Scientific Notation Converter (decimal ↔ scientific)
Two modes: decimal-to-scientific computes the coefficient and exponent for any number; scientific-to-decimal expands back. Engineering notation (multiples of 3 in the exponent) is also displayed.
How it works
What is scientific notation
Scientific notation expresses numbers as coef × 10^exponent, where coef is between 1 and 10 (usually 1 ≤ coef < 10). It's used for very large or very small numbers that would be cumbersome in decimal form.
Examples: speed of light = 3 × 10⁸ m/s. Avogadro's number = 6.022 × 10²³. Electron mass = 9.109 × 10⁻³¹ kg. The exponent tells you how many places to shift the decimal: positive shifts right (multiply), negative shifts left (divide).
E-notation in computers
E-notation (1.23e4 = 1.23 × 10⁴) is the computer-friendly version. JavaScript, Python, Excel, and most calculators use this. The 'e' is just notation — there's no 'e' (Euler's number) involved.
Why computers use E-notation: keyboards typically don't have superscript or '×' as easily-typed characters. Plain ASCII E or e works in any text input.
Note: 'e' in regex programming or other contexts means different things. In numbers it's specifically '× 10 to the'.
Engineering notation
Engineering notation is similar to scientific but the exponent is always a multiple of 3 (3, 6, 9, 12, …, or −3, −6, −9, …). This aligns with SI prefixes: kilo (10³), mega (10⁶), giga (10⁹), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹).
Example: 1.23 × 10⁴ in scientific is 12.3 × 10³ in engineering, which can be read as '12.3 kilo'. Useful in electronics, engineering, and any field that uses SI unit prefixes.
Tradeoff: scientific notation has a fixed-format coefficient (always 1 ≤ |coef| < 10); engineering allows wider coefficient range (1 ≤ |coef| < 1000) but cleaner SI prefix mapping.
Frequently asked questions
›Why is the exponent useful?
It tells you the order of magnitude. 10⁹ is a billion; 10⁻⁹ is a nanometer-scale number. For comparing very different scales (atomic vs astronomical), exponents are the natural language.
›Is 1.23e4 the same as 1.23 × 10⁴?
Yes — same number, different notation. 'e4' is a computer-friendly way to write '× 10⁴'. Most programming languages and calculators accept it as input.
›What's the precision of this calculator?
Floating-point precision (about 15-17 significant digits). For higher precision (1000+ digits), use a CAS like SymPy or Mathematica.
›Can I do math on scientific notation?
Multiply: multiply coefficients, add exponents. Divide: divide coefficients, subtract exponents. Add/subtract: bring to same exponent first, then add/subtract coefficients.
›Why does my number show as 'Infinity'?
Exponent too large for IEEE 754 double precision (about 308). For larger numbers, use a CAS or BigInt-based libraries.
›What's a 'mantissa'?
Older synonym for the coefficient — the part before the × 10^. Some textbooks still use it. Modern convention is 'coefficient' or 'significand'.
›Can I use scientific notation for negative coefficients?
Yes. -3 × 10⁵ = -300,000. The minus sign goes on the coefficient, not the exponent.
›Does the data leave my browser?
No. Calculation runs locally; nothing is sent to a server.
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