Final answer:
Multiplying and dividing numbers in scientific notation involves separate operations on the coefficient and powers of 10, while adding and subtracting numbers in scientific notation requires the powers of 10 to be the same before performing the operation. Examples are provided to illustrate the differences between the two operations.
Step-by-step explanation:
Multiplying and dividing numbers in scientific notation is different from adding and subtracting numbers in scientific notation in terms of the operations and the rules that apply. When multiplying and dividing numbers in scientific notation, you multiply or divide the coefficient separately from the powers of 10, and then adjust the powers of 10 accordingly. In contrast, when adding and subtracting numbers in scientific notation, the powers of 10 must be the same before you can perform the addition or subtraction of the coefficients.
For example:
Multiplying: (3.2 x 10^4) * (2.5 x 10^3) = (3.2 * 2.5) x (10^4 * 10^3) = 8 x 10^7
Dividing: (4.5 x 10^5) / (1.5 x 10^2) = (4.5 / 1.5) x (10^5 / 10^2) = 3 x 10^3
Adding: (6.2 x 10^4) + (4.8 x 10^3) = (0.062 x 10^6) + (0.048 x 10^6) = 0.11 x 10^6 = 1.1 x 10^5
Subtracting: (8.5 x 10^5) - (2.6 x 10^4) = (0.85 x 10^6) - (0.026 x 10^6) = 0.824 x 10^6 = 8.24 x 10^5
Learn more about Differences between multiplying/dividing and adding/subtracting numbers in scientific notation