Converting Repeating Decimals into Fractions

In this video, I cover how to convert repeating decimals into fractions using an infinite geometric series as well as doing it in a more algebraic way. I tried to start from the basics so that anyone who didn't know the sum of an infinite geometric series would not be in pure confusion. Lastly, I did a quick proof that 0.9 repeated equals 1, using an infinite geometric series. I decided to make this video since 3blue1brown announced his Summer Of Math Exposition #SoME1. It was a great opportunity to combine two things I like a lot, coding and math. If you spotted any mistakes, please comment below so I can mention them in the description! :D The animations in this video were created using Manim (https://github.com/ManimCommunity/manim) and Wolfram Mathematica. Check out the GitHub repository for the code: https://github.com/Sri-SriPod/manimat.... The geometric proof was taken from brilliant (https://brilliant.org/wiki/geometric-.... Thank you to them for being a great website! Timestamps: 0:00 Intro 0:28 Definition of a Repeating Decimal 1:47 Geometric Sequences 2:49 Geometric Series 5:51 Infinite Geometric Series 8:20 Infinite Geometric Series (Geometric Proof) 10:17 Converting Repeating Decimals into Fractions 12:44 Another way to convert repeating decimals into fractions 15:24 Proof that 0.99… = 1 If you read all the way down here, you are a true legend :)