# Greek numbers and their conversion

## Letters as decimal numbers

### 1-999

To compose a number from 1 through 999 in greek, the letters of the alphabet are used - included in this alphabet for numerical use are also the older letters stigma (ϛ), koppa (ϟ or ϙ) and sampi (ϡ).

α ι ρ 1 10 100 2 20 200 3 30 300 4 40 400 5 50 500 6 60 600 7 70 700 8 80 800 9 90 900 90

The values of the letters used are shown in the table. Although not a place-value system, numbers are written with the most signifigant value first, e.g. $\overline{\phi \mu \gamma }=543$ or $\overline{\psi \eta }=708$. Notably there is no zero.

To indicate that the letters mark a number, there is usually a horizontal stroke placed above them, as above. Alternatively an accent looking numeral sign is placed above to the right of the number, e.g. $\lambda ϛ\text{ʹ}=36$.

### 1000-9999

For thousands the letters α-θ are used again and placed to the left of the less significant letters with a comma looking stroke subscribed to its left, e.g. $\text{͵}\overline{\beta ϡϙϛ}=2996$.

### 10000 and above

For tens of thousands the sign Μ, for myriads was used, with the number of myriads written above or having this number follow the Μ and a dot. In the latter case there can also be a γ or ˚ above it. In another version the Μ could be replaced by two dots above the number of myriads, e.g. $\stackrel{\epsilon }{Μ}\text{͵}\overline{\gamma \psi \pi \beta }=Μ\epsilon \text{. ͵}\overline{\gamma \psi \pi \beta }=\stackrel{\mathrm{..}}{\epsilon }\text{͵}\overline{\gamma \psi \pi \beta }=53 782$.

There is also a variant with two dots above the tens of thousands and for even greater numbers Apollonius and Archimedes invented systems.

### Fractions

The greeks used mainly submultiples, e.g. $\delta \text{ʹ}=\frac{1}{4}$ , and had also some special signs $𐅵\text{ʹ}=𐅶\text{ʹ}=\frac{1}{2}\text{,}𐅷\text{ʹ}=\frac{2}{3}\text{and}𐅸\text{ʹ}=\frac{3}{4}$ . With these they tried to express fractions as a sum of submultiples, e.g. $𐅵\text{ʹ}\eta \text{ʹ}\xi \delta \text{ʹ}=\frac{1}{2}+\frac{1}{8}+\frac{1}{64}=\frac{41}{64}$ . The submultiples were placed, without any horizontal stroke placed above them, after the number's letters, e.g. $\overline{\gamma }\zeta \text{ʹ}=3\frac{1}{7}$ .

Diophantus used a more convenient method, similar to ours, but with the numbers at opposite places, e.g. $\frac{\tau \iota \eta }{\lambda \zeta }=\frac{37}{318}$ .

### Conversion

The applicationA A) Requires Javascript. below let's you convert from greek to arabic integers, or conversely. Just type the number to the left and press the button. Note that there is no way to add the overlineB B) The overline in this page is added using MathML. and it's therefore not needed. Also use the character M (latin or greek) with nothing above it and a comma for the character GREEK LOWER NUMERAL SIGN - which are output in the conversion.

What to convert: Result