To multiply m x 10a by n x 10b:
multiply the numbers (m x n)
add the powers (a + b)
(m x 10a) x (n x 10b) = mn x 10a+b
To divide m x 10a by n x 10b:
divide the numbers (m / n)
subtract the powers (a - b)
(m x 10a) / (n x 10b) = m/n x 10a-b
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A positive and a negative give you a negative. Two negatives give you a positive. This is true for multiplication and division.
20,000 + 3,400,000
Standard notation (in the UK) is the same as scientific notation. So the one rule to use is DO NOTHING!
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."
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.