Question

1. a unit of length called the “furlong” is used in horse racing. the units of length called the “chain” and the “link” are used in surveying. there are 8 furlongs in 1 mile, 10 chains in 1 furlong, and 100 links in 1 chain. to three significant figures, what is the length of 1 link in inches?

Explanation:

Step1: List known conversion factors

1 mile = 5280 feet, 1 foot = 12 inches, 1 mile = 8 furlongs, 1 furlong = 10 chains, 1 chain = 100 links

Step2: Convert miles to furlongs

$\frac{1 \text{ mile}}{8 \text{ furlongs/mile}} = \frac{1}{8} \text{ mile per furlong}$

Step3: Convert furlongs to chains

$\frac{1/8 \text{ mile per furlong}}{10 \text{ chains/furlong}} = \frac{1}{80} \text{ mile per chain}$

Step4: Convert chains to links

$\frac{1/80 \text{ mile per chain}}{100 \text{ links/chain}} = \frac{1}{8000} \text{ mile per link}$

Step5: Convert miles to inches

$\frac{1}{8000} \text{ mile} \times 5280 \frac{\text{feet}}{\text{mile}} \times 12 \frac{\text{inches}}{\text{foot}}$

Step6: Calculate final value

$\frac{5280 \times 12}{8000} = \frac{63360}{8000} = 7.92$ inches

Answer:

7.92 inches