Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 49d

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Chapter 1, Problem 49d

Carry out the following operations and express the answers with the appropriate number of significant numbers. (d) 0.0588/0.677

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Identify the number of significant figures in each number: 0.0588 has 3 significant figures, and 0.677 has 3 significant figures.

Perform the division operation: \( \frac{0.0588}{0.677} \).

Determine the number of significant figures for the result: The result should have the same number of significant figures as the number with the fewest significant figures in the operation, which is 3.

Round the result of the division to 3 significant figures.

Express the final answer with the appropriate number of significant figures.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When performing calculations, the result should reflect the precision of the least precise measurement, ensuring that the final answer is reported with the correct number of significant figures.

Division in Scientific Calculations

In scientific calculations, division involves determining how many times one number is contained within another. When dividing two numbers, the result should be rounded to the same number of significant figures as the measurement with the fewest significant figures. This ensures that the precision of the result is consistent with the least precise measurement used in the calculation.

Rounding Rules

Rounding rules dictate how to adjust a number to reflect the appropriate number of significant figures. If the digit to be dropped is less than five, the last retained digit remains unchanged; if it is five or greater, the last retained digit is increased by one. This process is crucial in ensuring that the final answer is both accurate and appropriately precise.

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Related Practice

(a) The diameter of Earth at the equator is 7926.381 mi. Round this number to three significant figures and express it in standard exponential notation.

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Textbook Question

(b) The circumference of Earth through the poles is 40,008 km. Round this number to four significant figures and express it in standard exponential notation.

Carry out the following operations and express the answers with the appropriate number of significant numbers. (c) (3.29×10⁴)(0.2501)

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Textbook Question

Carry out the following operations and express the answers with the appropriate number of significant numbers. (a) 320.5 − (6104.5/2.3)

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Textbook Question

Carry out the following operations and express the answers in exponential notation with the appropriate number of significant figures.

a. 2.791×10⁴+ 8.76×10³

b. 4.67×10² − 5.4437×10⁴

c. (2.481×10⁻²+ 7.33×10⁻⁴) × (1.924×10⁻²+ 6.70)

d. (1.3×10⁻⁴ − 3.746×10⁻²)/(1.3×10² − 3.746×10⁴)

Textbook Question

Carry out the following operations and express the answers in exponential notation with the appropriate number of significant figures.

a. 2.791×10⁴ + 8.76×10³

b. 4.67×10²− 5.4437×10⁴

c. (2.481×10⁻² + 7.33×10⁻⁴) × (1.924×10⁻²+ 6.70)

d. (1.3×10⁻⁴− 3.746×10⁻²)/(1.3×10²− 3.746×10⁴)