If the only thing you ever want to do with numbers is count coins in your pocket, then I agree with you -- there'd be no point in using 0.9[bar]. But there's more to numbers than counting things! Even in the grocery store things are measured in finite decimals, like 1.73 pounds, and 1.73 is just a way of writing the fraction 173/100. If 1.73 isn't a number, then what is it, and why can we add and subtract and multiply and compare with it just like a number?

You might represent fractions, but you can hardly show what they represent, so 1/3 is the problem, and not the solution; and 1/2 is the problem, and not the solution... The more these problems are changed in form the less the reveal any truth, that is: As a concept that can be compared to a reality

1/3 cup of water is an amount of water such that, when you put 3 of those amounts together, you get a cup of water. I can do that in my kitchen. I think that shows exactly what 1/3 represents. It's a little more complicated to represent than 1, and the representation depends on the idea of 1 cup for its existence; but the representation of 1/3 cup is just as precise and just as connected to reality as that of 1 cup of water.

One is one...If .9[bar]could represent one, then the world would spare me, and write one in place of it... We reduce our fractions... We would not try to say 3/3, or 5/5 were one, or put them needlessly in any equasion, let alone as an answer

I agree that we would not put them in an equation needlessly. The point is that sometimes there is a need. For example, suppose we wish to add 1/3 + 1/5. To do this we write

1/3 + 1/5 = 1*1/3 + 1*1/5 = (5/5)*(1/3) + (3/3)*(1/5) = 5/15 + 3/15 = 8/15.

In the middle steps of this solution, we represent 1 as both 3/3 and 5/5 because doing so allows us to create a common denominator for the fraction. The "reduced" form of 1 will not help us solve this problem -- a more complex representation of 1 is needed. Also, "answers" have no special status or special need to be reduced in math, because answers don't always answer all questions. Sometimes your answer becomes a tool to solve a new problem. But solving the new problem may require representing your old answer in a more complicated way. For example, our answer from the previous problem is 8/15. Suppose we want to sum 1/3 + 1/5 + 1/30. It will save us some work to use our answer from the previous problem: 1/3 + 1/5 = 8/15. But we need to turn our answer into 16/30 so that we can get it into a common denominator with 1/30 and get the final result, 17/30.

Therefore, the "simplest" representation of a number may not be the most useful or valuable one. It depends on what you're using the number for.

It's the same way with 0.9[bar]. For example, suppose you need to subtract 0.173 from 1. Is it easier to do the subtraction as 0.9999... - 0.173, or as 1.000... - 0.173? Most people would find the first subtraction easier to do, because the second would require several carries. And it would be much worse if you had to subtract an infinite decimal from 1. For example, suppose you wanted to subtract 0.12356[bar] from 1. Is that easier as 0.9[bar] - 0.12356[bar] or as 1 - 0.12356[bar]? Again, the first way requires no carries.

Numbers have many equivalent representations in math, and each representation has its own uses. Often (as with 1/3 or .9[bar]) each of those uses are good for different problems. But those problems are all real and important. They come from physics, finance, or even basic cooking. I agree that it's good to keep things simple, but we will not oversimplify to the point where all we can do with our math is count coins.