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Difficulty: MediumScientific Notation and Unit Conversions

A geophysicist studying volcanic emissions measures the mass of carbon dioxide (CO2CO_2) released by four different vents (Vents A, B, C, and D) in a hydrothermal field over a 1-hour period. The recorded masses are:

- Vent A: 4.2×105 mg4.2 \times 10^5 \text{ mg}
- Vent B: 0.052 kg0.052 \text{ kg}
- Vent C: 3.8×103 cg3.8 \times 10^3 \text{ cg}
- Vent D: 8.9×10−1 g8.9 \times 10^{-1} \text{ g}

Based on these measurements, arrange the vents in order from the smallest mass of CO2CO_2 released to the largest mass of CO2CO_2 released.

  1. 1Vent D (8.9×10−1 g8.9 \times 10^{-1} \text{ g})
  2. 2Vent C (3.8×103 cg3.8 \times 10^3 \text{ cg})
  3. 3Vent B (0.052 kg0.052 \text{ kg})
  4. 4Vent A (4.2×105 mg4.2 \times 10^5 \text{ mg})

Answer

The correct order of vents from smallest to largest mass of CO2CO_2 released is Vent D, Vent C, Vent B, then Vent A.
To compare the masses, they must be converted to a common unit, such as grams. Vent D releases 0.89 g0.89 \text{ g}, Vent C releases 38 g38 \text{ g}, Vent B releases 52 g52 \text{ g}, and Vent A releases 420 g420 \text{ g}. Comparing these quantities confirms the order from smallest to largest is Vent D, Vent C, Vent B, and Vent A.

Step-by-Step Solution

1
Convert the mass of Vent A from milligrams to grams.
4.2×105 mg×1 g103 mg=4.2×102 g=420 g4.2 \times 10^5 \text{ mg} \times \frac{1 \text{ g}}{10^3 \text{ mg}} = 4.2 \times 10^2 \text{ g} = 420 \text{ g}
Converting all masses to a single standard unit (grams) allows for a direct comparison.
2
Convert the mass of Vent B from kilograms to grams.
0.052 kg×103 g1 kg=52 g0.052 \text{ kg} \times \frac{10^3 \text{ g}}{1 \text{ kg}} = 52 \text{ g}
Converting kilograms to grams requires multiplying by the conversion factor of 103 g/kg10^3 \text{ g/kg}.
3
Convert the mass of Vent C from centigrams to grams.
3.8×103 cg×1 g102 cg=3.8×101 g=38 g3.8 \times 10^3 \text{ cg} \times \frac{1 \text{ g}}{10^2 \text{ cg}} = 3.8 \times 10^1 \text{ g} = 38 \text{ g}
Since centi- means 10−210^{-2}, converting centigrams to grams requires dividing by 10210^2.
4
Convert the mass of Vent D to a standard decimal value in grams.
8.9×10−1 g=0.89 g8.9 \times 10^{-1} \text{ g} = 0.89 \text{ g}
Expressing 8.9×10−1 g8.9 \times 10^{-1} \text{ g} in standard decimal format makes comparison straightforward.
5
Compare the converted masses in grams to order them from smallest to largest.
0.89 g<38 g<52 g<420 g0.89 \text{ g} < 38 \text{ g} < 52 \text{ g} < 420 \text{ g}
Comparing the values shows that Vent D releases the least mass (0.89 g0.89 \text{ g}), followed by Vent C (38 g38 \text{ g}), Vent B (52 g52 \text{ g}), and Vent A (420 g420 \text{ g}).

Key Concept

Scientific Notation and Unit Conversions
Estimated Time:1m 30s
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Topics

Scientific Notation and Unit Conversions

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