The Correct Answer and Explanation is:
The correct answer is 200 kg/L .
To convert 200 grams per milliliter (g/mL) to kilograms per liter ( kg/L ), we need to handle two separate unit conversions at the same time: converting the mass from grams to kilograms and converting the volume from milliliters to liters. We can do this step by step using conversion factors.
First, let’s establish the basic relationships between these units. For mass, we know that there are 1,000 grams in 1 kilogram. For volume, we know that there are 1,000 milliliters in 1 liter.
We can set up the conversion as a single calculation. We start with our given value, 200 g / 1 mL.
Our goal is to cancel out the “grams” and “milliliters” and be left with “kilograms” and “liters”.
- Convert grams to kilograms: To cancel out grams in the numerator, we need a conversion factor with grams in the denominator. The factor is (1 kg / 1000 g).
- Convert milliliters to liters: To cancel out milliliters in the denominator, we need a conversion factor with milliliters in the numerator. The factor is (1000 mL / 1 L).
Now, let’s combine these steps:
(200 g / 1 mL) × (1 kg / 1000 g) × (1000 mL / 1 L)
In this calculation, the “g” unit in the numerator cancels with the “g” unit in the denominator. Similarly, the “mL” unit in the denominator cancels with the “mL” unit in the numerator. This leaves us with the desired units of kg/L .
Next, we perform the numerical calculation:
(200 × 1 × 1000) / (1 × 1000 × 1)
As you can see, we have a 1000 in the numerator and a 1000 in the denominator. These two values cancel each other out. This leaves us with just 200.
Therefore, 200 g/mL is exactly equal to 200 kg/L . The numerical value does not change because the scaling factor for mass (dividing by 1000) is perfectly balanced by the scaling factor for volume (also dividing by 1000).
