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Mathematics
dukedadon:

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

Vocaloid:

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

Vocaloid:

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.

dukedadon:

thank you Voca (:

Vocaloid:

*convert to improper fraction not mixed number

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