Problem 101 - Algebra and Trigonometry

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 answer is \(5 \times 10^{3}\).

Step 1: Divide Coefficients

Let's first divide the coefficients, which are numbers in front of \(10^{n}\). So, \(2.4 \div 4.8 = 0.5\)

Step 2: Subtract Exponents

Next, for the powers of ten, subtract the exponent of the denominator from the exponent of the numerator. So, \(-2 -(-6) = 4\). Therefore, the result of this operation is \(0.5 \times 10^{4}\).

Step 3: Convert to Proper Scientific Notation

Finally, the exponent of 10 needs to increase by 1 (to 5), and the coefficient needs to be reduced to 5 in order that we represent the result as a number between 1 and 10 multiplied by a power of 10. Thus, the correct answer is \(5 \times 10^{3}\).