How to Use
- Enter a number
Input a number in standard form or in scientific/E-notation.
- Choose conversion direction
Select standard-to-scientific or scientific-to-standard conversion.
- View result
Click Convert to see the converted number.
What Is Scientific Notation?
Scientific notation is a way of writing numbers that have too many digits to handle comfortably in the compact form a × 10ⁿ. The key rule is that the absolute value of the coefficient a must be at least 1 and less than 10 (1 ≤ |a| < 10). Because only one representation satisfies this condition, every number has a single, consistent normalized form.
Why Use It
- You can write values like the speed of light, 3 × 10⁸ m/s, or the electron mass, 9.1 × 10⁻³¹ kg, concisely instead of stringing out long rows of zeros.
- The number of digits in the coefficient a equals the count of significant figures, clearly showing the precision of a measurement.
- It simplifies the multiplication and division of large numbers by turning them into the addition and subtraction of exponents.
It is the standard notation in physics, chemistry, astronomy, and engineering. On computers and scientific calculators, the same value is shown in E-notation, such as 3.2E5.
The Formula
The formula for converting an ordinary number into scientific notation is as follows.
n = ⌊log₁₀|x|⌋, a = x ÷ 10ⁿ
Here, x is the original number to convert, n is the power of 10 (an integer), and a is the coefficient. ⌊ ⌋ denotes the floor (round-down) operation.
Example) Converting 123456
① n = ⌊log₁₀123456⌋ = ⌊5.0915⌋ = 5
② a = 123456 ÷ 10⁵ = 1.23456
③ Result: 1.23456 × 10⁵
The reverse direction is calculated as x = a × 10ⁿ. For example, 4.2 × 10⁻⁴ = 4.2 ÷ 10000 = 0.00042. This calculator rounds the coefficient to 10 decimal places to suppress floating-point error.