Problem 97 - 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. $$\frac{3.6 \times 10^{4}}{9 \times 10^{-2}}$$

Step-by-Step Solution

Answer

The final answer is \(4 \times 10^{5}\).

Step 1: Divide the Coefficients

Divide the coefficient in the numerator \(3.6\) by the coefficient in the denominator \(9\). The quotient is \(0.4\)

Step 2: Subtract the Exponents

Then subtract the exponent in the denominator \(-2\) from the exponent in the numerator \(4\). This gives: \(4 - (-2) = 4 + 2 = 6\)

Step 3: Adjust the Final Answer

The final answer should be in standard scientific notation, which means the coefficient should be between 1 and 10. Multiply \(0.4\) by \(10\) to get \(4\), and subtract \(1\) from the exponent \(6\) to get \(5\).