One furlong is defined as one-eighth of a mile. How many km are there in a six-furlong (6.0) race? The following relations are exact: 1 mile = 5280 feet, 12 inches = 1 foot, 1 inch = 2.54 centimeters.
The Correct Answer and Explanation is:
Answer: 1.2 km
To determine the length of a six-furlong race in kilometers, a systematic conversion through different units of measurement is required, using the exact relationships provided.
The initial distance is 6.0 furlongs. The first step is to convert this distance into miles. According to the definition, one furlong is equal to one-eighth of a mile. Therefore, the distance in miles can be calculated as:
6.0 furlongs × (1 mile / 8 furlongs) = 0.75 miles
Next, this distance in miles is converted to feet. The relation given is 1 mile = 5280 feet. Applying this conversion factor gives:
0.75 miles × (5280 feet / 1 mile) = 3960 feet
The subsequent step is to convert feet into inches. With the exact relation of 12 inches = 1 foot, the calculation is:
3960 feet × (12 inches / 1 foot) = 47,520 inches
Now, the measurement can be converted from the imperial system to the metric system using the bridge conversion of 1 inch = 2.54 centimeters.
47,520 inches × (2.54 centimeters / 1 inch) = 120,700.8 centimeters
Finally, the distance in centimeters must be converted to kilometers. The standard metric system defines that there are 100 centimeters in a meter and 1000 meters in a kilometer. This means there are 100 × 1000 = 100,000 centimeters in one kilometer. The final conversion is:
120,700.8 centimeters × (1 kilometer / 100,000 centimeters) = 1.207008 kilometers
The initial measurement of the race was given as “6.0 furlongs,” which has two significant figures. The conversion factors are exact and do not limit the precision of the result. Therefore, the final answer should be rounded to two significant figures to match the precision of the initial measurement.
Rounding 1.207008 km to two significant figures yields 1.2 km.
