Scientific Notation Calculator
Convert between decimal numbers and scientific notation with step-by-step explanations
Number Conversion
Enter any decimal number to convert to scientific notation
Common Examples
| Decimal | Scientific Notation | E-notation |
|---|---|---|
| 4,500 | 4.5 x 10³ | 4.5e+3 |
| 0.001 | 5.7 x 10⁻⁴ | 5.7e-4 |
| 123,000,000 | 1.23 x 10⁸ | 1.23e+8 |
| 0 | 4.56 x 10⁻⁷ | 4.56e-7 |
| 299,792,458 | 2.998 x 10⁸ | 2.998e+8 |
| 0 | 1.6 x 10⁻⁶ | 1.6e-6 |
Scientific Notation Rules
Format
a x 10^n where 1 ≤ |a| < 10
Positive Exponent
When original number ≥ 10
Negative Exponent
When original number < 1
Zero Exponent
When 1 ≤ number < 10
Operations in Scientific Notation
Multiplication
(a x 10^m) x (b x 10^n) = (a x b) x 10^(m+n)
Multiply coefficients, add exponents
Division
(a x 10^m) ÷ (b x 10^n) = (a÷b) x 10^(m-n)
Divide coefficients, subtract exponents
Different Notation Formats
Standard
4.5 x 10³
E-notation
4.5e3 or 4.5E3
Calculator
4.5*10^3
Mathematical
4.5 x 10³
Quick Tips
Large numbers have positive exponents
Small numbers have negative exponents
Move decimal point to find exponent
Coefficient must be between 1 and 10
Understanding Scientific Notation
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 x 10^n, where 'a' is a number between 1 and 10 (called the coefficient or mantissa), and 'n' is an integer (the exponent).
Why Use Scientific Notation?
- •Simplicity: Makes very large or small numbers easier to write and read
- •Precision: Clearly shows the number of significant figures
- •Calculations: Makes multiplication and division easier
- •Science: Standard format in physics, chemistry, and engineering
Conversion Process
For Large Numbers (≥ 10)
Example: 4,500 → 4.5 x 10³
- 1. Move decimal left until coefficient < 10
- 2. Count moves = positive exponent
- 3. Write as coefficient x 10^exponent
For Small Numbers (< 1)
Example: 0.00057 → 5.7 x 10⁻⁴
- 1. Move decimal right until coefficient ≥ 1
- 2. Count moves = negative exponent
- 3. Write as coefficient x 10^(-exponent)
Real-World Applications
Astronomy
Distance to sun: 1.496 x 10⁸ km
Biology
Size of virus: 1.0 x 10⁻⁷ m
Physics
Speed of light: 2.998 x 10⁸ m/s