Question

Divide 44 °8' into two parts such that the number of Sexagesimal seconds in one part may be equal to the number of Centesimal seconds in the other part.

Answer 1

90° = 90 * 60 * 60 = 324000 arc seconds
90° = 100 * 100 * 100 = 1000000 centesimal seconds

44° 8" = (44 * 60 + 8) * 60 = 158880 arc seconds

Let x be the number of arc seconds for the first angle.
Let (324000/10000000)x be the number of arc seconds for the second angle.
Together these add to be 158880 arc seconds

x + (324000/1000000)x = 158880

(1324000/10000000)x = 158880
x = 158880 * 1000000 / 1324000
x = 120000 arc seconds
x = 120000 centesimal seconds

120000 arc seconds / 60 = 20000 arc minutes
2000 arc minutes / 60 = 33 degrees 40 minutes

Answer:
33° 40' = 120000 arc seconds
10° 28' = 120000 centesimal seconds

Answer 2

Let  x = centesimal seconds in one part and

x = sexagesimal seconds in another.

Then,

The total number of degrees 
x/1000+x/3600= 44 8/60= 116823.53 sec