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Length conversion is a common task in math and science, as different units of measurement are used around the world. One of the most common conversions is between inches and centimeters. To convert inches to centimeters, you multiply the length in inches by 2.54 since 1 inch equals 2.54 centimeters.
For instance:
The length of our rug is 38.4 inches. To convert this to centimeters, we calculate:
\(38.4 \text{ in} \times 2.54 \text{ cm/in} = 97.536 \text{ cm}\)
Similarly, for the width of the rug, which is 24.2 inches:
\(24.2 \text{ in} \times 2.54 \text{ cm/in} = 61.468 \text{ cm}\) This conversion helps in understanding and utilizing measurements in various applications, especially when working with international units.

Understanding significant figures is crucial for accuracy in calculations. Significant figures are the digits in a number that carry meaningful contributions to its measurement precision. For example: In the given length of 38.4 inches, there are three significant figures: 3, 8, and 4. Each digit is important for precision.
Similarly, in the width measurement of 24.2 inches there are also three significant figures: 2, 4, and 2.
When performing calculations, maintaining the correct number of significant figures is essential. This ensures the result maintains the precision of the measured values.
In our area calculation, we keep three significant figures because both the length (38.4 in) and width (24.2 in) of the rug have three significant figures. After finding the area in square centimeters, we round to three significant figures to maintain consistency. Proper use of significant figures prevents the introduction of error in computed results.

Calculating area involves multiplying length by width. In this exercise, we're calculating the area of a rectangle, specifically a rug, using our converted measurements in centimeters. The formula for the area is:
\( \text{Area} = \text{Length} \times \text{Width} \) Plugging in the values:
\( 97.536 \text{ cm} \times 61.468 \text{ cm} = 5991.091648 \text{ cm}^2 \) The raw calculation gives us a precise value, but since our length and width measurements each had three significant figures, we'll round our area result to match this precision.
Rounding 5991.091648 cm² to three significant figures gives us 5990 cm². Following these steps ensures our final area measurement retains the precision of our initial measurements.

• Convert length and width to desired unit (cm)
• Multipy to find area
• Round result according to significant figures of initial measurements

This method provides an accurate and precise area measurement based on given dimensions.