Final answer:
In scientific notation, multiplication involves multiplying the coefficients and adding the exponents, while division involves dividing the coefficients and subtracting the exponents. Both operations follow the regular sign rules for positive and negative numbers. This shorthand system greatly simplifies computations with large or small numbers.
Step-by-step explanation:
When working with multiplication and division in scientific notation, there are simple rules to follow which make the calculations easier than dealing with large numbers.
To multiply numbers in scientific notation, you multiply the coefficient (N) and add the exponents (n). An example of this could look like (2 x 103) * (3 x 104) which simplifies to 6 x 107 because 2*3=6 and 3+4=7.
Conversely, when we divide numbers in scientific notation, we divide the coefficient (N) and subtract the exponents of the powers of ten. So, (8 x 106) / (4 x 103) becomes 2 x 103, since 8/4=2 and 6-3=3.
It's important to note that the signs of numbers follow the same rules in multiplication and division. If you multiply or divide two positive numbers, or two negative numbers, the result will be positive. If you multiply or divide numbers with opposite signs, the result will be negative.
In scientific notation, significant figures are retained, and zeros reported in front of the multiplication sign are indeed significant. Understanding how to operate with scientific notation helps greatly in simplifying the multiplication and division of very large or small numbers, which is common in scientific calculations.
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