If it is unambiguous and can be recognized by a computer it's probably OK. For very large or very small numbers the format is normally n.nnnnn x 10m in the form n.nnnnnEm or similar. All integers have to be written out exactly.
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In scientific notation all numbers are written in the form: a*10b where a is a decimal number such that 1 ≤ a < 10 and b is an integer.
I don't know what you mean "how to write the rules." In the US, "standard" notation means "long form", i.e. 6,000,000, while "scientific" notation means the exponential form, 6x106. I had thought it was the same in the UK, but Mehtamatics says otherwise: "Standard notation and scientific notation are the same in terms of UK usage of these phrases."
Scientific notation is of little use for long mathematical expressions. It is used to express very large or very small numbers - not expressions.
Scientific Notation, Standard Form and Exponential Notation are used in different countries but all have the same meaning. It is a way of expressing a number as a value between 1 and 10 multiplied by a power of 10. 5.63 x 10² is the standard form number of 563. 8.6927 x 10^4 is the standard form number of 86927.
20,000 + 3,400,000