I was working on a spreadsheet in Excel (I'm a plebe, I know), and I came across a fraction that actually equated to 33.3% of a total number. While looking at it, and looking at the number that went with it, I realized that fractions of 1/3 continue on ad infinitum.
My question is this: Can fractions accurately be converted to decimals without rounding or assuming that .000 ad infinitum = 0 and still have the numbers reach the intended and proven result?
I don't wish for this to be specifically for Excel. I'm asking for more of a theoretical question about the continuation of fractions to an infinite number of places.
From what I know of fractions, 1/3 would equate to .333... ad infinitum. By my reasoning, the difference between 1 and "3/3" would be infinitesimally smaller the further you go. With that logic TECHNICALLY 9.99... != 10.0 or is there something I'm missing? I understand that in practice the numbers match, but given infinite places, when graphed the numbers would never intersect, but would get infinitesimally smaller.
Example: 3.33.... + 6.66.... = 9.99.... != 10.00....
Given an infinite number of decimal places, then
Note: I have no idea how to use the MathJax equations. If anyone wants to edit that in, I'd be appreciative.