Sum of doubles giving incorrect value

[Matthew Jenkins]

I have a table (of accounts) with a balance field that is of type 'double'. If the accounts balance, the sum of the balance field of all records should equal 0:

mysql> select balance from accounts;
+---------+
| balance |
+---------+
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| -847 |
| 0 |
| 805.01 |
| 41.99 |
+---------+
12 rows in set (0.01 sec)

So, "SELECT SUM(balance) FROM accounts" should return 0, yes?

mysql> select sum(balance) from accounts;
+---------------------+
| sum(balance) |
+---------------------+
| -7.105427357601e-15 |
+---------------------+
1 row in set (0.00 sec)

I know it's almost 0, but that's gotta be a bug, right?

# /usr/local/libexec/mysqld --version
/usr/local/libexec/mysqld Ver 5.1.49 for portbld-freebsd8.1 on i386 (FreeBSD port: mysql-server-5.1.49)