Postgres columns of latitude and longitude from varchar to numeric
You need the USING clause to ALTER TABLE ... TYPE ..., e.g.:

ALTER TABLE mytable
  ALTER COLUMN "Longitude" TYPE NUMERIC(14, 11) 
    USING ("Longditude"::NUMERIC(14,11)),
  ALTER COLUMN "Latitude" TYPE NUMERIC(14, 11) 
    USING ("Latitude"::NUMERIC(14,11));


assuming you want a numeric with precision 14 and scale 11 and your columns really do have an upper case first letter.

For more details see the manual on ALTER TABLE.

after edit:

You seem to be using a broken client that's trying to prepend an EXPLAIN to the ALTER TABLE. You can't EXPLAIN an ALTER TABLE statement.