Mantissa / Significand IntervalMetrological Invariant [1 <= |a| < 10]
Under ISO 80000-1 and IUPAC mathematical rules, the mantissa (or significand a) in normalized scientific notation must satisfy 1 <= |a| < 10. Exactly one non-zero digit must precede the decimal point, ensuring a unique and unambiguous representation for any real number.
Default: 1.0 <= |a| < 10.0
Base-10 Exponent (Power of Ten)Integer Order of Magnitude [b in Z]
The exponent b represents the exact integer power to which base 10 is raised. Positive exponents indicate values >= 10 (decimal point shifted left), negative exponents indicate fractional values between 0 and 1 (decimal point shifted right), and zero denotes numbers in the interval [1, 10).
Default: b in {-300, ..., +300}
Engineering Notation Modulo-3 ConstraintEngineering Standard [b' = 3k, k in Z]
Engineering notation restricts the power-of-ten exponent to integer multiples of 3 (..., -6, -3, 0, 3, 6, 9, ...), adjusting the mantissa into the interval 1 <= |a'| < 1000. This directly aligns numerical outputs with international SI metric prefixes such as micro, milli, kilo, and mega.
Default: b' mod 3 == 0 (1 <= |a'| < 1000)
E-Notation Calculator Display SyntaxDigital Display Format [aEb]
Standardized shorthand notation replacing 'x 10^' with the letter 'e' or 'E' (such as 5.2e-4). Widely mandated across digital handheld calculators, lab instruments, and spreadsheet software (Excel, Google Sheets) to display extreme quantities on compact screens.
Default: m.ddde+/-xx
Significant Figures ConservationMetrological Precision Invariant
All digits appearing in the mantissa of scientific notation are strictly significant. Converting from standard decimal to scientific notation clarifies precision: 5,200 is ambiguous (2 to 4 sig figs), whereas 5.20 x 10^3 unambiguously specifies exactly 3 significant figures.
Default: Preserved from Mantissa
