Listing real numbers as countable like listing rational numbers

Question

like proving the set of positive rational numbers are countable, where we list the rationals as the following list, why can't we represent real numbers like the same?

If positive Rational numbers (p/q) can be listed as,

1/1 2/1 3/1 4/1 .. ..
1/2 2/2 3/2
1/3 2/3
1/4
..
..

why can't real numbers (d1d2d3.... x 10^{d'1 d'2 d'3 ...}) be listed as the following to prove they are countable

  ..         (-2x10^-1)(-2x10^0) (-2x10^1)
   .    ..   (-1x10^-1)(-1x10^0)    ..
  ..         ( 0x10^-1)( 0x10^0)           ...  
.... 1x10^-2   1x10^-1   1x10^0   1x10^1 1x10^2 .....
  ..             ..      2x10^0   2x10^1 ..
   .             ..      3x10^0   3x10^1 ..     ..

if r in R is represented as d1 d2 d3 ... x 10^ (d'1 d'2 d'3 ..) The x axis representing the d1d2d3.. and y axis representing the powers of 10 (d'1 d'2 d'3 ..)

I can always find a number big enough and its powers of ten small enough to find a real number.

Answer 1

It is impossible, because reals are uncountable. One of methods of proving it is the famous Cantor diagonal argument: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

Answer 2

Consider $\pi $ so that is $3$ on one side and $.1415926.....$ on the other. So you list it in the 3rd column and the 1415926.... row. Which is what row exactly?

The problem is that the "powers of ten" are not integers and not enumerable as integers. They have an infinite number of digits whereas integers always have a finite number of digits, and that makes all the difference, as Cantor famously showed.

You say you can always find powers of ten small enough. But you find way too many of them. Between .2 and .3 there are an uncountable many in between.