Multiplying Scientific Notation Calculator
Multiply numbers in scientific notation with step-by-step solutions and multiple output formats
Scientific Notation Multiplication
First Number (a × 10^n)
Number 1: 3.2 × 10^5
Decimal: 3,20,000
Second Number (b × 10^m)
Number 2: 1.5 × 10^-3
Decimal: 0.002
Quick Examples:
Multiplication Result
Input Numbers
Number 1: 3.2 × 10^5
Number 2: 1.5 × 10^-3
Scientific Notation
E-Notation
Decimal
Step-by-Step Solution
(3.2 × 10^5) × (1.5 × 10^-3)
= (3.2 × 1.5) × 10^(5 + -3)
= 4.800000000000001 × 10^2
= 4.8 × 10^2 (6 sig figs)
Rule: (a × 10^n) × (b × 10^m) = (a × b) × 10^(n+m)
Scientific Notation Rules
Standard Form
a × 10^n
Where 1 ≤ |a| < 10 and n is an integer
Multiplication Rule
(a × 10^n) × (b × 10^m) = (a × b) × 10^(n+m)
Multiply coefficients, add exponents
Normalization
Adjust coefficient to be between 1 and 10
Move decimal point and adjust exponent accordingly
Common Examples
Large Numbers
Speed of light: 3.0 × 10^8 m/s
Avogadro's number: 6.022 × 10^23
Small Numbers
Electron mass: 9.109 × 10^-31 kg
Planck constant: 6.626 × 10^-34 J⋅s
Notation Formats
Scientific Notation
2.5 × 10^3
Standard mathematical format
E-Notation
2.5e3 or 2.5E3
Calculator and computer format
Decimal
2500
Standard decimal representation
Tips & Reminders
Coefficient must be between 1 and 10
E-notation is equivalent to scientific notation
Large exponents indicate very large/small numbers
Always normalize the final result
Understanding Scientific Notation Multiplication
What is Scientific Notation?
Scientific notation is a way to express very large or very small numbers in a compact form. It consists of a coefficient (between 1 and 10) multiplied by a power of 10.
Why Use Scientific Notation?
- • Makes calculations with very large/small numbers easier
- • Clearly shows significant figures
- • Prevents calculation errors with many zeros
- • Standard in scientific and engineering fields
Multiplication Process
Step 1: Multiply Coefficients
Multiply the decimal parts (a × b)
Step 2: Add Exponents
Add the powers of 10 (n + m)
Step 3: Normalize
Adjust coefficient to be between 1 and 10