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A bridge connecting two cities separated by a lake has a length of 4542.658 yd. Use the table of conversion facts to find the length of the bridge in miles. Round your answer to the nearest tenth.
Certainly! Let's work through this problem step-by-step to find the length of the bridge in miles.
1. Given Information: - The length of the bridge is 4542.658 yards.
2. Conversion Factor: - We know that 1 mile is equivalent to 1760 yards.
3. Calculating the Length in Miles: - To convert the length from yards to miles, we can use the following relationship: [tex]\[
\text{Length in miles} = \frac{\text{Length in yards}}{\text{Yards per mile}}
\][/tex] - Substituting the given values, we get: [tex]\[
\text{Length in miles} = \frac{4542.658 \text{ yards}}{1760 \text{ yards per mile}}
\][/tex]
4. Performing the Division: - Let's calculate this division: [tex]\[
\text{Length in miles} = \frac{4542.658}{1760} \approx 2.581055681818182
\][/tex]
5. Rounding to the Nearest Tenth: - To round the result to the nearest tenth, we look at the first digit after the decimal point: - The number [tex]\(2.581055681818182\)[/tex] has [tex]\(5\)[/tex] in the hundredths place. - Since [tex]\(5\)[/tex] is equal to or greater than [tex]\(5\)[/tex], we round up the tenths place.
Therefore, the rounded result is: [tex]\[
2.6
\][/tex]
Conclusion:
The length of the bridge in miles, rounded to the nearest tenth, is 2.6 miles.
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