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Zorluk: ZorMetric System Conversions

A logistics officer is preparing a cargo flight and needs to balance the weight distribution of four different shipping pallets. Arrange the following pallets in order from the LIGHTEST to the HEAVIEST total mass.

  1. 1Pallet 4: 250 water purification filters, each weighing 50,000 centigrams
  2. 2Pallet 1: 150 medical kits, each weighing 850 grams
  3. 3Pallet 3: 60 ration boxes initially weighing 2.2 kilograms each, with a total of 4,000 grams of packaging removed from the overall pallet
  4. 4Pallet 2: 45 emergency generators, each weighing 3,000,000 milligrams

Cevap

The correct order from lightest to heaviest is: Pallet 4, Pallet 1, Pallet 3, and Pallet 2.
By converting all measurements to kilograms, we find that Pallet 4 is 125 kg, Pallet 1 is 127.5 kg, Pallet 3 is 128 kg, and Pallet 2 is 135 kg. Ordering these mathematical products from lightest to heaviest yields Pallet 4, Pallet 1, Pallet 3, then Pallet 2.

Adım Adım Çözüm

1
Select a common metric base unit for direct comparison.
Kilograms (kg) is chosen as the standard unit.
Comparing multiple quantities with different metric prefixes requires standardizing the units to avoid magnitude errors.
2
Calculate the total mass of Pallet 1.
150×0.85 kg=127.5 kg150 \times 0.85 \text{ kg} = 127.5 \text{ kg}.
Convert 850 g850 \text{ g} to kg by dividing by 1,0001,000, resulting in 0.85 kg0.85 \text{ kg} per kit. Multiply by the 150150 kits.
3
Calculate the total mass of Pallet 2.
45×3 kg=135 kg45 \times 3 \text{ kg} = 135 \text{ kg}.
Convert 3,000,000 mg3,000,000 \text{ mg} to kg by dividing by 1,000,0001,000,000 (since 1 kg=1,000,000 mg1 \text{ kg} = 1,000,000 \text{ mg}), resulting in 3 kg3 \text{ kg} per generator. Multiply by the 4545 generators.
4
Calculate the total mass of Pallet 3.
132 kg−4 kg=128 kg132 \text{ kg} - 4 \text{ kg} = 128 \text{ kg}.
Find the initial mass (60×2.2 kg=132 kg60 \times 2.2 \text{ kg} = 132 \text{ kg}). Convert the removed packaging to kg (4,000 g÷1,000=4 kg4,000 \text{ g} \div 1,000 = 4 \text{ kg}), and subtract it from the total.
5
Calculate the total mass of Pallet 4.
250×0.5 kg=125 kg250 \times 0.5 \text{ kg} = 125 \text{ kg}.
Convert 50,000 cg50,000 \text{ cg} to kg by dividing by 100,000100,000 (since 1 kg=100,000 cg1 \text{ kg} = 100,000 \text{ cg}), resulting in 0.5 kg0.5 \text{ kg} per filter. Multiply by the 250250 filters.
6
Order the final mass values from least to greatest.
Pallet 4 (125 kg125 \text{ kg}) < Pallet 1 (127.5 kg127.5 \text{ kg}) < Pallet 3 (128 kg128 \text{ kg}) < Pallet 2 (135 kg135 \text{ kg}).
The question asks for the arrangement from lightest to heaviest.

Anahtar Kavram

Metric Unit Conversions and Multi-Step Operations
Tahmini Süre:3m 0s
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Metric System Conversions

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