Problem 94 - College Algebra Essentials

Question

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. $$\left(8.2 \times 10^{8}\right)\left(4.6 \times 10^{4}\right)$$

Step-by-Step Solution

Answer

The product of \((8.2 \times 10^{8}) \) and \((4.6 \times 10^{4})\) is \(3.77 \times 10^{13}\)

Step 1: Multiply the coefficients

Start by multiplying the coefficients, which are the numbers in front of the exponential part. This gives: \(8.2 \times 4.6 = 37.72\)

Step 2: Add the exponents

Next, add the exponents from the original numbers. This gives: \(8 + 4 = 12\)

Step 3: Combine the results

Combine the results from the previous steps into a new number in scientific notation. This gives: \(37.72 \times 10^{12}\)

Step 4: Adjust to scientific notation standards

Scientific notation standards maintain that the coefficient part should be between 1 and 10. Therefore, adjust the resulting number to meet the standards by moving the decimal point. The final result should be \(3.77 \times 10^{13}\), rounding the coefficient to two decimal places.