Does 0.4999... Round Up or Down? The Truth About Infinite Decimals 🔢

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 Check out the coolest math clothes in the world: https://mathshion.com/ Join Wrath of Math to get exclusive videos, lecture notes, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 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/1lukdbz/when_rounding_to_the_nearest_whole_number_does/ https://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