Why MySQL reduce float precision and recover back would not change the number?

Here is the test:

1. First I create a field with float(11, 9) and insert a number 0.12345679, when selecting this row, it shows 0.123456791;
2. Second I alter the field to float(11, 4) and select it out, it shows 0.1235;
3. Third I alter the field back to float(11, 9) and get the number, it shows 0.123456791;

Why the action changing field precision would not lose the data's precision, and wondering why.

mysql> create table `test`.`test_float`(id int primary key auto_increment, `num` float(11, 9));
Query OK, 0 rows affected, 1 warning (0.03 sec)

mysql> insert into test.test_float(num) values(0.123456789);
Query OK, 1 row affected (0.00 sec)

mysql> select * from test.test_float\G
*************************** 1. row ***************************
 id: 1
num: 0.123456791
1 row in set (0.00 sec)

mysql> alter table test.test_float modify num float(11, 4);
Query OK, 0 rows affected, 1 warning (0.01 sec)
Records: 0  Duplicates: 0  Warnings: 1

mysql> select * from test.test_float\G
*************************** 1. row ***************************
 id: 1
num: 0.1235
1 row in set (0.00 sec)

mysql> alter table test.test_float modify num float(11, 9);
Query OK, 0 rows affected, 1 warning (0.01 sec)
Records: 0  Duplicates: 0  Warnings: 1

mysql> select * from test.test_float\G
*************************** 1. row ***************************
 id: 1
num: 0.123456791
1 row in set (0.00 sec)