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Understanding unit conversion is essential when dealing with measurements in different systems. In everyday scenarios, you might encounter lengths specified in either imperial or metric units. For instance, in this exercise, one distance is in miles, a unit from the imperial system, while the other is in meters, a metric unit. To smoothly switch between these units, you need to know that one mile equals approximately 1609.34 meters. It is important to use this conversion factor when you want to compare two distances stated in different units. By multiplying the number of miles by 1609.34, you convert those miles to meters, which allows for a direct comparison.

Calculating percentages is a useful skill in finding out how one quantity compares to another as a fraction of 100. In this race problem, knowing how to compute percentage increase tells you how much longer the one-mile race is compared to the 1500-meter race. The process begins with finding the difference in length. First, calculate how much longer one quantity is than the other, and express this difference as a fraction of the second quantity, usually the smaller one. Then, convert this fraction to a percentage by multiplying it by 100. In our case, we take the difference between the one-mile race (1609.34 meters) and the 1500-meter race. This difference, 109.34 meters, is then divided by 1500 meters to obtain the fraction. Multiply this by 100 to find the percentage, resulting in an approximate 7.29% increase.

Comparing race distances puts the different lengths into perspective. Here, you discover how significantly different two races are in terms of their lengths. By converting both distances into the same metric (meters, in this example), you can identify and measure the difference directly. This step establishes a common ground for straightforward comparison. In practical terms, this comparison not only gives a numerical difference (109.34 meters longer), but also expresses it as a percentage (7.29% longer). It provides a clearer understanding of how these distances relate to each other in competitive sports like running or cycling.