Scientific Notation Converter
Provide a number below to get its scientific notation, E-notation, engineering notation, and real number format. It accepts numbers in the following formats: 3672.2, 2.3e11, or 3.5x10^(-12).
Scientific Notation Calculator
Use the calculator below to perform calculations using scientific notation.
Scientific Notation
Scientific notation is a way to express numbers in a form that makes numbers that are too small or too large more convenient to write and perform calculations with. It is commonly used in mathematics, engineering, and science, as it can help simplify arithmetic operations.
In scientific notation, numbers are written as a base, b, referred to as the significand, multiplied by 10 raised to an integer exponent, n, which is referred to as the order of magnitude:
b × 10n
Examples
| Decimal Notation | Scientific Notation |
|---|---|
| 5 | 5 × 100 |
| 700 | 7 × 102 |
| 1,000,000 | 1 × 106 |
| 0.0004212 | 4.212 × 10-4 |
| -5,000,000,000 | -5 × 109 |
Calculations with Scientific Notation
Addition and Subtraction
To add or subtract in scientific notation, convert all numbers to the same power of 10. Then add or subtract the base values.
Example:1.432 × 102 + 800 × 10-1 − 0.001 × 105
Convert to same exponent:1.432 × 102 + 0.8 × 102 − 1 × 102
Combine:(1.432 + 0.8 − 1) × 102 = 1.232 × 102
Multiplication
Multiply the base values, then add the exponents of 10.
Example:1.432 × 102 × 800 × 10-1 × 0.001 × 105
Multiply digits:1.432 × 800 × 0.001 = 1.1456
Add exponents:102+(-1)+5 = 106
Final result:1.1456 × 106
Division
Divide the base values, then subtract the exponents of 10.
Example:(1.432 × 102) ÷ (800 × 10-1) ÷ (0.001 × 105)
Divide digits:1.432 ÷ 800 ÷ 0.001 = 1.79
Subtract exponents:102 - (-1) - 5 = 10-2
Final result:1.79 × 10-2
If result was 0.179 × 10-2, convert to standard form:1.79 × 10-3
Engineering Notation
Engineering notation is similar to scientific notation, but the exponent is a multiple of 3 (e.g., 0, 3, 6, 9…). This allows easy reading with SI prefixes like kilo (103), mega (106), and giga (109).
Example:
Scientific: 1.234 × 108
Engineering: 123.4 × 106
E-Notation
E-notation is a compact version of scientific notation used in calculators and programming. It replaces “× 10” with the letter “E”.
Format: bEn where b is the base and n is the exponent.
| Scientific Notation | E-Notation |
|---|---|
| 5 × 100 | 5E0 |
| 7 × 102 | 7E2 |
| 1 × 106 | 1E6 |
| 4.212 × 10-4 | 4.212E-4 |
| -5 × 109 | -5E9 |
Note: In some programming languages and calculators, the “E” may be lowercase as e.
Related Calculators:
Big Number Calculator, Quadratic Formula Calculator, Exponent CalculatorExternal Resources:
Scientific Notation Calculator on calculator.net