It occurs at the beginning of each subsequent sura of the Qur'an...
It occurs at the beginning of each subsequent sura of the Qur'an, except for the ninth sura (see, however, the discussion of the 8th and 9th chapters of the Qur’an at eighth sura), but is not numbered as a verse except, in the currently most common system, in the first sura (chapter). The Basmala occurs twice in the 27th sura, at the beginning and in verse 30 (where it prefaces a letter from Sulayman (Prophet Solomon) to the Queen of Sheba, Balqees (or Balqis).
The Basmala has a special significance for Muslims, who are to begin each task after reciting the verse. It is often preceded by Ta’awwudh. In Arabic calligraphy, it is the most prevalent motif, more so even than the Shahada. The three definite nouns of the Basmala, Allah, ar-Rahman and ar-Rahim correspond to the first three of the traditional 99 Names of Allah in Islam. Both ar-Rahman and ar-Rahim are from the same triliteral root, rahm "to feel sympathy or pity".
According to Lane, ar-rahman is more intensive, including in its objects the believer and the unbeliever, and may be rendered as "The Compassionate", while ar-rahim has for its peculiar object the believer, considered as expressive of a constant attribute, and may be rendered as "The Merciful". In a commentary on the Basmala in his Tafsir at-Tabari writes: “The Messenger of Allah (ﺹ) said that Jesus was handed by his mother Mary over to a school in order that he might be taught.
[The teacher] said to him: ‘Write “Bism (In the name of)”.’ And Jesus said to him: ‘What is “Bism”?’ The teacher said: ‘I do not know.’ Jesus said: ‘The “Ba” is Baha’u'llah (the glory of Allah), the “Sin” is His Sana’ (radiance), and the “Mim” is His Mamlakah (sovereignty).” The total value of the letters of "Bismillah ar-Rahman ar-Rahim" according to one Arabic system of numerology is 786. There are two methods of arranging the letters of the Arabic alphabet.
One method is the most common alphabetical order (used for most ordinary purposes), beginning with the letters Alif ا, ba ب, ta ت, tha ث etc. The other method is known as the “Abjad nimerals’ method” or ordinal method. In this method the letters are arranged in the following order:: Abjad, Hawwaz, Hutti, Kalaman, Sa'fas, Qarshat, Sakhaz, Zazagh; and each letter has an arithmetic value assigned to it from one to one thousand.