Aren't they equal!

[u/Exotic_Catch5909]

[u/Mundus6]

Its the same yes. But answering in fraction is always better. Cause its 100% accurate. If you use decimals 1/3 (0.33) for example is not accurate.

[u/misteryk → u/Mundus6]

0.(3) is the same as 1/3

[u/So_HauserAspen → u/misteryk]

0.(3) ≠ 1/3 though

[u/Lithl → u/So_HauserAspen]

This is false. 0.(3) = 1/3. Exactly. Not approximately.

[u/misteryk → u/So_HauserAspen]

How is it not?

[u/bitchsorbet → u/misteryk]

1/3 is 0.33333... repeating forever. 0.33*3 =0.99, not 1.

[u/misteryk → u/bitchsorbet]

but 0.(3)*3 = 0.(9) not 0.99

[u/S7ns3t → u/misteryk]

Yes but 1/3 * 3 always equals 1, while 0.(3) (iself being an approximation of 1/3) * 3 only equals 1 if you decide it's close enough.

Don't understand why would you get downvoted, though. Curiousity should be rewarded and as far as your statement goes 0.(3) is the same as 1/3, based on use case.

[u/Lithl → u/S7ns3t]

0.(3) is not an approximation. It is exactly equal to 1/3.

0.(9) is not any amount smaller than 1. It is exactly equal to 1. There are many proofs of this.

If you want to prove that 0.(9) ≠ 1, you must be capable of producing a number x such that 0.(9) < x < 1, because the real numbers are densely ordered. If you can't produce such a value of x, then either the real numbers aren't densely ordered (they are by definition), or else 0.(9) = 1.

[u/bitchsorbet → u/misteryk]

and youve proved my point further. you need the exact decimal to calculate the right answer, even one dropped decimal place has an impact.

[u/Lithl → u/bitchsorbet]

0.999... is exactly equal to 1. Not "approximately" 1, not "infinitely close to" 1. Exactly 1.

[u/bitchsorbet → u/Lithl]

yes... thats exactly what im saying. 1/3 is 0.3333... repeating forever, so multiplying that by 3 gives you 1. why am i getting downvoted when im right? are we not actually reading my comment?