Problem 101 - 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. $$\frac{2.4 \times 10^{-2}}{4.8 \times 10^{-6}}$$

Step-by-Step Solution

Answer

The result of \(\frac{2.4 \times 10^{-2}}{4.8 \times 10^{-6}}\) in scientific notation rounded to two decimal places is \(5 \times 10^{3}\).

Step 1: Division of Coefficients

To solve this problem, first divide the coefficients, so that is, \(2.4\) divided by \(4.8\). The result is \(0.5\). \(0.5\) is the coefficient of the first part of our answer.

Step 2: Subtraction of Exponents

Next, we subtract the exponents using the rule \(a^{m}/a^{n} = a^{m-n}\). Thus the next step would be \(-2 - (-6)\) which results in \(4\). So the exponent for the answer is \(4\).

Step 3: Write in Scientific Notation

Combine the coefficient and the exponent from the previous steps. The notation would be \(0.5 \times 10^{4}\).

Step 4: Adjust to Proper Scientific Notation

However, to put this in proper scientific notation, we should adjust it to have a coefficient between \(1\) and \(10\). To do this, \(0.5\) should be expressed as \(5 \times 10^{-1}\). The result would be \(5 \times 10^{-1} \times 10^{4} = 5 \times 10^{3}\).