Scientific Notation Calculator
Convert numbers to/from scientific notation and perform calculations while maintaining proper scientific format.
Scientific Notation Rules
Format
Scientific notation expresses numbers in the form:
a × 10b
Where:
- a (coefficient) is a number between 1 and 10 (1 ≤ |a| < 10)
- b (exponent) is an integer
Examples
| Standard Form | Scientific Notation |
|---|---|
| 3,500,000 | 3.5 × 106 |
| 0.000042 | 4.2 × 10-5 |
| -12,000 | -1.2 × 104 |
| 0.0078 | 7.8 × 10-3 |
Calculation Rules
Multiplication:
(a × 10b) × (c × 10d) = (a × c) × 10b+d
Division:
(a × 10b) ÷ (c × 10d) = (a ÷ c) × 10b-d
Addition/Subtraction:
Numbers must have the same exponent. Adjust as needed:
(a × 10b) + (c × 10b) = (a + c) × 10b
Understanding Scientific Notation
Scientific notation is a way to express very large or very small numbers concisely. It’s widely used in science, engineering, and mathematics to handle numbers of extreme magnitudes.
Why Use Scientific Notation?
- Simplifies calculations with extremely large or small numbers
- Clearly indicates precision through significant figures
- Standardizes number representation across scientific disciplines
- Saves space and reduces errors when working with extreme values
Common Applications
Astronomy
Expressing distances between celestial bodies (e.g., 1.5 × 108 km from Earth to Sun)
Physics
Describing subatomic particles (e.g., electron mass = 9.1 × 10-31 kg)
Chemistry
Working with Avogadro’s number (6.02 × 1023 particles/mol)
Engineering
Measuring electrical properties (e.g., 5.6 × 10-6 F capacitance)
E Notation
In computing and calculators, scientific notation is often written using “E” or “e”:
3.5 × 106 becomes 3.5E6 or 3.5e6
4.2 × 10-5 becomes 4.2E-5 or 4.2e-5