Question

What is the rational number equivalent to 3 point 24 with a bar over 24?

Answer 1

3.24242424...

let x = 0.242424 (just the repeating part)

if we multiply x by 100, we get 100x = 24.242424...

subtracting 100x - x we get 99x = 24 (notice how the decimal part cancels out)

therefore, x = 24/99

now, the original number is 3.242424... or 3 + x in terms of x, or 3 + 24/99

convert to a mixed number

Answer 2

shortcut method for future problems:

you have 2 repeating digits, 2 and 4. we can write 9 two times (99) and put the repeating 24 over 99 to get 24/99 as the repeating decimal part, then add 3. the previous post shows you why this works.

Answer 3

thank you Voca (:

Answer 4

*convert to improper fraction not mixed number