Scientific Notation, Explained

The rules

1. Move the decimal point until exactly one non-zero digit is to its left
2. Count the number of places moved — that's the exponent
3. Moved left → exponent positive; moved right → exponent negative

Doing math with it

(a × 10ᵐ)(b × 10ⁿ) = (a × b) × 10ᵐ⁺ⁿ

(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10ᵐ⁻ⁿ

Engineering notation

Engineering notation forces exponents to multiples of 3, so the coefficient lands between 1 and 1000. 47,000 V = 47 × 10³ V = 47 kV — clean read-off into kilo/mega/giga SI prefixes.

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