In a decomposition reaction, a single substance decomposes, producing two or more different substances. That is, two or more substances are formed in this type of reactions from a compound. The atoms that form a compound are separated to give the products according to the formula:
AB → A + B
This type of reactions can occur spontaneously or caused by certain external factors that promote the breakdown of the molecule into simpler substances.
So in this case 2 KClO₃ → 2 KCl + 3 O₂ is a decomposition reaction. Potassium chlorate decomposes to give potassium chloride and oxygen gas as a product.
And one mole of a hydrogen atom is of 1.008 grams. So, 2 hydrogen moles weighs 2.016 grams. Hence, one mole of water has 2.016 grams of hydrogen mole. Therefore, the percentage composition of hydrogen would be 2.016/18.0152 = 11.19%.