What is 33 1/3% as a fraction and decimal?

I might miss understand your question but from what I understand you're asking what is 33% as a fraction and #1/3# as a decimal in which case:

33% in a fraction is just #1/3#, because #100/3# is 33% which is #1/3#

So 33% in fraction form is #1/3# because to get from 33 to 100 you have to take 33 times 3 so you know:

#33% = 1/3#

#color(blue)("Some initial thoughts")#

When dealing with percentage consider the symbol % as representing: #xx1/100#. Including the multiply sign.

Lets look at the numbers. We are given #33 1/3#

The #1/3# will crop up quite often in mathematics so it is really worth committing to memory that #1/3=0.33333...# with the threes going on for ever. You can write it like this: #0.33bar3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

#color(brown)("As the fraction")#

#33 1/3 color(white)("d.d")%#
#color(white)("ddddd.d")uarr#
#33 1/3 color(white)("d")obrace(xx1/100) color(white)("d")=(33 1/3)/100#

Multiply by 1 and you do not change the value. However, 1 comes in many forms

#color(green)( (33 1/3)/100color(red)(xx1) color(white)("dddd")-> color(white)("dddd")(33 1/3)/100color(red)(xx3/3) color(white)("d")color(white)("d")=color(white)("d")100/300color(white)("d") =color(white)("d") 1/3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("As the decimal")#

Write as: #color(white)("d")33+1/3#

But we know that #1/3=0.33bar3#

So #33+1/3=33.33bar3#

However, the whole thing is:

#(33 1/3)xx1/100color(white)("d")=color(white)("d")33.33bar3xx1/100color(white)("d")=color(white)("d")0.33bar3#