Is 99% Enough?

Have you ever heard someone mention they are 99% done, completed, or finished? Some would say, let us know when you are 100% complete.

I would argue that 99% is complete and we can prove it.

First think of 99% as a number, as 0.999… (a repeating decimal). Next 100% would be equal to 1.00. Now, let’s look at the fraction 1/3. When you divide the number 1 by 3 on a calculator you will get 0.333… as repeating decimal. Therefore, 1/3 + 1/3 + 1/3 is equal to 3/3 which is 1. Meaning 0.333… + 0.333… + 0.333… is equal to 0.999… which is 1.

We can also come to the same conclusion if we look at 1/9.

1/9 = 0.111…

Multiplying both sides by 9 and we would get

9/9 = 0.999…

Which is, 1 equals 0.999…

Not convinced?

Try looking at 0.999… and set it equal to a variable.

We would have X = 0.999…

Multiple this equation by 10

10X = 9.999…

Subtract X from both sides of the equation and we are left with

10X – X = 9.999… - X

9X = 9.999… - X

Substitute 0.999… for the variable on the right side of the equation and we are left with

9X = 9.999… - 0.999…

9X = 9.000

Dividing both sides of the equation by 9 and

X = 1

Substitute X back to the original equation (X = 0.999…) and we have

1 = 0.999…

So the next time someone mentions they are 99% done, you can let them know they are finished!

These proofs along with additional ones can be explored on https://math.fandom.com/wiki/Proof:The_Decimal_0.999..._is_Equivalent_to_1