Video: Converting Volumes from Liters to Cubic Decimeters

If the capacity of a tin is 42.4 liters, what is its volume in cubic decimeters?

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Video Transcript

If the capacity of a tin is 42.4 liters, what is its volume in cubic decimeters?

In order to answer this question, we need to recall some of our conversions. The prefixes deci-, centi-, and milli- mean one-tenth, one-hundredth, and one-thousandth, respectively. This means that a decimeter is one-tenth of a meter. A centimeter is one-hundredth of a meter. And a milliliter is one-thousandth of a liter. As there are 10 centimeters in one decimeter, we can calculate the number of cubic centimeters in one cubic decimeter by cubing both sides. 10 cubed is equal to 1000, so there are 1000 cubic centimeters in one cubic decimeter.

We know from the prefix milli- that there are 1000 milliliters in one liter. We now need to recall how we can convert from units of capacity to units of volume. One milliliter of capacity is equal to one cubic centimeter of volume. This means that one liter of capacity must be equal to one cubic decimeter of volume. As the ratio of cubic decimeters to liters is one to one, then 42.4 liters will be equal to 42.4 cubic decimeters.

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