Answer
$HClO_{4}$
$H = 1\%$
$Cl = 35.3\%$
$O = 63.7\%$
Work Step by Step
We can tell from the acid name with the $per-$ prefix and $-ic$ suffix that the compound is a perchlorate ion balanced by hydrogen ions. Since a perchlorate ($ClO_{4}^{-1}$) ion has a -1 charge we need 1 ($H^{+}$) ion to balance the charge. Therefore the formula is $HClO_{4}$. Adding up the molar masses of the constituent elements we get $100.46\frac{g}{mol}$ as the molar mass of the compound. So to find the percent composition we just multiply the molar mass of each element (found on the periodic table) by how many times it occurs, divide by the molar mass of the whole molecule and multiply by 100%. Here is Hydrogen as an example:
$\frac{1.01\frac{g}{mol}}{100.46\frac{g}{mol}}×100\%=1\%$
