The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick. (a) How many quarters would have to be stacked to reach 575 ft, the height of the Washington Monument?

검증된 단계별 안내

Convert the height of the Washington Monument from feet to millimeters. Use the conversion factors: 1 foot = 12 inches and 1 inch = 25.4 mm.

Calculate the total height in millimeters by multiplying the height in feet by the conversion factors.

Determine the number of quarters needed by dividing the total height in millimeters by the thickness of one quarter (1.55 mm).

Ensure the units are consistent throughout the calculation to avoid any errors.

Verify the calculation by considering the reasonableness of the result, ensuring it aligns with the expected height.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this question, it is essential to convert the height of the Washington Monument from feet to millimeters, as the thickness of a quarter is given in millimeters. Understanding how to perform these conversions accurately is crucial for solving the problem.

Volume and Density

While the question primarily involves stacking quarters, understanding the concepts of volume and density can provide context. The mass of a quarter (5.67 g) and its dimensions can help in calculating the total volume occupied by a stack of quarters. This knowledge is useful for visualizing how many quarters would fit into a given height.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one set of units to another and to check the consistency of equations. In this problem, it involves determining how many quarters, each with a thickness of 1.55 mm, are needed to reach a total height of 575 ft. This method ensures that the calculations are logically sound and that the final answer is in the correct units.