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Chapter 1: Problem 43

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) \(\mathrm{mm}\) to \(\mathrm{nm},\) (b) \(\mathrm{mg}\) to \(\mathrm{kg}\), (c) \(\mathrm{km}\) to \(\mathrm{ft},\) (d) \(\mathrm{in} .{ }^{3}\) to \(\mathrm{cm}^{3}\).

Short Answer

Expert verified
To convert the given units, use the following conversion factors: 1. mm to nm: \(10^6\) 2. mg to kg: \(10^{-6}\) 3. km to ft: approximately 3,280.84 4. in^3 to cm^3: approximately 16.387

Step by step solution

01

1. Millimeters to nanometers

To convert millimeters to nanometers, we need to know the relationship between the two units. Both are metric units, and we know that 1 mm equals 1,000,000 nm or \(1 mm = 10^6 nm\). So, the conversion factor is \(10^6\).
02

2. Milligrams to kilograms

For converting milligrams to kilograms, we need to understand the relationship between these metric units of mass. We know that 1 kg equals 1,000,000 mg, or \(1 kg = 10^6 mg\). Therefore, the conversion factor is \(\frac{1}{10^6}\) or \(10^{-6}\).
03

3. Kilometers to feet

To convert kilometers to feet, we need to know the relationship between both units. It's necessary to go through meters first because kilometers and meters are metric units, while feet are an English unit. We know that 1 km equals 1,000 m or \(1 km = 10^3 m\), and then 1 m equals 3.28084 ft or \(1 m = 3.28084 ft\). Therefore, to convert from km to ft, we first convert km to m, then m to ft. The conversion factor is \(10^3\times3.28084\), which is approximately equal to 3,280.84.
04

4. Cubic inches to cubic centimeters

To convert cubic inches to cubic centimeters, we need to understand the relationship between inches and centimeters first. We know that 1 in equals 2.54 cm, or \(1 in = 2.54 cm\). To convert cubic inches to cubic centimeters, we need to cube the linear relationship of inches to cm: \((1 in^3 = 2.54^3 cm^3 = 16.387 cm^3)\). So, the conversion factor is approximately 16.387.

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Most popular questions from this chapter

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

Water has a density of \(0.997 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C} ;\) ice has a density of \(0.917 \mathrm{~g} / \mathrm{cm}^{3}\) at \(-10^{\circ} \mathrm{C}\). (a) If a soft-drink bottle whose volume is \(1.50 \mathrm{~L}\) is completely filled with water and then frozen to \(-10^{\circ} \mathrm{C},\) what volume does the ice occupy? (b) Can the ice be contained within the bottle?

Is the use of significant figures in each of the following statements appropriate? Why or why not? (a) Apple sold 22,727,000 iPods during the last three months of 2008 . (b) New York City receives 49.7 inches of rain, on average, per year. (c) In the United States, \(0.621 \%\) of the population has the surname Brown. (d) You calculate your grade point average to be \(3.87562 .\)

Carry out the following operations, and express the answer with the appropriate number of significant figures. (a) \(320.5-(6104.5 / 2.3)\) (b) \(\left[\left(285.3 \times 10^{5}\right)-\left(1.200 \times 10^{3}\right)\right] \times 2.8954\) (c) \((0.0045 \times 20,000.0)+(2813 \times 12)\) (d) \(863 \times[1255-(3.45 \times 108)]\)

Give the chemical symbol or name for each of the following elements, as appropriate: (a) carbon, (b) nitrogen, (c) titanium, \((\mathbf{d})\) zinc, \((\mathbf{e})\) iron, \((\mathbf{f}) \mathrm{P},(\mathrm{g}) \mathrm{Ca},(\mathbf{h}) \mathrm{He},(\mathbf{i}) \mathrm{Pb},(\mathbf{j}) \mathrm{Ag} .\)
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