Question

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

Answer 1

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`

Answer 2

As a fraction: `1/3`

As a decimal: `0.33bar3` where `bar3` means the 3's go on repeating for ever.

Explanation:

`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`