Math & Statistics · 科学计数法（Scientific Notation） · Updated 2026-10-25
What Is Scientific Notation?
Definition
Scientific notation writes numbers as a×10^n: the mantissa a carries precision and the exponent n carries magnitude. Multiplication multiplies mantissas and adds exponents ((3×10⁴)×(2×10³)=6×10⁷); division divides and subtracts; addition requires matching exponents first. It is everywhere: lightspeed 3×10⁸ m/s, Avogadro 6.02×10²³, float epsilon 1e-16, the 1e9 literal in code. Its real gift is order-of-magnitude intuition — an exponent gap of 3 means a thousandfold.
Formula
(a×10^m)×(b×10^n) = ab×10^(m+n); align exponents before adding
Worked Example
(6×10⁸)÷(3×10⁵)=2×10³; a day is 86,400 s ≈ 8.64×10⁴, so a year ≈ 3.15×10⁷ s — enough to eyeball "a decade ≈ 3×10⁸ s."
Common Misconception
"1e5 is just 100000" — it is a floating-point literal; assigning to an integer in some languages fails, though 1e5===100000 compares true. And don't add exponents when adding numbers: same-exponent sums add mantissas (2×10³+3×10³=5×10³).
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