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Ch 01: Units, Physical Quantities & Vectors
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 01: Units, Physical Quantities & VectorsProblem 14c
Chapter 1, Problem 14c

With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is the perimeter of the rectangle?

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Identify the measurements given: length = 12 mm and width = 5.98 mm.
Recall the formula for the perimeter of a rectangle: \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width.
Add the length and width: \( l + w = 12 + 5.98 \).
Multiply the sum by 2 to find the perimeter: \( P = 2 \times (12 + 5.98) \).
Determine the number of significant figures for the final result. The length has 2 significant figures, and the width has 3 significant figures. The perimeter should be reported with the least number of significant figures, which is 2.

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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 measurement that contribute to its precision. They include all non-zero digits, zeros between significant digits, and trailing zeros in a decimal. When performing calculations, the result should be reported with the same number of significant figures as the measurement with the fewest significant figures.
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Measurement Precision

Measurement precision refers to the consistency and exactness of a measurement. It is influenced by the instrument used and the method of measurement. In this context, the wooden ruler provides a less precise measurement compared to micrometer calipers, affecting the significant figures in the final calculation.
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Perimeter Calculation

The perimeter of a rectangle is calculated by adding twice the length and twice the width. In this problem, the length is measured as 12 mm and the width as 5.98 mm. The calculation must respect the rules of significant figures, ensuring the final result reflects the precision of the least precise measurement.
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