(51.48016103 % * mass of tablet)/100 = mass of base in tablet:
(51.48016103 % * 0.5749 g)/100 = 0.2959447 g = 296 mg
Looks OK, although I would take slightly different route - you know tablet was 0.5749 g, and you took 0.1006 g of that. That means to scale amount of the base to the mass of the tablet you need to multiply it by 0.5749/0.1006 - which is "how many 0.1006 g samples are in the 0.5749 g tablet". But the final result will be the same.
Please don't abuse significant digits - while it is correct to use all digits in calculations, when you report intermediate results, report them rounded down (so not 51.48016103%, but just 51.5%, although you should use 51.48016103 in calcualtions).