How much water and how much solid is needed to prepare 100 mL of 10% sodium hydroxide solution.

First thing we have to check is what will be the mass of the final solution. In case of diluted solutions it is common practice to assume density of solution to be just 1 g/mL. However, 10% is too much for this assumption to hold.

Value found in the density tables is 1.1111 g/mL, so mass of our solution will be 100×1.1111=111.11 g.

Now we can use definition of mass percentage 1.1, rearranging it to the form:

So we need 10/100×111.11=11.111 g NaOH. As in the question only 2 significant digits were given (10%) it will be enough to weight 11 g of solid.

It is common error in such situations to omit the density in the calculation. Concentration conversion calculator uses correct densities always so you don't have to check them.