Problem 49 - Chemistry: An Atoms-Focused Approach

Question

Olympic Mile An Olympic "mile" is actually 1500 m. What percentage is an Olympic mile of a U.S. mile \((5280 \mathrm{ft}) ?\)

Step-by-Step Solution

Answer

Answer: An Olympic mile is approximately 93.209% of a U.S. mile.

Step 1: Convert the Olympic mile to feet

To convert the Olympic mile (1500 meters) to feet, we use the conversion factor 1 meter = 3.28084 feet. We multiply 1500 meters by the conversion factor to get the Olympic mile in feet: \(1500 \times 3.28084 = 4921.26 \, \text{ft}\)

Step 2: Calculate the ratio of the Olympic mile to the U.S. mile

Now, we can divide the Olympic mile expressed in feet (4921.26 feet) by the U.S. mile (5280 feet) to get the ratio between them: \(\frac{4921.26 \, \text{ft}}{5280 \, \text{ft}} = 0.93209\)

Step 3: Find the percentage

Finally, we need to multiply the ratio we obtained in Step 2 by 100% to find the percentage of the Olympic mile in relation to the U.S. mile: \(0.93209 \times 100\% = 93.209 \%\) An Olympic mile is approximately 93.209% of a U.S. mile.

Key Concepts

Metric System

The metric system is a universal measurement system based on meters, kilograms, and seconds. It provides a standard way to measure physical quantities, boasting uniformity and ease of conversion.

In this exercise, we convert meters to feet. Conversions are straightforward due to the consistent decimal relationship. For example:

• 1 meter = 100 centimeters
• 1 kilometer = 1000 meters

To convert meters to another unit, you multiply or divide by a conversion factor. This system simplifies calculations and comparisons globally, especially in scientific contexts.

Length Measurement

Length measurements can use either the metric or imperial system. In this problem, we deal with two units: meters (metric) and feet (imperial).

For conversion, we use the factor:

• 1 meter = 3.28084 feet

Performing conversions like these helps in standardizing measurements across different regions.

Let's take 1500 meters as an example. Converting from meters to feet requires multiplying by the conversion factor, resulting in:
\(1500 \times 3.28084 = 4921.26 \, \text{ft}\).
These conversions facilitate understanding and comparing distances in varied measurement systems.

Percentage Calculation

Percentage calculations are handy for comparing quantities, showing how one value relates to another as a part of 100. In this exercise, we calculate what percentage an Olympic mile (measured in feet) is of a U.S. mile.

Here's how you do it:

• First, determine the ratio: \( \frac{4921.26 \, \text{ft}}{5280 \, \text{ft}} = 0.93209\).
• Then, convert the ratio to a percentage: \(0.93209 \times 100\% = 93.209\%\).

This result shows that an Olympic mile is approximately 93.209% of a U.S. mile. Percentages easily express comparisons or proportions in a clear, understandable way.