## Conversion to sexagesimal

The question of converting into the babylonian sexagesimal expression is answered thusly:

First, write as a fraction:

Now Babylonian sexagesimal numbers have the form

where is the whole number portion of the number , and the other integers are the numerators of the fractions of the powers of

For , it is clear that The numerator is determined as the largest integer such that

In this case (Clearly, the next integer gives is negative.)

Now subtract to get

In general we now perform the same arithmetic with respect to the denominator . Thus we solve for the largest integer

Since we conclude that Also, there is no excess from the subtraction; so the process stops.

Example

Here's another example. Find the sexagesimal representation of

Solution

First Now subtract . Solve for the largest integer such that

or . We see that . The difference is therefore . Since we see that .Thus we have exhausted powers of sixty needed. It follows that

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