Starting with the definition 1 in. = 2.54 cm, find the number of kilometers in 1.00 mile

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Start by understanding the conversion factors needed. We know that 1 inch is equal to 2.54 cm. We also need to know that 1 mile is equal to 5280 feet, and 1 foot is equal to 12 inches.

Convert miles to inches first. Multiply the number of miles by the number of feet per mile, and then by the number of inches per foot: \(1.00 \text{ mile} \times 5280 \text{ feet/mile} \times 12 \text{ inches/foot}\).

Now, convert inches to centimeters using the given conversion factor: \( \text{inches} \times 2.54 \text{ cm/inch} \).

Convert centimeters to meters by dividing by 100, since there are 100 centimeters in a meter: \( \text{cm} \div 100 \text{ cm/m} \).

Finally, convert meters to kilometers by dividing by 1000, since there are 1000 meters in a kilometer: \( \text{m} \div 1000 \text{ m/km} \). This will give you the number of kilometers in 1.00 mile.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. It involves using conversion factors, which are ratios that express how many of one unit are equivalent to another. In this problem, converting inches to centimeters is the first step in converting miles to kilometers.

Dimensional Analysis

Dimensional analysis is a method used to convert units by multiplying by conversion factors that cancel out unwanted units and introduce desired units. This technique ensures that calculations are consistent and accurate, allowing for the conversion of miles to kilometers by systematically applying known conversion factors.

Metric System

The metric system is an international decimal system of measurement based on meters, liters, and grams. Understanding the metric system is crucial for converting miles to kilometers, as kilometers are a metric unit of distance. Familiarity with metric prefixes, such as 'kilo-' meaning 1000, helps in understanding and performing conversions.

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