how to prepare 100 mL of exactly 5.00% (w/w) aqueous hydrogen solution? If given that initial it is 50.0% (w/w) and has density of 1.18 g mL^-1

in the final solution, 10 grams is hydrogen compound.

so you want then 10=.5*1.18*V of the original solution.

V= 16.94 ml of the stock.

Remainder is water (100-16.94)ml

check my thinking.