Problem 104 - 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. $$\frac{282,000,000,000}{0.00141}$$

Step-by-Step Solution

Answer

The result of the computation is \(2 \times 10^{14}\).

Step 1: Identification of Scientific Notation

Firstly, convert the given numbers into scientific notation. The number \(282,000,000,000\) can be written as \(2.82 \times 10^{11}\), and \(0.00141\) can be written as \(1.41 \times 10^{-3}\).

Step 2: Perform Division

Next, divide the numbers, retaining the scientific notation format. The operation will look like this: \(\frac{2.82 \times 10^{11}}{1.41 \times 10^{-3}}\). This division can be broken down into two parts for simplification: the division of the actual numbers and the division of powers-of-ten.

Step 3: Division of Actual Numbers

First, divide \(2.82\) by \(1.41\). The resultant is approximately \(2\).

Step 4: Division of Powers-of-Ten

Second, divide \(\frac{10^{11}}{10^{-3}}\). This operation simplifies to \(10^{11+3}\), which equals \(10^{14}\).

Step 5: Combine Results

Lastly, combine the results of the division of actual numbers and the division of powers-of-ten, which gives \(2 \times 10^{14}\).