Determine exactly how many digits the number 2 144,000 has in sexagesimal (base 60) . show all work.

Assuming the number is , note that this number requires 144,001 digits in binary. On average, a single digit in base 60 requires about binary digits. But obviously, we have to use a whole number of digits, so we round up to the next integer; in other words, given a number in base 60 with digits, we should expect in base 2 to have .

So, if the "conversion rate" from base 60 to base 2 is about 5.9069, then the reverse rate would be , i.e. the solution to . Again, we'd have to round up, so if in base 2 has digits, then in base 60 should have digits.

This means in base 60 would have digits.