Problem 92 - 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. $$\left(5.1 \times 10^{-8}\right)\left(3 \times 10^{-4}\right)$$

Step-by-Step Solution

Answer

The result of the multiplication rounded to two decimal places in scientific notation is \(1.53 \times 10^{-11}\).

Step 1: Understanding the Multiplication of Scientific Notation

The first rule of multiplication in scientific notation is to multiply the coefficient (decimal values) and then add the exponent values. Here the coefficient is \(5.1\) and \(3\), and the exponent values are \(-8\) and \(-4\) respectively for each number.

Step 2: Multiply the coefficient

Multiply the two coefficients \(5.1\) and \(3\) which gives \(15.3\).

Step 3: Add the Exponents

Add the two exponent values \(-8\) and \(-4\) which gives \(-12\).

Step 4: Combine the Results

Combine the results of the multiplication and the addition to get the answer in scientific notation. This gives an unrounded result as \(15.3 \times 10^{-12}\).

Step 5: Rounding

As per the instructions in the exercise, round the decimal factor in the scientific notation answer to two decimal places. This results in the final answer of \(1.53 \times 10^{-11}\).