Why is the set of Real numbers uncountable?

For example, counting a 2D array as incrementing diagonally such as:

<table> <tr><td>0</td><td>1</td><td>3</td><td>...</td></tr> <tr><td>2</td><td>4</td><td>7</td><td>...</td></tr> <tr><td>5</td><td>8</td><td>12</td><td>...</td></tr> <tr><td>...</td><td>...</td><td>...</td><td>...</td></tr> </table>

...and writing out the Real numbers in that array as incrementing +/- along one axis, and dividing by 10 on the other, such as:

<table> <tr><td>0</td><td>0.0</td><td>0.00</td><td>...</td></tr> <tr><td>1</td><td>0.1</td><td>0.01</td><td>...</td></tr> <tr><td>-1</td><td>-0.1</td><td>-0.01</td><td>...</td></tr> <tr><td>2</td><td>0.2</td><td>0.02</td><td>...</td></tr> <tr><td>...</td><td>...</td><td>...</td><td>...</td></tr> <tr><td>314</td><td>31.4</td><td>3.14</td><td>...</td></tr> <tr><td>...</td><td>...</td><td>...</td><td>...</td></tr> </table>

...how is this not the set of Reals being countable? For example, any value of PI to anu given number of decimal places appears in this table (and therefore has a countable index).

The only problem is that the first row is all the same number, so index 0, 1, 3 etc' all result in 0, so is it only that it's uncountable because it is not bijective.