# How much is a zillion

## Zillion

**Zillion** is an indefinite number word for a very large number. Conway and Guy understand the -th zillion generally the -th number on *-illion* (So in the long ladder the -th power of millions).^{[1]}

Jeffrey Hankins defined a zillion, based on the definition of Googolplex, as a one with a zillion zeros, i.e. as a solution to the equation *x* = 10^{x}. Solutions to this equation (which actually exist for complex numbers) can be expressed with the analytical continuation of Lambert's W-function leading to a number *x* delivers its product logarithm, i.e. the number *y* With *x* = *ye*^{y}: −W_{n}(−ln 10) / ln 10.^{[2]} The main value (*n* = 0) is −0.1191930 ... - 0.7505832 ... also of one *n*-Azillion are spoken so that words like *Bazillion* makes sense.

Given that zillions made the Form 10^{6n} (long ladder) or 10^{3n + 3} (short ladder), it makes more sense to give the definition *x* = 10^{6x} or. *x* = 10^{3x + 3} to use. The main value is −W (−6ln 10) / (6ln 10) = −0.1172249… - 0.1595608… i or −W (−3 000ln 10) / (3ln 10) = −0.9904834… - 0 , 3993152 ... i. A zillion could in turn mean a thousand zillion or a one with six zillion three zeros, i.e. a number *x*, for the *x* = 10^{6x + 3} applies. Solutions to this equation can be expressed using the analytical continuation of the Lambertian W-function: −W_{n}(−6 000ln 10) / (6ln 10). The main value (*n* = 0) is −0.5398940… - 0.2015360… i.

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