Problem 88 - 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. $$\left(2 \times 10^{4}\right)\left(4.1 \times 10^{3}\right)$$

Step-by-Step Solution

Answer

The answer is \(8.2 \times 10^7\)

Step 1: Identify the terms

Identify the numerical and exponential parts of the terms. Here they are: \(2 \times 10^{4}\) and \(4.1 \times 10^{3}\).

Step 2: Multiply the numerical parts

Multiply the numerical parts of both terms. This gives us \(2 \times 4.1 = 8.2\)

Step 3: Add the exponents

Since the bases in question (10's) are the same, the exponents can be added when multiplying. This gives us \(10^{4+3} = 10^7\)

Step 4: Express the final answer in scientific notation

Multiply the result from step 2 (8.2) with the result from step 3 (\(10^7\)). Thus, the final answer in scientific notation is \(8.2 \times 10^7\)