Problem 102 - 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. $$\frac{1.5 \times 10^{-2}}{3 \times 10^{-6}}$$

Step-by-Step Solution

Answer

The short answer for the division computation is \(0.5 \times 10^4\).

Step 1: Separate the Coefficients and Exponents

Start by splitting the given expression into two parts, separating the coefficients (also known as the decimal factors) and the exponents. This yields the following: \( \frac{1.5}{3} \times \frac{10^{-2}}{10^{-6}} \)

Step 2: Perform Division on Coefficients

Perform the division operation on the coefficients. The calculation is \( \frac{1.5}{3} = 0.5 \)

Step 3: Apply the Rules of Exponents

Now, apply one the rules of exponents which states that when you divide two powers with the same base, you subtract the exponents. The calculation is \( \frac{10^{-2}}{10^{-6}} = 10^{-2-(-6)} = 10^4 \)

Step 4: Combine the Results and Round

Combine the results from step 2 and step 3 and express it in scientific notation. Before that, remember that the coefficient (decimal factor) should be between 1 (inclusive) and 10 (exclusive). The number 0.5 is already within this range so we do not need to adjust the coefficient and the exponent further. Therefore, the answer is \( 0.5 \times 10^4 \). If necessary, round the coefficient to two decimal places. Since there are no more than two decimal places in this coefficient, no rounding is necessary