Question

How do you express .33 as a fraction in simplest form?

Answer 1

`33/100`

Answer 2

As you wrote the question `33/100`

If you meant `0.333333..-> 0.33bar3" "` then `" "1/3`

Explanation:

It all depends on what you mean by `0.33`

If you meant it to be exactly as written then we have

`3/10+3/100`

Write as `(3/10xx1)+3/100`

But 1 may be written as `10/10`

`(3/10xx10/10)+3/100`

`30/100+3/100 = 33/100`

`color(red)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")`

If you meant what you wrote to mean `0.33 larr` 3 going on for ever

`0.333333333.....` written as `0.33bar3`

`color(brown)("Then this is very different:")`

Let `x=0.33bar3`

thus `10x=3.33bar3`

`10x-x=3`

`9x=3`

`x=3/9 = 1/3`