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

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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