Problem 89 - 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. $$\left(1.6 \times 10^{15}\right)\left(4 \times 10^{-11}\right)$$

Step-by-Step Solution

Answer

The result is \(6.4 \times 10^4\).

Step 1: Identify the Coefficients and Exponents

The two numbers to multiply are \(1.6 \times 10^{15}\) and \(4 \times 10^{-11}\). Here, the coefficients are 1.6 and 4, and the exponents are 15 and -11.

Step 2: Multiply the Coefficients

Start by multiplying the coefficients 1.6 and 4, which gives 6.4.

Step 3: Add the Exponents

Next, add the exponents 15 and -11. Adding 15 and -11 gives 4.

Step 4: Combine the Results

Combine the results from Steps 2 and 3 to write the scientific notation. This gives \(6.4 \times 10^4\).

Step 5: Round Off the Results

In this case, no rounding off is necessary as the decimal factor in the scientific notation is already up to two decimal places.