## 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 | 1 | ι | 10 | ρ | 100 |
---|---|---|---|---|---|

β | 2 | κ | 20 | σ | 200 |

γ | 3 | λ | 30 | τ | 300 |

δ | 4 | μ | 40 | υ | 400 |

ε | 5 | ν | 50 | φ | 500 |

ϛ | 6 | ξ | 60 | χ | 600 |

ζ | 7 | ο | 70 | ψ | 700 |

η | 8 | π | 80 | ω | 800 |

θ | 9 | ϙ | 90 | ϡ | 900 |

ϟ | 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. $\overline{\mathrm{\phi \mu \gamma}}=543$ or $\overline{\mathrm{\psi \eta}}=708$. 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. $\mathrm{\lambda \u03db}\text{\u0374}=36$.

### 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. $\text{\u0375}\overline{\mathrm{\beta \u03e1\u03d9\u03db}}=2996$.

### 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.
$\stackrel{\mathrm{\epsilon}}{\mathrm{{\rm M}}}\text{\u0375}\overline{\mathrm{\gamma \psi \pi \beta}}=\mathrm{{\rm M}}\mathrm{\epsilon}\text{. \u0375}\overline{\mathrm{\gamma \psi \pi \beta}}=\stackrel{\mathrm{..}}{\mathrm{\epsilon}}\text{\u0375}\overline{\mathrm{\gamma \psi \pi \beta}}=\mathrm{53\; 782}$.

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. $\mathrm{\delta}\text{\u0374}=\frac{1}{4}$ , and had also some special signs $\mathrm{\U00010175}\text{\u0374}=\mathrm{\U00010176}\text{\u0374}=\frac{1}{2}\text{,}\mathrm{\U00010177}\text{\u0374}=\frac{2}{3}\text{and}\mathrm{\U00010178}\text{\u0374}=\frac{3}{4}$ . With these they tried to express fractions as a sum of submultiples, e.g. $\mathrm{\U00010175}\text{\u0374}\mathrm{\eta}\text{\u0374}\mathrm{\xi \delta}\text{\u0374}=\frac{1}{2}+\frac{1}{8}+\frac{1}{64}=\frac{41}{64}$ . The submultiples were placed, without any horizontal stroke placed above them, after the number's letters, e.g. $\overline{\mathrm{\gamma}}\mathrm{\zeta}\text{\u0374}=3\frac{1}{7}$ .

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

### Conversion

The application^{A} 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 *overline*^{B} 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.