#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#
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#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#
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#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#