Does 0.4999... Round Up or Down? @WrathofMath

Uploaded July 2025 | Updated September 2026, 2 weeks ago

Pretty much everyone knows that 0.999... = 1, and certainly, even if you argue about that - you might concede that if we were to round 0.999... it would round to 1. But what about 0.4999...? Does this round to 0 or to 1? Today we answer this question by exploring rounding conventions and discussing why 0.4999... is 0.5 in the first place. This question comes from r/askmath. #maths #reddit

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SOURCES
reddit.com/r/askmath/comments/1lukdbz/when_rounding_to_the_nearest_whole_number_does
en.wikipedia.org/wiki/Rounding

0:00 Intro
1:00 Floor and Ceiling
2:12 The Nearest Whole
5:01 Why Round Up?
9:04 Banker's Rounding
11:51 Mathshion
12:28 Why 0.4999...=0.5
16:58 Final Question
18:04 "Mathematically"
18:52 Conclusion

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$the math teacher can’t figure it out This seemingly simple geometry problem got a lot of traffic recently on r/askmath, as many tried to solve it, got it wrong, and got stuck. The OP’s wife, a math teacher, was unable to solve it - and this time that’s not because the teacher is incompetent but the problem is simply much harder than it looks. We’ll solve this variation of Langley’s Adventitious Angles using some clever geometric constructions and basic properties of triangles. #geometryproblems #mathchallenge Join Wrath of Math to get exclusive videos, lecture notes, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join Check out the coolest math clothes in the world: https://mathshion.com/ More Math Chats: https://www.youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO Outro music: https://youtube.com/shorts/tfifiSdTZRg Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu SOURCES https://www.reddit.com/r/askmath/comments/1lq21qv/my_wife_math_teacher_cannot_figure_this_out https://www.reddit.com/r/askmath/comments/1lqy3vj/comment/n18lc4a/?context=3 https://mathwithbaddrawings.com/2015/06/10/trick-or-technique/ Tripp, Colin. “Adventitious Angles.” The Mathematical Gazette, vol. 59, no. 408, 1975, pp. 98–106. JSTOR, https://doi.org/10.2307/3616644. https://www.duckware.com/tech/worldshardesteasygeometryproblem.html Adventitious angles problem: the lonely fractional derived angle by Yong Kong and Shaowei Zhang MUSIC Special World 8 (Crown) - Super Mario 3D Land Athletic BGM (Super Mario World 2 - Yoshis Island) - Mario Kart World Musee Champignon Aquatic Ambience Torigoth - Night Ordon Village Dire Dire Docks Mario 64 End Theme 0:00 Intro 1:09 Hogwash Montage 3:19 Whats the Deal? 5:33 Adventitious 7:25 Solution 19:10 Conclusion$