In converting numbers into scientific notation, first you should move the decimal point such that there would be one significant figure to the left of the decimal point.
Examples:
299792458 -> 2.99792458
0.0000000000667428 -> 6.67428
Then, count the number of times you moved the decimal point. Note the direction of movement.
Examples:
299792458 -> 2.99792458 (8 digits to the left)
0.0000000000667428 -> 6.67428 (11 digits to the right)
Lastly, express the number as a product of the modulus (the number with the decimal point moved) and a power of ten.
Examples:
299792458 -> 2.99792458 x 108 (If the decimal point was moved to the left, the power is positive)
0.0000000000667428 -> 6.67428 x 10-11 (If the decimal point was moved to the right, the power is negative)
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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.
Scientific notation is of little use for long mathematical expressions. It is used to express very large or very small numbers - not expressions.
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."