Textbook Question
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. (2.4×10^−2)/(4.8×10^-6)
Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, 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. 282,000,000,000/0.00141
Verified step by step guidance1
Identify the problem as a division of two numbers: \(282,000,000,000 \div 0.00141\).
Rewrite both numbers in scientific notation. For example, express \$282,000,000,000$ as \(2.82 \times 10^{11}\) and \(0.00141\) as \(1.41 \times 10^{-3}\).
Set up the division using the scientific notation forms: \(\frac{2.82 \times 10^{11}}{1.41 \times 10^{-3}}\).
Divide the decimal parts: \(\frac{2.82}{1.41}\), and subtract the exponents in the powers of 10: \(10^{11} \div 10^{-3} = 10^{11 - (-3)} = 10^{14}\).
Combine the results to get the quotient in scientific notation: \((\text{result of decimal division}) \times 10^{14}\). If necessary, adjust the decimal factor to be between 1 and 10 and round it to two decimal places.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Scientific Notation
Scientific notation expresses numbers as a product of a decimal factor between 1 and 10 and a power of 10. It simplifies handling very large or small numbers, making calculations and comparisons easier. For example, 282,000,000,000 can be written as 2.82 × 10^11.
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Division of Numbers in Scientific Notation
When dividing numbers in scientific notation, divide the decimal factors and subtract the exponents of 10. This method streamlines calculations involving large or small values. For instance, dividing (a × 10^m) by (b × 10^n) equals (a/b) × 10^(m-n).
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Rounding Decimal Factors
Rounding decimal factors involves adjusting the decimal part of a number to a specified number of decimal places, here two. This ensures answers are concise and standardized, especially in scientific notation. For example, 1.2345 rounded to two decimals is 1.23.
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