Problem 99 - 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. $$\frac{4.8 \times 10^{-2}}{2.4 \times 10^{6}}$$

Step-by-Step Solution

Answer

The result is \(2 \times 10^{-8}\).

Step 1: Convert from Scientific Notation to Decimal Notation

We're given \(4.8 \times 10^{-2}\) and \(2.4 \times 10^{6}\). To transform these from scientific notation to normal decimal notation, we shift the decimal point. For \(4.8 \times 10^{-2}\), we move the decimal point two places to the left, yielding 0.048. For \(2.4 \times 10^{6}\), we shift the decimal point six places to the right, resulting in 2,400,000.

Step 2: Perform the Calculation

Now, we divide the two numbers we calculated in the previous step: \(\frac{0.048}{2400000} = 2 \times 10^{-8}\).

Step 3: Convert Back to Scientific Notation

Recognizing that 2 falls between 1 and 10, this is correct scientific notation. Therefore, the final result in scientific notation is \(2 \times 10^{-8}\).