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.
