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Chapter 1: Problem 58

Carry out the following conversions: (a) 0.105 in. to \(\mathrm{mm}\), (b) \(0.650 \mathrm{qt}\) to \(\mathrm{mL}\), (c) \(8.75 \mu \mathrm{m} / \mathrm{s}\) to \(\mathrm{km} / \mathrm{hr}\) (d) \(1.955 \mathrm{~m}^{3}\) to \(\mathrm{yd}^{3}(\mathbf{e}) \$ 3.99 / \mathrm{lb}\) to dollars per \(\mathrm{kg}\), (f) \(8.75 \mathrm{lb} / \mathrm{ft}^{3}\) to $\mathrm{g} / \mathrm{mL}$.

Short Answer

Expert verified
\(a) 2.667\mathrm{~mm}, b) 615.130\mathrm{~mL}, c) 0.0315\mathrm{~km/hr}, d) 2.555\mathrm{~yd}^{3}, e) 8.800\mathrm{~dollars/kg}, f) 140.162\mathrm{~g/mL}\)

Step by step solution

01

Identify the conversion factor

We know 1 inch (in) = 25.4 millimeters (mm).
02

Apply the conversion factor

Multiply 0.105 in by 25.4 mm/in. \(0.105 \times 25.4 = 2.667\mathrm{~mm}\) b) Conversion of 0.650 qt to mL
03

Identify the conversion factor

We know 1 quart (qt) = 946.353 milliliters (mL).
04

Apply the conversion factor

Multiply 0.650 qt by 946.353 mL/qt. \(0.650 \times 946.353 = 615.130\mathrm{~mL}\) c) Conversion of \(8.75 \mu \mathrm{m} / \mathrm{s}\) to \(\mathrm{km} / \mathrm{hr}\)
05

Identify the conversion factors

We know 1 micrometer (µm) = 1e-6 meters (m), 1 kilometer (km) = 1000 meters (m), and 1 hour (hr) = 3600 seconds (s).
06

Apply the conversion factors

Convert micrometers to kilometers and seconds to hours. \((8.75 \times 10^{-6})\mathrm{~m/s} \times \frac{1\mathrm{~km}}{1000\mathrm{~m}} \times \frac{3600\mathrm{~s}}{1\mathrm{~hr}} = 0.0315\mathrm{~km/hr}\) d) Conversion of \(1.955 \mathrm{~m}^{3}\) to \(\mathrm{yd}^{3}\)
07

Identify the conversion factor

We know 1 cubic meter (m³) = 1.3080 cubic yards (yd³).
08

Apply the conversion factor

Multiply 1.955 m³ by 1.3080 yd³/m³. \(1.955 \times 1.3080 = 2.555\mathrm{~yd}^{3}\) e) Conversion of \(3.99 / \mathrm{lb}\) to dollars per \(\mathrm{kg}\)
09

Identify the conversion factor

We know 1 pound (lb) = 0.453592 kilograms (kg).
10

Apply the conversion factor

Divide 3.99 \(/\mathrm{lb}\) by 0.453592 kg/lb. \(\frac{3.99}{0.453592} = 8.800\mathrm{~dollars/kg}\) f) Conversion of \(8.75 \mathrm{lb} / \mathrm{ft}^{3}\) to \(\mathrm{g} / \mathrm{mL}\)
11

Identify the conversion factor

We know 1 pound per cubic foot (lb/ft³) = 16.0185 grams per milliliter (g/mL).
12

Apply the conversion factor

Multiply 8.75 lb/ft³ by 16.0185 g/mL/lb/ft³. \(8.75 \times 16.0185 = 140.162\mathrm{~g/mL}\)

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