Problem 87 - 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. $$\left(3 \times 10^{4}\right)\left(2.1 \times 10^{3}\right)$$

Step-by-Step Solution

Answer

The answer to \( \left(3 \times 10^{4}\right)\left(2.1 \times 10^{3}\right)\) in scientific notation is \(6.3 \times 10^{7}\).

Step 1: Multiply the decimal parts

Start by multiplying the decimal parts of each number. Hence, \(3 \times 2.1 = 6.3\).

Step 2: Multiply the exponent parts

Next, multiply the powers of 10 together. When you multiply powers with the same base, you simply add the exponents. So, \(10^{4} \times 10^{3} = 10^{4+3} = 10^{7}\).

Step 3: Write result in scientific notation

Combine the results from steps 1 and 2 to write the final answer in scientific notation. Based on the obtained results, the answer is \(6.3 \times 10^{7}\).