# Category:Definitions/Number-Naming Systems

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

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

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: $\ds = 1 \, 000 \, 000 \, 000$ $\ds = 10^9$ one billiard $\ds = 1 \, 000 \, 000 \, 000 \, 000 \, 000$ $\ds = 10^{15}$

## Subcategories

This category has the following 7 subcategories, out of 7 total.

## Pages in category "Definitions/Number-Naming Systems"

The following 6 pages are in this category, out of 6 total.