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Chapter 1: Problem 102

Of the following masses, two are expressed to the nearest milligram. The two are (a) \(32.7 \mathrm{g}\); (b) \(0.03271 \mathrm{kg} ;(\mathrm{c}) 32.7068 \mathrm{g} ;(\mathrm{d}) 32.707 \mathrm{g} ;(\mathrm{e}) 30.7 \mathrm{mg};\) (f) \(3 \times 10^{3} \mu g.\)

Short Answer

Expert verified
The two masses expressed to the nearest milligram are (a) \(32.7 \, \mathrm{g}\) and (f) \(3 \times 10^{3} \, \mu g.\)

Step by step solution

01

Convert all masses to milligrams

First, all mass values are converted from grams (g), kilograms (kg) and micrograms (μg) to milligrams (mg). One gram is equivalent to 1000 milligrams, one kilogram is equivalent to 1,000,000 milligrams, and one microgram is equivalent to 0.001 milligrams. Therefore:\n(a) \(32.7 \, \mathrm{g}\) = 32,700\, \mathrm{mg}\n(b) \(0.03271 \, \mathrm{kg}\) = 32,710 \, \mathrm{mg}\n(c) \(32.7068 \, \mathrm{g}\) = 32,706.8 \, \mathrm{mg}\n(d) \(32.707 \, \mathrm{g}\) = 32,707 \, \mathrm{mg}\n(e) \(30.7 \, \mathrm{mg}\) = 30.7 \, \mathrm{mg}\n(f) \(3 \times 10^{3} \, \mu g.\) = 3 \, \mathrm{mg}
02

Identify masses expressed to the nearest milligram

Next, take note of which masses do not have decimals in their milligram form, as they are expressed to the nearest milligram.\nSo, from the calculations in the previous step, the masses which do not contain decimals are (a) 32,700 \, \mathrm{mg} and (f) 3 \, \mathrm{mg}.

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