Proving a Repeating Decimal (Rational or Irrational?)

Can a repeating decimal really be written as a fraction?
In this video, we take a repeating decimal and prove—using algebra—whether it is rational or irrational. We also explain why a common shortcut for repeating decimals works.

🧠 This video was inspired by a community poll and discussion:
👉 https://www.youtube.com/post/UgkxUneDYWdiE1I0_Yh7uDmSgEZYJmWef6BM

💬 Your turn:
Comment a number that is not rational and explain why — or share a repeating-decimal shortcut you use.

☕ Buy me a coffee: https://ko-fi.com/mathematicsfanatic

00:00 What does “rational” mean?
00:18 Let x equal the repeating decimal
00:32 Shifting the decimal
00:46 The subtraction trick
01:01 Why this proves it’s rational
01:15 Comment challenge
01:38 Shortcut explained
02:03 Extension challenge

Видео Proving a Repeating Decimal (Rational or Irrational?) канала Mathematics Fanatic