What is Scientific notation? — Mathematics

Definition 63.12 Primary & Middle School Mathematics · Chapter 63 — Fractions and Powers

The scientific notation of a positive decimal number is the unique way of writing it as

a \times 10^n, \qquad\text{with } 1 \leq a < 10 \text{ and } n \text{ an integer.}

Examples

Example 63.13

The Earth–Sun distance is about $149\,600\,000$ km $= 1.496 \times 10^8$ km. The size of a water molecule is about $0.000\,000\,000\,28$ m $= 2.8 \times 10^{-10}$ m. To compute with such numbers, group the decimal parts and the powers of ten:

(3 \times 10^5) \times (2.5 \times 10^{-2}) = (3 \times 2.5) \times 10^{5 + (-2)} = 7.5 \times 10^{3}.

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