Suppose you have two numbers in scientific notation.
· Rename them so that the exponents (powers of 10) are the same,
· add the two mantissae to form the new mantissa, and append the 10 and exponent,
· if the resulting mantissa is less tahn 1 then rename the mantissa and adjust the exponent accordingly.
For the first stage you may rename both numbers or either one.
For example,
3.5*10^4 - 4.5*10^3 = 35*10^3 - 4.5*10^3 = (35-4.5)*10^3 = 30.5*10^3 = 3.05*10^4
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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.
If you are adding or subtracting two numbers in scientific notation, you must rewrite one of the numbers to the same power of ten as the other, before performing the addition (or subtraction).