust to proper scientific notation (move decimal one place left, increase exponent by 1):

Final Answer:

Key Points

• Always express your final answer in the form with .

• Multiplying in scientific notation is efficient for handling very large or very small numbers.