[split] 0.999... equals 1

[Meatball]

You can also think of it as a side effect of the system we use to represent numbers.

1/10, though very simple in decimal(base10) notation, is infinitely long when represented in binary(base2).

.1(decimal) = 1/10 (decimal) = 0.00110011...(binary)
or
0.333...(base10) = 1/3 (base10) = 0.1 (base3)

Also,

In base2, 0.111... = 1.
In base3, 0.222... = 1.
In base16, 0.fff... = 1.

Sorta unrelated, but I suggest looking into other number systems. It's really fascinating and will change the way you think about math. For example, we all know that computers generally use binary(or hexadecimal as a means of representing binary). Did you know that the Mayans used a base20 counting system? Or that the Yuki tribe of Native Americans used a base8 number system, because they counted using the spaces between their fingers, rather than the fingers themselves, which one might conclude is the basis of our decimal system?

It's really fascinating stuff, even if you aren't a math geek.