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Dotz
Formal writing is the proper writing with specific word choices that is suitable for a formal audience. So, basically if you are planning on writing to a business, giving a speech, or sending in academic work, then formal writing is necessary. However, if you are writing a letter to your best friend or sending a text message to one of your siblings, then you will probably write informally with slang words, etc. It all depends on who the writing is aimed at but keep in mind that it should always be formal in formal situations such as a conference, email to a teacher, etc. 

Let me know if you need anything else. :)

          - Dotz