Scientific Notation Calculator
Convert between decimal and mantissa × 10ⁿ form.
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Formula
x = m × 10ⁿ where 1 ≤ |m| < 10 (standard form) · n = ⌊log₁₀|x|⌋
Scientific notation moves the decimal point so one non-zero digit sits left of the point (the mantissa), then records how many places moved as the exponent on 10. It tames very large and very small numbers in science and engineering.
Worked example
Avogadro's number becomes 6.0220 × 10²³ — four decimal places in the mantissa, exponent 23 because the decimal moved 23 places left from the original integer.
Where this can give the wrong answer
- Zero displays as 0 × 10⁰ — strictly speaking mantissa form is ambiguous for zero, but the headline makes the special case clear.
- Reverse mode (mantissa × 10^exponent → decimal) overflows if the exponent is extreme — stay within ±308 for finite doubles.
- E-notation (6.022e23) is shown alongside superscript-style text for copy-paste into spreadsheets.
FAQ
- Engineering notation restricts exponents to multiples of 3 (10³, 10⁶, …) so SI prefixes (kilo, mega) align. Scientific notation allows any integer exponent.