Carry out the following conversions. (b) How tall in meters is the Willis Tower, formerly called the Sears Tower, in Chicago (1454 ft)?

Verified step by step guidance

1. Identify the conversion factor between feet and meters. The standard conversion is 1 foot = 0.3048 meters.
2. Set up the conversion equation using the given height of the Willis Tower in feet (1454 ft) and the conversion factor. This can be expressed as: \( \text{Height in meters} = 1454 \text{ ft} \times 0.3048 \text{ m/ft} \).
3. Multiply the number of feet by the conversion factor to convert the height from feet to meters.
4. Ensure that the units cancel appropriately, leaving the result in meters.
5. Review the calculation to ensure accuracy and that the final answer is expressed in meters.

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this case, we need to convert feet to meters. The conversion factor between feet and meters is that 1 foot is approximately 0.3048 meters. Understanding how to apply this conversion factor is essential for accurately determining the height of the Willis Tower in meters.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one set of units to another. It involves multiplying the quantity by a conversion factor that has the desired units in the numerator and the original units in the denominator. This method ensures that units cancel appropriately, leading to the correct final unit. It is crucial for solving problems involving different measurement systems.

Metric System

The metric system is an internationally recognized decimal-based system of measurement used in science and most countries around the world. It includes units such as meters for length, liters for volume, and grams for mass. Understanding the metric system is important for interpreting measurements and performing conversions, especially in scientific contexts where precision is key.