Best How To :

First try to use Parameters as already mentioned in the comments. Second, use the SqlCommand.Prepare() statement. The actual speed also depends on your machine capacities (HD Write Speed/RAM). Here is the example (you may have to edit the SqlDbTypes according to your Colum Types)

    private static void RemoveUnits(string connectionString, string tableName, string columnID, string columnToFix)
    {
        Dictionary<int, string> rowsToEdit = new Dictionary<int, string>();

        using (SqlConnection connection = new SqlConnection(connectionString))
        {
            connection.Open();

            using (SqlCommand command = connection.CreateCommand())
            {
                command.CommandText = "SELECT " + columnID + "," + columnToFix + " FROM " + tableName;

                using (var reader = command.ExecuteReader())
                {
                    var indexOfR_MEASUREDVALUEID = reader.GetOrdinal(columnID);
                    var indexOfT_VALUE = reader.GetOrdinal(columnToFix);

                    while (reader.Read())
                    {
                        string t_value = reader.GetString(indexOfT_VALUE);
                        int t_id = reader.GetInt32(indexOfR_MEASUREDVALUEID);

                        string newValue = getWithoutUnit(t_value);
                        if (newValue != null)
                        {
                            // save values in dictionary
                            rowsToEdit[t_id] = newValue;
                        }
                    }
                }
            }

            Console.WriteLine("start writing " + rowsToEdit.Count + " entries?");
            Console.ReadLine();

            string updateCmd = "UPDATE " + tableName + " SET " + columnToFix + "= @Value WHERE " + columnID + "= @Key;";

            using (SqlTransaction transaction = connection.BeginTransaction())
            {
                SqlCommand sqlCmd = connection.CreateCommand();
                sqlCmd.CommandText = updateCmd;
                sqlCmd.Parameters.Add("@Value", System.Data.SqlDbType.NVarChar, -1);
                sqlCmd.Parameters.Add("@Key", System.Data.SqlDbType.Int);

                // important for performance
                sqlCmd.Prepare();

                foreach (var update in rowsToEdit)
                {
                    // change values of parameters
                    sqlCmd.Parameters["@Key"].Value = update.Key;
                    sqlCmd.Parameters["@Value"].Value = update.Value;

                    // and execute it
                    sqlCmd.ExecuteNonQuery();
                }

                transaction.Commit();
            }
        }
        Console.WriteLine(rowsToEdit.Count + " commands executed");
    }

Edit: if getWithoutUnit(string) does something not very complex, you could probably do your operation with a single statement using TSQL, which comes with various string manipulation capabilities. Like UPDATE TableName SET StringColumn = <string manipulation TSQL here>, see http://msdn.microsoft.com/en-us/library/ms181984.aspx

Edit2: added transaction from comment hint (indeed should be faster as well), strongly typed columns