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Chapter 1: Problem 23

The length of the river span of the Brooklyn Bridge is \(1595.5 \mathrm{ft} .\) The total length of the bridge is \(6016 \mathrm{ft}\). Find the length and the order of magnitude in meters of (a) the river span and (b) the total bridge length?

Short Answer

Expert verified
Answer: The river span length is 486.745 meters with an order of magnitude of 100 meters. The total bridge length is 1833.376 meters with an order of magnitude of 1000 meters.

Step by step solution

01

Convert river span length from feet to meters

To convert the length of the river span from feet to meters, we need to use the conversion factor: 1 ft = 0.3048 m. So, the formula to convert feet to meters is: length (m) = length (ft) * 0.3048. River span length in meters = \(1595.5\ \mathrm{ft}\times 0.3048\ \mathrm{m/ft}\) River span length in meters = \(486.745\ \mathrm{m}\).
02

Determine the order of magnitude of the river span length

To find the order of magnitude of the river span length, we need to round the length to the nearest power of 10. The river span length is 486.745 meters, which is closer to 100 than 1000. Therefore, the order of magnitude of the river span length is 100 meters. In conclusion, the river span length is \(486.745\ \mathrm{m}\) and its order of magnitude is \(100\ \mathrm{m}\). #b) Total bridge length and order of magnitude#
03

Convert total bridge length from feet to meters

To convert the total bridge length from feet to meters, we can use the same conversion factor as before: 1 ft = 0.3048 m. Total bridge length in meters = \(6016\ \mathrm{ft}\times 0.3048\ \mathrm{m/ft}\) Total bridge length in meters = \(1833.376\ \mathrm{m}\).
04

Determine the order of magnitude of the total bridge length

To determine the order of magnitude of the total bridge length, we need to round the length to the nearest power of 10. The total bridge length is 1833.376 meters, which is closer to 1000 than 10,000. Therefore, the order of magnitude of the total bridge length is 1000 meters. In conclusion, the total bridge length is \(1833.376\ \mathrm{m}\) and its order of magnitude is \(1000\ \mathrm{m}\).

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