Problem 103 - 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. $$\frac{480,000,000,000}{0.00012}$$

Step-by-Step Solution

Answer

The result of the division is \(4 \times 10^{15}\).

Step 1: Transform to Scientific Notation

The given numbers, i.e., the numerator, \(480,000,000,000\), and the denominator, \(0.00012\), need to be transformed into scientific notation. The numerator \(480,000,000,000\) can be written as \(4.8 \times 10^{11}\) and the denominator \(0.00012\) can be written as \(1.2 \times 10^{-4}\).

Step 2: Performing Division

Now, the division is performed separately on the base numbers and exponents. \(4.8\) divided by \(1.2\) yields \(4\), and for the powers of 10, subtract the exponent of the denominator from the exponent of the numerator, i.e., \( 11 - (-4) = 15 \)

Step 3: Writing Final Answer in Scientific Notation

So the final answer in scientific notation is \(4 \times 10^{15}\).