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

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

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

Problem 50a

Chapter 1, Problem 50a

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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Identify the operations to be performed: subtraction and division.

Perform the division first: \( 6104.5 \div 2.3 \).

Determine the number of significant figures for the division result. The number 6104.5 has 5 significant figures, and 2.3 has 2 significant figures, so the result should have 2 significant figures.

Subtract the division result from 320.5: \( 320.5 - \text{(division result)} \).

Determine the number of significant figures for the subtraction result. The number 320.5 has 4 significant figures, so the final answer should be rounded to the least number of decimal places present in the numbers involved in the subtraction.

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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 be reported with the same number of significant figures as the measurement with the least number of significant figures to ensure accuracy.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In the given question, division must be performed before subtraction to arrive at the correct answer.

Arithmetic Operations with Decimals

When performing arithmetic operations with decimal numbers, it is essential to align the decimal points and maintain precision throughout the calculation. For subtraction, the result should be rounded to the least precise decimal place of the numbers involved. This ensures that the final answer reflects the accuracy of the original measurements.

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Related Practice

Textbook Question

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 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 with the appropriate number of significant numbers. (a) 14.3505 + 2.65 (b) 952.72 - 73.4201

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Textbook Question

You have a graduated cylinder that contains a liquid (see photograph). Write the volume of the liquid, in milliliters, using the proper number of significant figures.

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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 with the appropriate number of significant numbers. (d) 0.0588/0.677

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