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Chapter 0: Problem 104

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. $$\frac{282,000,000,000}{0.00141}$$

Short Answer

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

Step by step solution

01

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 \(1.41 \times 10^{-3}\).
02

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.
03

Division of Actual Numbers

First, divide \(2.82\) by \(1.41\). The resultant is approximately \(2\).
04

Division of Powers-of-Ten

Second, divide \(\frac{10^{11}}{10^{-3}}\). This operation simplifies to \(10^{11+3}\), which equals \(10^{14}\).
05

Combine Results

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

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