In more detail
12,300 = 1.23 × 10⁴ and 0.0045 = 4.5 × 10⁻³: the exponent counts how many places the decimal point moved, positive for large numbers and negative for small ones. In normalised form the coefficient is at least 1 and less than 10, so 45 × 10³ becomes 4.5 × 10⁴. Multiplying multiplies the coefficients and adds the exponents; dividing divides the coefficients and subtracts the exponents. Engineering notation restricts exponents to multiples of 3 (12.3 × 10³) to match prefixes like kilo and mega.
Why it matters
Calculators and code print it as E-notation, 1.23e4 or 1.23E+04, and it shows the limits of floating point: a double can hold about 1.8 × 10³⁰⁸ at most. Spreadsheets may read text such as 1E5 as the number 100,000, silently corrupting product codes or identifiers; import such columns as text. The coefficient also shows precision: 1.20 × 10³ states three Significant figures, which plain 1200 cannot.
Example
(3 × 10⁸) × (2 × 10⁻³) = 6 × 10⁵
(1.8 × 10⁻³) × (4 × 10⁵) = 7.2 × 10²
(6.4 × 10⁶) / (1.6 × 10⁻³) = 4 × 10⁹
>>> f"{12300:.2e}", float("1E5")
('1.23e+04', 100000.0)