Scientific notation converter

Scientific notation keeps exactly one non-zero digit before the decimal point, so 45,000 is 4.5 × 10⁴ and 0.00045 is 4.5 × 10⁻⁴. The rule is strict, which is what makes two numbers in the notation directly comparable — you compare exponents first and mantissas only if they match.

Engineering notation relaxes the rule to allow one, two or three digits before the point, in exchange for exponents that are always multiples of three. That is not arbitrary: it matches the SI prefixes exactly, so 12,345 becomes 12.345 × 10³ and reads directly as 12.345 kilo-something. Electronics and engineering use it for that reason — a component value in engineering notation converts to picofarads or megohms by inspection, where scientific notation needs a step of arithmetic.

E notation — 4.5e-4 — is the same thing typed on a keyboard that has no superscripts. It is what calculators, spreadsheets and every programming language produce, and it is worth knowing that the e means "times ten to the power of", not Euler’s number. A spreadsheet showing 4.5E-04 has not corrupted your data; it has run out of column width.

One precision caution: a double-precision float holds about 15–17 significant digits, so a mantissa longer than that is not preserved. Expanding 6.022 × 10²³ gives 6.0219999999999996 × 10²³, which is the nearest representable value and not an error in the conversion.