Scientific Notation Converter
Convert decimal ↔ scientific notation. Standard form a × 10^b with 1 ≤ |a| < 10.
Result
How to use this calculator
- Pick direction.
- Enter values.
- Calculator normalizes mantissa to 1 ≤ a < 10.
About this calculator
Scientific notation expresses very large or small numbers as a × 10^b with 1 ≤ |a| < 10. 0.000456 = 4.56 × 10⁻⁴; 6.022 × 10²³ = 602,200,000,000,000,000,000,000 (Avogadro's number). Programmers and engineers use "e-notation" (1.5e-4 = 1.5 × 10⁻⁴). For everyday numbers (1 to 10000), it's overkill; for atomic-to-cosmic scales, essential.
How it works — the formula
x = a × 10ⁿ with 1 ≤ |a| < 10 (normalised form)
or 0 when x = 0Scientific notation expresses a number as a coefficient (mantissa) between 1 and 10 multiplied by an integer power of 10. The "normalised" form is unique for non-zero numbers; engineering notation is similar but constrains n to multiples of 3 to align with SI prefixes (kilo, mega, giga). Scientific notation is the IEEE 754 standard's representation of floating-point numbers, with binary instead of decimal radix.
Worked examples
- Inputs:
- x = 12,345
- Output:
- 1.2345 × 10⁴
- Inputs:
- x = 0.000567
- Output:
- 5.67 × 10⁻⁴
- Inputs:
- x = 12,345
- Output:
- 12.345 × 10³ — engineering form pairs with kilo prefix
Limitations
- IEEE 754 double precision provides 15–17 significant decimal digits — values requiring more digits cannot be represented exactly.
- Very large or small magnitudes (|n| > 308 in double precision) overflow / underflow to ±Infinity or 0.
- Coefficient must satisfy 1 ≤ |a| < 10 for the canonical form; some engineering uses normalize differently.
- Different display conventions: 1.23e4, 1.23E4, 1.23 × 10⁴ — semantically identical but visually distinct.
Conversion is exact for representable values; trailing-digit differences vs hand calculations come from binary-decimal floating-point round-off.