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 area of the rectangle?

Verified step by step guidance

1. Identify the measurements given: length = 12 mm and width = 5.98 mm.
2. Understand the concept of significant figures: The number of significant figures in a measurement is determined by the precision of the measuring tool used.
3. Determine the number of significant figures for each measurement: The length (12 mm) has 2 significant figures, and the width (5.98 mm) has 3 significant figures.
4. Calculate the area of the rectangle using the formula: Area = length × width. In MathML, this is represented as $A=l\times w$.
5. Apply the rules for significant figures in multiplication: The result should be reported with the same number of significant figures as the measurement with the least number of significant figures, which is 2 significant figures in this case.

Key Concepts

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.

Measurement Precision

Measurement precision refers to the consistency and exactness of a measurement. It is determined by the instrument used and the method of measurement. In this context, the wooden ruler provides a less precise measurement (12 mm) compared to the micrometer calipers (5.98 mm), affecting the significant figures in the calculated area.

Area Calculation

The area of a rectangle is calculated by multiplying its length by its width. In this problem, the length is 12 mm and the width is 5.98 mm. The calculation must consider significant figures, so the area should be reported with the same number of significant figures as the least precise measurement, which is 12 mm (two significant figures).