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Chapter 9: Problem 13

Use dimensional analysis to convert the quantity to the indicated unit. If necessary, round the answer to two decimal places. \(23,760 \mathrm{ft}\) to \(\mathrm{mi}\)

Short Answer

Expert verified
After conversion, \(23,760 ft\) is approximately \(4.5 mi\).

Step by step solution

01

Identify the Conversion Factor

To convert from feet to miles, it's important to know how these two units relate. There are \(5280 \) feet in \(1 \) mile, so the conversion factor is \( \frac{1 mi}{5280 ft}\). The reciprocal of this, \( \frac{5280 ft}{1 mi}\), is also a conversion factor.
02

Setup the Conversion.

Now multiply the given quantity by the conversion factor. Line up the units so that 'feet' cancels and 'miles' remains. Therefore, \(23,760ft * \frac{1mi}{5280ft}\), so 'feet' in the numerator and 'feet' in the denominator will cancel each other out, leaving us with 'miles'.
03

Perform Calculation and Round Off

Perform the multiplication to get the answer. \(23,760ft * \frac{1mi}{5280ft}= 4.5mi\). If rounding is necessary, this result is already to two decimal places.

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