Questions: Perform the multiplication shown below. Then submit your answer in decimal form. (2 × 10^-3)(7 × 10^-2)

Transcript text: Problem 7 of 15 Submit Perform the multiplication shown below. Then submit your answer in decimal form. \[ \left(2 \times 10^{-3}\right)\left(7 \times 10^{-2}\right) \]

Solution

Solution Steps

To solve the given multiplication problem involving scientific notation, we need to multiply the coefficients and then add the exponents of the powers of 10.

Step 1: Multiply the Coefficients

First, we multiply the coefficients of the two numbers: \[ 2 \times 7 = 14 \]

Step 2: Add the Exponents

Next, we add the exponents of the powers of 10: \[ -3 + (-2) = -5 \]

Step 3: Combine the Results

We combine the results from the previous steps to get the final answer in scientific notation: \[ 14 \times 10^{-5} \]

Step 4: Convert to Decimal Form

Finally, we convert the scientific notation to decimal form: \[ 14 \times 10^{-5} = 0.00014 \]