We need to calculate the concentration of the stock solution in terms of molarity.

Molarity: The molarity of a substance can be defined as a mole of solute per volume of solution in Litre. The formula of molarity is:

`Molarity = ( Mol e of solute (mol)) / (volume of solution (L))`

The unit of molarity is `mol L^-1` or "M"

Given:

Mass of red dye #3 = 0.0453 g

Volume of solution = 100.0 mL

Step 1: To convert the mass of dye to mole using the molar mass of red dye #3 as:

Molar mass of red dye #3 = 879.86 `g/(mol)`

Mole of red dye #3 = `0.0453 g xx (1mol)/(879.86g) = 5.15xx10^(-5)mol `

Step 2: To convert the volume of solution from mL to L using conversion factor 1 L = 1000mL as:

Volume of Solution = `100.0mL xx (1L)/(1000mL) = 0.1 L`

Step 3: Plugging the values of mole and volume in formula of molarity as:

Molarity = `(5.15 xx 10^(-5)mol)/(0.1L)= 5.15 xx 10^(-4) (mol)/(L)`

Hence, the concentration of stock solution is `5.15 xx 10^(-4) (mol)/(L)`