7. A character conversion process for converting inputted characters by using an information processing apparatus which has an input unit including a character input key and one or more select keys, a data processing unit, and a display device, comprising: recording and holding a table and a conversion database in the information processing apparatus, where the table contains characters and total numbers of times the character input key is to be pressed down before inputting the characters, the total numbers of times being assigned to the characters respectively, and the conversion database contains strings of one or more characters and converted data items which are converted from the strings of one or more characters and correspond to the strings of one or more characters respectively; making, by the data processing unit, a predictive search of the conversion database for a plurality of conversion candidates on the basis of one or more characters inputted by use of the character input key; obtaining, by the data processing unit, an unconverted character included in each of the plurality of conversion candidates and immediately following the one or more characters, obtaining, in reference to the table, the total number of times the character input key is to be pressed before inputting the unconverted character, and determining an order of display, on a screen of a display device, of the plurality of conversion candidates to align with a descending order of the total number of times the character input key is to be pressed down before inputting the unconverted character; displaying, by the display device, the plurality of conversion candidates in the order of display on the screen; and receiving, by the data processing unit, confirmation of one of the plurality of conversion candidates which is selected by use of the one or more select keys as a converted data item, where a position of selection on the screen can be shifted among the plurality of conversion candidates according to the order of display when one of the one or more select keys is pressed down.
7. A character conversion process for converting inputted characters by using an information processing apparatus which has an input unit including a character input key and one or more select keys, a data processing unit, and a display device, comprising: recording and holding a table and a conversion database in the information processing apparatus, where the table contains characters and total numbers of times the character input key is to be pressed down before inputting the characters, the total numbers of times being assigned to the characters respectively, and the conversion database contains strings of one or more characters and converted data items which are converted from the strings of one or more characters and correspond to the strings of one or more characters respectively; making, by the data processing unit, a predictive search of the conversion database for a plurality of conversion candidates on the basis of one or more characters inputted by use of the character input key; obtaining, by the data processing unit, an unconverted character included in each of the plurality of conversion candidates and immediately following the one or more characters, obtaining, in reference to the table, the total number of times the character input key is to be pressed before inputting the unconverted character, and determining an order of display, on a screen of a display device, of the plurality of conversion candidates to align with a descending order of the total number of times the character input key is to be pressed down before inputting the unconverted character; displaying, by the display device, the plurality of conversion candidates in the order of display on the screen; and receiving, by the data processing unit, confirmation of one of the plurality of conversion candidates which is selected by use of the one or more select keys as a converted data item, where a position of selection on the screen can be shifted among the plurality of conversion candidates according to the order of display when one of the one or more select keys is pressed down. 10. The character conversion process according to claim 7 , wherein the conversion database stores frequency-of-use information indicating frequency of previous use of converted data items, the frequency-of-use information is updated according to confirmation of one of the plurality of conversion candidates as the converted data item, and in a case where conversion candidates searched out includes a character which immediately follows the one or more already inputted characters and total number of times the character input key is to be pressed down before inputting the character is identical to each other in the searched out conversion candidates, an order of display of the searched out conversion candidates is determined so that the total number of times one of the one or more select keys is to be pressed down before selecting each of the searched out conversion candidates decreases with increase in frequency of previous use of the searched out conversion candidates.