\begin{definition}[Definition:Number-Naming System/Long Scale]
The '''long scale system''' is the number-naming system which uses:
:the word '''million''' for $10^6 = 1 \, 000 \, 000$
:the Latin-derived prefixes '''bi-''', '''tri-''', '''quadri-''', '''quint-''', etc. for each further multiple of $1 \, 000 \, 000$, appended to the root '''-(i)llion''', corresponding to the indices $2$, $3$, $4$, $5$, $\ldots$
Thus:
{{begin-axiom}}
{{axiom | lc= one billion:
        | m = = 1 \, 000 \, 000 \, 000 \, 000
        | mm= = 10^{12} = 10^{2 \times 6}
}}
{{axiom | lc= one trillion
        | m = = 1 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000
        | mm= = 10^{18} = 10^{3 \times 6}
}}
{{axiom | lc= one quadrillion
        | m = = 1 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000
        | mm= = 10^{24} = 10^{4 \times 6}
}}
{{axiom | lc= one quintillion
        | m = = 1 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000
        | mm= = 10^{30} = 10^{5 \times 6}
}}
{{end-axiom}}
Thus '''one $n$-illion''' equals $10^{6 n}$.
Additional terms are occasionally found to fill some of the gaps, but these are rare nowadays:
{{begin-axiom}}
{{axiom | lc= one milliard:
        | m = = 1 \, 000 \, 000 \, 000
        | mm= = 10^9
}}
{{axiom | lc= one billiard
        | m = = 1 \, 000 \, 000 \, 000 \, 000 \, 000
        | mm= = 10^{15}
}}
{{end-axiom}}
\end{definition}