To convert any fraction to percent, it helps to take note of what the word percent means exactly. The etymology of percent comes from the Latin phrase per centum, meaning "for each hundred."
What that phrase tells us mathematically is that a percentage like #3%# simply means "#3# for each hundred," or, as a fraction, #3/100#. Crucially, this means that hundredths and percentages are interchangeable. The % sign is simply different notation used to represent the same thing.
To convert #1/3# to a percentage is the same thing as converting it to hundredths; we can set up for this conversion with the equation
#1/3=x/100#
Now, we simply solve for #x#, which we carry out by multiplying each side of the equation by #100#:
#(100)1/3=x/100(100)#
#100/3=x#
#33 1/3=x#
So, #1/3=(33 1/3)/100#, which by definition means that #1/3=33 1/3%#.
