A person measures mass of 3 different particles as 435.42 g, 226.3 g and 0.125 g. According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be.

Write the three measured masses with their decimal places aligned:
$$\begin{array}{r} 435.42 \\[2pt] 226.3 \\[2pt] \;0.125\\ \hline \end{array}$$

Rule for addition/subtraction with significant figures:
The final result must be rounded off to the same number of decimal places as the quantity having the least number of decimal places.

Count decimal places in each measurement:
435.42 g  → 2 decimal places
226.3 g  → 1 decimal place (least among the three)
0.125 g  → 3 decimal places

Perform the addition without rounding first:
$$435.42 + 226.3 + 0.125 = 661.845$$ g

The least number of decimal places is 1, so retain only one digit after the decimal and round the result accordingly:
661.845 g  → 661.8 g (since the next digit 4 is less than 5)

Therefore, the correct sum expressed with proper significant figures is $$661.8$$ g.

Hence, the required option is Option C.