Scientific Notation Calculator
Convert numbers to scientific notation or convert scientific notation back to standard form.
Result
Famous Numbers
What Is Scientific Notation?
Scientific notation is a way of expressing very large or very small numbers in a compact form. A number is written as a coefficient between 1 and 10 multiplied by a power of 10.
a × 10n
where 1 ≤ |a| < 10
Examples
| Standard Form | Scientific Notation | E Notation |
|---|---|---|
| 1,000,000 | 1 × 10⁶ | 1e6 |
| 0.001 | 1 × 10⁻³ | 1e-3 |
| 299,792,458 | 2.998 × 10⁸ | 2.998e8 |
| 0.00000001 | 1 × 10⁻⁸ | 1e-8 |
Why Use Scientific Notation?
- • Clarity: Makes extremely large or small numbers easier to read
- • Precision: Shows significant figures clearly
- • Calculations: Simplifies multiplication and division
- • Standard: Used universally in science and engineering
Arithmetic in Scientific Notation
One of the biggest advantages of scientific notation is how it simplifies calculations with extreme numbers. The rules for arithmetic follow directly from the laws of exponents.
Multiplication: Add exponents
(3 × 10⁴) × (2 × 10³) = (3×2) × 10^(4+3) = 6 × 10⁷
Division: Subtract exponents
(8 × 10⁶) ÷ (4 × 10²) = (8÷4) × 10^(6−2) = 2 × 10⁴
Addition: Match exponents first
3.5 × 10⁴ + 2.0 × 10³ = 3.5 × 10⁴ + 0.2 × 10⁴ = 3.7 × 10⁴
Adjust result if coefficient is out of range
12 × 10³ → 1.2 × 10⁴ (move decimal left, add 1 to exponent)
0.5 × 10⁵ → 5 × 10⁴ (move decimal right, subtract 1 from exponent)
Famous Numbers in Scientific Notation
| Constant | Scientific Notation | Field |
|---|---|---|
| Speed of light (m/s) | 2.998 × 10⁸ | Physics |
| Avogadro's number (mol⁻¹) | 6.022 × 10²³ | Chemistry |
| Electron charge (C) | 1.602 × 10⁻¹⁹ | Physics |
| Planck's constant (J·s) | 6.626 × 10⁻³⁴ | Quantum mechanics |
| Earth–Sun distance (m) | 1.496 × 10¹¹ | Astronomy |
| Hydrogen atom diameter (m) | 1.06 × 10⁻¹⁰ | Atomic physics |
| Observable universe (m) | 8.8 × 10²⁶ | Cosmology |
Step-by-Step Conversion Examples
Convert 0.000345 to scientific notation
- Move the decimal right until you get a number between 1 and 10
- 0.000345 → 3.45 (moved 4 places right)
- Moving right means negative exponent: 3.45 × 10⁻⁴
Convert 7.8 × 10⁵ to standard form
- Positive exponent: move decimal right 5 places
- 7.8 → 780000 (add zeros as needed)
- Result: 780,000
Multiply: (2.5 × 10³) × (4.0 × 10⁻²)
- Multiply coefficients: 2.5 × 4.0 = 10.0
- Add exponents: 3 + (−2) = 1
- Raw result: 10.0 × 10¹ = 10 × 10¹
- Adjust coefficient: 10 = 1.0 × 10¹ → final: 1.0 × 10²