Scientific Notation Calculator
Convert numbers to and from scientific notation with step-by-step explanations
a × 10ⁿ (where 1 ≤ |a| < 10)
Scientific notation expresses numbers as a coefficient times a power of 10
Enter the coefficient and power of 10 (e.g., 3.5 × 10⁶)
First Number
Second Number
Quick Examples
Scientific Notation
E-Notation
Coefficient
Exponent
Standard Form
From:
Result
Step-by-Step Breakdown
Powers of 10 Reference
| Power | Value | Name |
|---|---|---|
| 10¹² | 1,000,000,000,000 | Trillion |
| 10⁹ | 1,000,000,000 | Billion |
| 10⁶ | 1,000,000 | Million |
| 10³ | 1,000 | Thousand |
| 10⁰ | 1 | One |
| 10⁻³ | 0.001 | Thousandth |
| 10⁻⁶ | 0.000001 | Millionth |
| 10⁻⁹ | 0.000000001 | Billionth |
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About Scientific Notation Calculator
What is Scientific Notation?
Scientific notation is a way of expressing very large or very small numbers in a compact form. It's written as:
a × 10ⁿ
Where:
- a is the coefficient (a number between 1 and 10)
- n is the exponent (an integer)
How to Convert to Scientific Notation
For Large Numbers
- Move the decimal point left until you have a number between 1 and 10
- Count how many places you moved
- That count becomes your positive exponent
Example: 12,500,000
- Move decimal 7 places left: 1.25
- Result: 1.25 × 10⁷
For Small Numbers
- Move the decimal point right until you have a number between 1 and 10
- Count how many places you moved
- That count becomes your negative exponent
Example: 0.00035
- Move decimal 4 places right: 3.5
- Result: 3.5 × 10⁻⁴
Converting Back to Standard Form
- Positive exponent: Move decimal right
- Negative exponent: Move decimal left
Example: 2.5 × 10³ = 2,500
Operations in Scientific Notation
Multiplication
(a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10ᵐ⁺ⁿ
Division
(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10ᵐ⁻ⁿ
Addition/Subtraction
Must have same exponent first, then add/subtract coefficients.
Common Powers of 10
| Power | Value | Name |
|---|---|---|
| 10¹² | 1,000,000,000,000 | Trillion |
| 10⁹ | 1,000,000,000 | Billion |
| 10⁶ | 1,000,000 | Million |
| 10³ | 1,000 | Thousand |
| 10⁰ | 1 | One |
| 10⁻³ | 0.001 | Thousandth |
| 10⁻⁶ | 0.000001 | Millionth |
| 10⁻⁹ | 0.000000001 | Billionth |
Applications
- Astronomy - Distances between stars and galaxies
- Chemistry - Avogadro's number (6.022 × 10²³)
- Physics - Speed of light (3 × 10⁸ m/s)
- Biology - Size of cells and microorganisms
- Computing - Memory and storage capacities
E-Notation
In calculators and programming, scientific notation is often written as:
- 1.25E+7 instead of 1.25 × 10⁷
- 3.5E-4 instead of 3.5 × 10⁻⁴
The 'E' stands for 'exponent'.