jmc

There are 9000 four-digit numbers, from 1000 to 9999, inclusive. Rather than counting the numbers with repeated digits, we'll count the numbers without a repeated digit. In this case, there are 9 choices for the first digit (all except 0), 9 choices for the second digit (all except the first), 8 choices for the third digit (two are already picked), and 7 choices for the fourth digit (three are already picked). Therefore, there are $9\cdot 9\cdot 8\cdot 7$ numbers without a repeated digit, leaving $9000-9\cdot 9\cdot 8\cdot 7$ numbers with a repeated digit. To find the percent, we divide this result by 9000, so we get $$\frac{9000-9\cdot 9\cdot 8\cdot 7}{9000}=\frac{1000-504}{1000}=.496$$which is $49.6$ percent. Therefore, $x=\boxed{49.6}.$