Video Transcript
Fill in the blank. A liquid has a volume of 200 milliliters and a mass of 4000 grams. The density of this liquid is blank kilograms per liter.
We need to determine the density of a liquid. But the question did not provide us with an equation to solve for the density. But we do know that the unit of density is kilograms per liter. We can use this unit to help us determine an equation for density. The symbol kg represents the unit kilograms, a unit of mass. A capital L represents liters, a unit of volume. As the unit of density given in this question is a kilogram per liter, this implies that we can solve for the density by dividing a mass in kilograms by a volume in liters.
The question gives us a volume and mass. However, neither unit matches the units needed for our equation. We can convert the mass in grams into kilograms and the volume in milliliters into liters by using dimensional analysis, a problem-solving method for converting between units. In dimensional analysis, a unit is converted by multiplying the original value by a conversion factor or several conversion factors if necessary.
A conversion factor is a relationship of two equal quantities that have different units. We need a conversion factor that will relate kilograms to grams and liters to milliliters. The prefix kilo- means 1000. Thus, one kilogram is equal to 1000 grams. The prefix milli- means one thousandth. This means that a milliliter is one thousandth the size of a liter. In other words, one liter is equal to 1000 milliliters.
We now know the conversion factors needed to convert the units given in the question to the units needed for our density equation. Let’s start by converting the 4000 grams into kilograms. We need to multiply the original mass value given in grams by the conversion factor. To do this, the conversion factor will need to be rewritten as a fraction. The conversion factor can either be written as one kilogram per 1000 grams or 1000 grams per one kilogram. But which of these representations of the conversion factor should we choose?
We’re trying to convert the unit grams into kilograms. This means that we must find a way to cancel the unit grams. When multiplying and dividing, like units will cancel when they’re found in both the numerator and the denominator. This means that we should use the conversion factor written as one kilogram per 1000 grams as the unit grams appears in the denominator. With the conversion factor in place, the unit grams will cancel, leaving us with the desired unit kilograms. We perform the calculation and determine that 4000 grams are equal to four kilograms.
We’ll use the same process to convert milliliters into liters. The unit milliliters is in the numerator. For this unit to cancel, milliliters must appear in the denominator of the conversion factor. This means that we should write the conversion factor as one liter per 1000 milliliters. The unit milliliters will cancel, leaving us with the desired unit liters. We perform the calculation and determine that 200 milliliters are equal to 0.2 liters.
Now that the mass and volume have been converted into the correct units, we can substitute the values into the density equation. We perform the calculation and determine the density of the liquid to be 20 kilograms per liter.
We should fill in the blank with the value 20.
