Math  /  Numbers & Operations

QuestionWhen converting 1.50 kg/L1.50 \mathrm{~kg} / \mathrm{L} into g/mL\mathrm{g} / \mathrm{mL}, what are the two missing steps needed to complete the calculation? 1.50 kgL×??×??\frac{1.50 \mathrm{~kg}}{L} \times \frac{?}{?} \times \frac{?}{?} 1000 g1Kg\frac{1000 \mathrm{~g}}{1 \mathrm{Kg}} 1L1000 mLL\frac{1 L}{1000 \mathrm{~mL} L} 1 mL1000 L\frac{1 \mathrm{~mL}}{1000 \mathrm{~L}} 1000 kg1 g\frac{1000 \mathrm{~kg}}{1 \mathrm{~g}} 1 g1000 kg\frac{1 \mathrm{~g}}{1000 \mathrm{~kg}} 1000L1mL\frac{1000 L}{1 m L}

Studdy Solution

STEP 1

1. We are converting a density from kg/L \mathrm{kg/L} to g/mL \mathrm{g/mL} .
2. We need to find the correct conversion factors to complete the calculation.
3. We know that 1 kg=1000 g 1 \mathrm{~kg} = 1000 \mathrm{~g} and 1 L=1000 mL 1 \mathrm{~L} = 1000 \mathrm{~mL} .

STEP 2

1. Identify the conversion factor for mass.
2. Identify the conversion factor for volume.
3. Apply the conversion factors to complete the calculation.

STEP 3

Identify the conversion factor for mass from kilograms to grams.
The conversion factor is:
1000 g1 kg\frac{1000 \mathrm{~g}}{1 \mathrm{~kg}}

STEP 4

Identify the conversion factor for volume from liters to milliliters.
The conversion factor is:
1 L1000 mL\frac{1 \mathrm{~L}}{1000 \mathrm{~mL}}

STEP 5

Apply the conversion factors to complete the calculation.
Given:
1.50 kgL×1000 g1 kg×1 L1000 mL\frac{1.50 \mathrm{~kg}}{\mathrm{L}} \times \frac{1000 \mathrm{~g}}{1 \mathrm{~kg}} \times \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}}
Simplify the expression:
1.50×1000 g1×1000 mL=1500 g1000 mL=1.50 g/mL\frac{1.50 \times 1000 \mathrm{~g}}{1 \times 1000 \mathrm{~mL}} = \frac{1500 \mathrm{~g}}{1000 \mathrm{~mL}} = 1.50 \mathrm{~g/mL}
The two missing steps needed to complete the calculation are:
1. 1000 g1 kg\frac{1000 \mathrm{~g}}{1 \mathrm{~kg}}
2. 1 L1000 mL\frac{1 \mathrm{~L}}{1000 \mathrm{~mL}}

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