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A bridge connecting two cities separated by a lake has a length of [tex]$5684.106$ \, \text{yd}$[/tex]. Use the table of facts to find the length of the bridge in miles. Round your answer to the nearest tenth.

\begin{tabular}{|r|}
\hline Conversion facts for length \\
\hline 12 inches (in) = 1 foot (ft) \\
\hline 3 feet (ft) = 1 yard (yd) \\
\hline 36 inches (in) = 1 yard (yd) \\
\hline 5280 feet (ft) = 1 mile (mi) \\
\hline 1760 yards (yd) = 1 mile (mi) \\
\hline
\end{tabular}

[tex]\square \, \text{mi}[/tex]



Answer :

GinnyAnswer
To find the length of the bridge in miles, given its length in yards, we can use the provided conversion fact that 1760 yards equal 1 mile. Here is the detailed, step-by-step solution:

1. Identify the given data:
- The length of the bridge is [tex]\(5684.106\)[/tex] yards.

2. Identify the relevant conversion factor:
- According to the conversion table, [tex]\(1760\)[/tex] yards is equal to [tex]\(1\)[/tex] mile.

3. Convert the length from yards to miles:
- To convert from yards to miles, divide the length in yards by the number of yards per mile:
[tex]\[ \text{Length in miles} = \frac{\text{Length in yards}}{\text{Yards per mile}} \][/tex]
- Substituting the given numbers:
[tex]\[ \text{Length in miles} = \frac{5684.106}{1760} \approx 3.2296056818181818 \][/tex]

4. Round the converted length to the nearest tenth:
- To round to the nearest tenth, look at the hundredths place. Since it is 2, we round down.
[tex]\[ 3.2296056818181818 \approx 3.2 \][/tex]

Therefore, the length of the bridge in miles, rounded to the nearest tenth, is [tex]\(3.2\)[/tex] miles.

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