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2: Using and Converting Units
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factor must have hours on the bottom and minutes on the top Just repeat this process until you arrive at the units you want Then do all the multiplying and dividing of the numbers and rest assured that the resulting calculation is the right one for the final units
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A silly chemistry student measures the mass of a sample of mystery metal to be 05 pounds and measures the sample s dimensions to be 1 cubic inch When she realizes her error, she attempts to convert her measurements into proper SI units What should her units be, and what s the density of her sample (in those units) The units should be g/mL or g/cm3, and the density is 14 10-2 g/mL The proper SI units for density are g/mL (g/cm3), so she should use the following method: 05 lbs 1 in 254 cm 1 in 3
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3 1000g 1 kg = 0014 g mL 1 cm 1 mL 22 lbs 1 kg
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Notice that the conversion factors have been cleverly chosen so that all the non-SI units cancel, leaving only SI units behind This answer is a little awkward and ought to be converted to scientific notation (see 1), such as 14 10 2 Or, you can be extra sneaky and use a metric conversion factor, which allows you to do away with the scientific notation 0014g 100 cg = 14 cg mL mL g
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How many meters are in 15 feet
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If Steve weighs 175 pounds, what s his weight in grams
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Part I: Getting Cozy with Numbers, Atoms, and Elements
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If the dimensions of a cube of sample are 3 inches x 6 inches x 1 foot, what s the volume of that cube in cubic centimeters Give your answer in scientific notation or use a metric system prefix
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If there are 565 kilograms per every half liter of a particular substance, which of the following is that substance: liquid mercury (density 135 g/cm3), lead (113 g/cm3), or tin (73 g/cm3)
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2: Using and Converting Units
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Answers to Questions on Using and Converting Units
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The following are the answers to the practice problems presented in this chapter
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a b c
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1 107 nm Both 102 centimeters and 109 nanometers equal 1 meter Set the two equal to one another (102 cm = 109 nm) and solve for centimeters by dividing This conversion tells you that 1 cm = 109/102 nm, or 1 107 nm 25 kg Because there are 1,000 grams in 1 kilogram, simply divide 2,500 by 1,000 to get 25 1 Pa = 1 kg ms 2
First, you write out the equivalents of Pascals and Newtons as explained in the problem: 1 kgm 1 Pa = 1N 1N = m 2 and s2 Now, substitute Newtons (expressed in fundamental units) into the equation for the Pascal to 1 kgm s2 get 1 Pa = m2 1 Pa = 1 kgm m 2 s 2 and cancel out the meter, which appears in both the top
Simplify this equation to
1 kg and the bottom, leaving Pa = ms 2
12 g/mL Because a milliliter is equivalent to 1 cubic centimeter, the first thing to do is to convert all the length measurements to centimeters: 1 cm, 15 cm, and 05 cm Then, multiply the converted lengths to get the volume: 1 cm 15 cm 05 cm = 075 cm3, or 075 mL The mass should be expressed in grams rather than Dg; there are 10 grams in 1 decogram, so 09 Dg = 9g Using the formula D = m / V, you calculate a density of 9 grams per 075 milliliter, or 12 g/mL 330m Set up the conversion factor as shown 100m 33 ft = 330m 1 1m
251 mm Hg 033 atm 760 mm Hg = 251mm Hg 1 1 atm
Part I: Getting Cozy with Numbers, Atoms, and Elements
112 105 km 20,000 leagues 56 km = 112 10 5 km 1 1 league The radius of the Earth is only 6,378 km 20,000 leagues is 175 times that radius! So, the ship would ve burrowed through the Earth and been halfway to the orbit of Mars if it had truly sunk to such a depth Jules Verne intended the title to imply a distance traveled across the sea, not a depth!