To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/zhuli . The first 200 of you will get 20% off Brilliant’s annual premium subscription. How can we multiply all of these different things together? What does it mean? In this video, we will take a detailed dive into dimensional analysis, to better understand how we can do arithmetic with units, and how it is applied to solving problems. Can you come up with any other interesting ways to apply dimensional analysis? My Patreon: https://www.patreon.com/zhulimath/ 0:05 Introduction and Outline 1:18 What is a unit / dimension? 1:50 Add/Subtract Commensurable Units 2:38 Dividing Units 3:13 Multiplying Units 4:54 Part I Summary 5:36 Base and Derived Units 6:10 Conversion Factors 8:30 Example Problem 1 10:07 Example Problem 2 11:09 Example Problem 3 12:57 Sanity Check 13:56 Special Insights: Percents 14:46 Special Insights: Degrees 16:36 Fuel Economy as... area?? 18:11 Arbitrary Analysis 20:03 Conclusion Joseph Newton's video, Cursed Units: https://www.youtube.com/watch?v=kkfIXUjkYqE Kieran Borovac's video, Seven Dimensions: https://www.youtube.com/watch?v=bI-FS7aZJpY Intro riff taken from: Nikolai Kapustin - 8 Concert Etudes, Op. 40: III. Toccatina Music Credit: Seeking Song / American Legion Aligned / Hara Noda Blues for the Lonesome / Rikard From The First Fall of Snow / Johannes Bornlof Winter Is upon Us / Sayuri Hayashi Egnell Blank Stare Happy / American Legion Forest Moon / Gavin Luke Groove Retrospective / Will Harrison courtesy of www.epidemicsound.com This video was sponsored by Brilliant.