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Not to be confused with quinquagintillion.

A quinquadragintillion is equal to $$10^{138}$$ or $$10^{270}$$ in France and Germany.[1]

In the long scale which is commonly used in France and Germany, $$10^{138}$$ is called trevigintillion.

## Approximations

For short scale:

Notation Lower bound Upper bound
Scientific notation $$1\times10^{138}$$
Arrow notation $$10\uparrow138$$
Steinhaus-Moser Notation 73[3] 74[3]
Copy notation 9[138] 1[139]
Taro's multivariable Ackermann function A(3,455) A(3,456)
Pound-Star Notation #*(3,2,7,11,8,2,9,1)*10 #*(5,11,7,12,11,1)*16
BEAF {10,138}
Hyper-E notation E138
Bashicu matrix system (0)(0)(0)(0)(0)[20535] (0)(0)(0)(0)(0)[20536]
Hyperfactorial array notation 89! 90!
Fast-growing hierarchy $$f_2(449)$$ $$f_2(450)$$
Hardy hierarchy $$H_{\omega^2}(449)$$ $$H_{\omega^2}(450)$$
Slow-growing hierarchy $$g_{\omega^{\omega^2+\omega3+8}}(10)$$

For long scale:

Notation Lower bound Upper bound
Scientific notation $$1\times10^{270}$$
Arrow notation $$10\uparrow270$$
Steinhaus-Moser Notation 128[3] 129[3]
Copy notation 9[270] 1[271]
Taro's multivariable Ackermann function A(3,893) A(3,894)
Pound-Star Notation #*((7101))*10 #*((7102))*10
BEAF {10,270}
Hyper-E notation E270
Bashicu matrix system (0)(0)(0)(0)(0)(0)[16548] (0)(0)(0)(0)(0)(0)[16549]
Hyperfactorial array notation 153! 154!
Fast-growing hierarchy $$f_2(887)$$ $$f_2(888)$$
Hardy hierarchy $$H_{\omega^2}(887)$$ $$H_{\omega^2}(888)$$
Slow-growing hierarchy $$g_{\omega^{\omega^22+\omega7}}(10)$$

## List of prefixed numbers derived from quadragintillion

Name Short scale Long scale