Scientific notation is a common number notation used to express large and small numbers in the form \(x \times 10^y\), where \(1 \leq |x| < 10\) and \(y \in \mathbb Z\).[1] In general[2], 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
- \(1\times10^9\) = 1,000,000,000
- \(1\times10^{10}\) = 10,000,000,000
- \(1\times10^{27}\) = 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 \(a\times(10^{b})\)
| Notation | Equal value |
|---|---|
| Arrow notation | \(a\times 10\uparrow b\) |
| BEAF | \(a\times\{10,b\}\) |
Sources[]
- ↑ [1] Mathworld by Wolfram.
- ↑ Baidu Baike https://baike.baidu.com/item/%E7%A7%91%E5%AD%A6%E8%AE%B0%E6%95%B0%E6%B3%95/1612882 for the Chinese