Carry out the following conversions. (c) How large in square meters is the land area of Australia (2,941,526 mi^2)?

Verified step by step guidance

1. Start by identifying the conversion factor between square miles and square meters. The conversion factor is 1 square mile = 2,589,988.11 square meters.
2. Write down the given area of Australia in square miles: 2,941,526 mi^2.
3. Set up the conversion by multiplying the area in square miles by the conversion factor to convert it to square meters.
4. The equation will look like this: \( 2,941,526 \, \text{mi}^2 \times 2,589,988.11 \, \text{m}^2/\text{mi}^2 \).
5. Perform the multiplication to find the area in square meters.

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this case, we need to convert square miles to square meters. This involves using conversion factors, where 1 square mile is equivalent to 2.58999 square kilometers, and 1 square kilometer equals 1,000,000 square meters.

Area Measurement

Area measurement refers to the quantification of a two-dimensional space. It is typically expressed in square units, such as square meters or square miles. Understanding how to calculate area is essential for interpreting land sizes, as it allows for comparisons between different regions or properties.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one set of units to another by multiplying by conversion factors. It ensures that the units cancel appropriately, leading to the desired unit in the final answer. This method is crucial in solving problems involving different measurement systems, such as converting land area from imperial to metric units.