Question

Calculate (3.78×103)×(7.21×102) in scientific notation and rounded to the correct number of significant figures.

A. 2.73×10^6
B. 2.7×10^6
C. 2.7×10^5
D. 2.7×10^4

Answer 1

To find the product of (3.78×103)×(7.21×102) and express it in scientific notation with the correct significant figures, multiply the coefficients and add the exponents. The result is 2.73×106, which should be rounded to three significant figures.

Step-by-step explanation:

To calculate (3.78×103)×(7.21×102) in scientific notation and rounded to the correct number of significant figures, follow these steps:

1. Multiply the coefficients (3.78 and 7.21) to get 27.2658.
2. Add the exponents (3 and 2) to get 105 since when multiplying powers of 10, you add the exponents.
3. Combine the results from steps 1 and 2 to form the unrounded scientific notation expression, which is 27.2658×105.
4. Now, the original numbers have 3 and 3 significant figures, respectively, so our final answer should also have 3 significant figures.
5. Round 27.2658 to 27.3 and express it in scientific notation to get 2.73×106.

Thus, the answer in scientific notation, rounded to three significant figures, is 2.73×106, which corresponds to option A.