Category:Definitions/Number-Naming Systems

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This category contains definitions related to Number-Naming Systems.


There are various number-naming systems for naming large numbers (that is: greater than $1 \, 000 \, 000$).


Short Scale

The short 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 $1 \, 000$, appended to the root -(i)llion, corresponding to the indices $2$, $3$, $4$, $5$, $\ldots$


Thus:

one billion:    \(\displaystyle = 1 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^9 = 10^{2 \times 3 + 3} \)             
one trillion    \(\displaystyle = 1 \, 000 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^{12} = 10^{3 \times 3 + 3} \)             
one quadrillion    \(\displaystyle = 1 \, 000 \, 000 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^{15} = 10^{4 \times 3 + 3} \)             
one quintillion    \(\displaystyle = 1 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^{18} = 10^{5 \times 3 + 3} \)             

Thus one $n$-illion equals $1000 \times 10^{3 n}$ or $10^{3 n + 3}$


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:

one billion:    \(\displaystyle = 1 \, 000 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^{12} = 10^{2 \times 6} \)             
one trillion    \(\displaystyle = 1 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^{18} = 10^{3 \times 6} \)             
one quadrillion    \(\displaystyle = 1 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^{24} = 10^{4 \times 6} \)             
one quintillion    \(\displaystyle = 1 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^{30} = 10^{5 \times 6} \)             

Thus one $n$-illion equals $10^{6 n}$.


Additional terms are occasionally found to fill some of the gaps, but these are rare nowadays:

one milliard:    \(\displaystyle = 1 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^9 \)             
one billiard    \(\displaystyle = 1 \, 000 \, 000 \, 000 \, 000 \, 000 \)    \(\displaystyle = 10^{15} \)             

Subcategories

This category has the following 4 subcategories, out of 4 total.

B

C

M

V