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Scientific notation is a common number notation used to express large and small numbers in the form \(x \cdot 10^y\), where \(1 \leq |x| < 10\) and \(y \in \mathbb Z\).[1] In general, the formulas for finding \(x\) and \(y\) are

\(x = \frac{N}{10^{\left\lfloor log_{10} |N|\right\rfloor}}\)

and

\(y = \left\lfloor log_{10} |N|\right\rfloor\).

Examples Edit

  • \(1\times10^2\) = 100
  • \(1.234\times10^3\) = 1,234
  • \(9.5\times10^4\) = 95,000
  • \(86.4\times10^7\) = 86,400,000
  • \(1\times10^{10}\) = 10,000,000,000
  • \(1\times10^{29}\) = octillion
  • \(1\times10^{100}\) = googol
  • \(1\times10^{303}\) = centillion
  • \(1\times10^{1,000,000}\) = milliplexion

Growth rateEdit

Scientific notation can express numbers that can be produced with the \(f_2 (n)\) function of the fast-growing hierarchy.

Sources Edit

  1. [1]