I don't understand how there is an uncountable infinite amount of real numbers. Why can't we do the same thing with fractions (there is a countable amount of fractions). We do this by creating a table where the horizontal axis lists all the numbers from 0 too infinity. The vertical axes lists all the powers of ten from 0 too -infinity. If we would fill the table we would have all real numbers. We can make a list of this by drawing a line criss-cross through the table. This table can be viewed by clicking the link.
Could somebody please explain what is wrong with my thinking. Thank you.
Your method isn't even counting all rational numbers. For instance, the number $\frac13=0.\overline3$ doesn't occur in the table because there is no such natural number as $\overline3$ with an infinite number of digits.