Well, everyone knows that putting … at the end of three nines in a row means that 9 goes on infinitely, so you answered false. 0.999… could never equal 1, right?
Answer: Nope. Wrong. It is, in fact, equal to one. Here’s a proof to prove it:
The Explanation: The reason this is so hard to grasp is because the concept of infinity is just kind complicated to grasp in the first place. Most people just imagine that there’s a last 9 somewhere down the line. But the thing is, the 9s are never-ending.
It’s also important to remember that just because two numbers look different doesn’t mean they’re not the same value. 0.5 is definitely the same as 1/2. And 2 + 2 is the same as 4. And 0.999… is absolutely equal to 1. It’s just two different ways of expressing the same value.
Here’s another, even simpler proof that might help you understand. We all agree that 1/3 = 0.333… repeating, right? Well, check this out:
See! It’s actually pretty simple! If you’re still having a hard time grasping it, let expert YouTube explainer, ViHart, explain it to you in complete detail (and with fun doodles).
