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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 $$y \in \mathbb Z$$. 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

• $$1\times10^2$$ = 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 rate

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

## Values in other notations

values for $$a*(10^{b})$$

Notation Equal value
Arrow notation $$a*10\uparrow b$$
BEAF $$a*\{10,b\}$$

## Sources

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