Problem 95 - 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. $$\frac{8.4 \times 10^{8}}{4 \times 10^{5}}$$

Step-by-Step Solution

Answer

The final answer is \(2.1 \times 10^{3}\).

Step 1: Identifying the numbers

Firstly, identify and separate the numbers from the scientific notation and the powers of ten: \(8.4\) and \(10^{8}\) from the numerator, and \(4\) and \(10^{5}\) from the denominator.

Step 2: Dividing the numbers

Next, divide \(8.4\) by \(4\), which gives \(2.1\). Separately divide \(10^{8}\) by \(10^{5}\) using the property of exponents that \(a^{m}/a^{n}=a^{m-n}\), which gives \(10^{3}\).

Step 3: Combining the results

Finally, multiply the results obtained from the above step \(2.1 \times 10^{3}\).

Step 4: Checking and expressing the answers in Scientific notation

The answer is thus \(2.1 \times 10^{3}\) which is already in the correct scientific notation form and doesn't need to be rounded.