In Exercises 87–106, 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. 282,000,000,000/0.00141

Verified step by step guidance

1. Convert both numbers to scientific notation. The number 282,000,000,000 can be written as \(2.82 \times 10^{11}\). The number 0.00141 can be written as \(1.41 \times 10^{-3}\).
2. Set up the division of the two numbers in scientific notation: \(\frac{2.82 \times 10^{11}}{1.41 \times 10^{-3}}\).
3. Divide the decimal parts: \(\frac{2.82}{1.41}\).
4. Subtract the exponents of 10: \(11 - (-3) = 11 + 3 = 14\).
5. Combine the results from the previous steps to express the answer in scientific notation: \(\text{result of the division} \times 10^{14}\).

Key Concepts

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form. It is written as the product of a number (the coefficient) between 1 and 10 and a power of ten. For example, 282,000,000,000 can be expressed as 2.82 x 10^11. This notation simplifies calculations and comparisons of very large or small values.

Division of Decimals

Dividing decimals involves shifting the decimal point to convert the divisor into a whole number, which simplifies the division process. In the given problem, dividing 282,000,000,000 by 0.00141 requires adjusting the decimal point in 0.00141 to make it a whole number, which also necessitates shifting the decimal in the dividend accordingly. This ensures that the division is performed correctly.

Rounding Numbers

Rounding numbers is the process of adjusting a number to a specified degree of accuracy, often to make it simpler to work with. In this case, the problem specifies rounding the decimal factor in scientific notation to two decimal places. This means that after performing the division, the result should be rounded to the nearest hundredth, which helps in presenting the answer in a clear and concise manner.