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Scientific notation

Scientific notation is a compact way to write very large or very small numbers. The number is written as a mantissa between 1 and 10 multiplied by a power of ten, and unit prefixes such as kilo and milli are built on the same idea.

t = a\cdot 10^n,\quad 1 \le |a| < 10

scientific notation

\text{k} = 10^3,\ \text{m} = 10^{-3},\ \mu = 10^{-6}

common unit prefixes

Symbols

$a$	mantissa
$n$	integer exponent

Example

$\dfrac{(2.0\cdot 10^5)\cdot(3.0\cdot 10^{-2})}{4.0\cdot 10^3} = 1.5\cdot 10^0 = 1.5$ .

Make sure the mantissa always ends up between 1 and 10, otherwise it is not scientific notation.

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Part of Foundations of Mathematics: Powers, roots and scientific notation.