PUZZLE #10 Responses & hints

Congrats to all who worked on this one!

If you are still thinking about it, do not look below.

A puzzle like this is sometimes hard to discuss on paper and/or online!

You really need face - to – face communication.

I think all were able to get the first part,

1/9 = 0.11111 . . .

2/9 = 0.22222 . . .

and so on.

The pattern is pretty obvious.

This made the calculation about 1/9 + 2/9 = 1/3 = 0.3333 . . . easy.

When you calculate 1/9 + 8/9 you get 9/9 = 1, but when you compute with decimals

(by hand) you get 0.11111 . . . + 0.88888 . . . = 0.99999 . . . ??

So is 1 = 0.99999 . . .?

It has to be! (but why?)

And why does your calculator give 1 instead of 0.99999 . . . ?

Think about it some more if you need to.