Questions: Perform the indicated operation. Write your answer in scientific notation. (2 x 10^4)(4.1 x 10^3) A) 82 x 10^8 B) 8.2 x 10^-7 C) 0.82 x 10^-6 D) 8.2 x 10^7

Transcript text: 15. Perform the indicated operation. Write your answer in scientific notation. \[ \left(2 \times 10^{4}\right)\left(4.1 \times 10^{3}\right) \] A) $82 \times 10^{8}$ B) $8.2 \times 10^{-7}$ C) $0.82 \times 10^{-6}$ D) $8.2 \times 10^{7}$

Solution

Solution Steps

To solve the problem, we need to multiply the two numbers given in scientific notation. We multiply the coefficients (2 and 4.1) and add the exponents of 10 (4 and 3). Finally, we express the result in scientific notation.

Step 1: Multiply the Coefficients

We start by multiplying the coefficients of the two numbers: \[ 2 \times 4.1 = 8.2 \]

Step 2: Add the Exponents

Next, we add the exponents of 10: \[ 4 + 3 = 7 \]

Step 3: Write the Result in Scientific Notation

Combining the results from the previous steps, we express the product in scientific notation: \[ 8.2 \times 10^{7} \]