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Googlek is equal to $$16^{256} = 2^{1024}$$, intended as a hexadecimal analog of googol.[1] It was described on a page on the site "intuitor.com" which proposes a method for pronouncing numbers in hexadecimal. To the best of our knowledge, the page was written in 2007 by Tom Rogers, a high school teacher in South Carolina, USA.

It is approximately $$1.797 \times 10^{308}$$. It is the smallest power of two not expressible as a double-precision floating point number according to IEEE 754 (a double has an exponent width of 11 bits, one of which is the sign, so the exponent has a maximum of 210 - 1). Also, it is the floating-point limit for numbers in many programming languages. For example, numbers equal to this or larger in JavaScript will simply be expressed as "Infinity".

It is approximately 179.769 uncentillion in the short scale and about 179.769 unquinquagintillion in the long scale.

JavaScript HyperCalc maxes out at a power tower of tens this many terms high, or $$10\uparrow\uparrow(2^{1024})$$.

2^1024 is the maximum amount of money, coins etc. for games like AdVenture Capitalist or Cookie Clicker.

## Digit expansions Edit

Its full decimal expansion is:

179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Its full binary expansion is:

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

## ApproximationsEdit

Notation Lower bound Upper bound
Scientific notation $$1.797\times10^{308}$$ $$1.798\times10^{308}$$
Arrow notation $$16\uparrow256$$
Steinhaus-Moser Notation 143[3] 144[3]
Copy notation 1[309] 2[309]
Taro's multivariable Ackermann function A(3,1021) A(3,1022)
Pound-Star Notation #*((560))*11 #*((561))*11
BEAF {16,256}
Hyper-E notation E[16]2#2
Bashicu matrix system (0)(0)(0)(0)(0)(0)[65536]
Hyperfactorial array notation 170! 171!
Fast-growing hierarchy $$f_2(1014)$$ $$f_2(1015)$$
Hardy hierarchy $$H_{\omega^2}(1014)$$ $$H_{\omega^2}(1015)$$
Slow-growing hierarchy $$g_{\omega^{\omega^2}}(16)$$

## Sources Edit

1. Hexadecimal Number Words. Retrieved November 2015.
2. Part 1 - My Large Numbers