Question Video: Converting Liters into Milliliters Mathematics

Benjamin and Ethan are calculating how many liters there are in 40 milliliters. Benjamin thinks the result is 40,000 L, and Ethan thinks it is 0.04 L. Who is correct?


Video Transcript

Benjamin and Ethan are calculating how many liters there are in 40 milliliters. Benjamin thinks the result is 40000 liters, and Ethan thinks it is 0.04 liters. Who is correct?

In this question, we’re thinking about how many liters there are in 40 milliliters. In order to answer this, we should recall the conversion that in one liter, there’s 1000 milliliters. However, even when we do remember this conversion, sometimes it can be complicated if we’re changing from milliliters to liters to remember if we divide by 1000 or multiply by 1000. This is the problem that Benjamin and Ethan are having; Benjamin has multiplied by 1000 and Ethan has divided by 1000. So, let’s think through this problem logically.

When we have 1000 milliliters equal to one liter, that means that the numerical value gets smaller when we change from milliliters to liters. In other words, we must divide by 1000 when we’re changing a quantity in milliliters into liters. We could also think of this in terms of finding out 10 milliliters in liters. In order to go from 1000 milliliters to 10 milliliters, we must divide by 100. Therefore, we need to do the same with our value in liters. One divided by 100 is the fraction one hundredth or the decimal value 0.01 liters.

In order to find the number of liters in 40 milliliters, we then think how we go from 10 milliliters to 40 milliliters. We could do this by multiplying by four, so we must do the same on the other side for our liter value. 0.01 multiplied by four is 0.04 liters or four hundredths liters. Another way to think through this question would have been to think of some real-world examples of quantities of milliliters and liters.

In terms of measuring quantities, one teaspoon or one small spoon is about five milliliters. To get 40 milliliters, we’d have approximately eight teaspoons. Compare this to the size of a one-liter bottle, for example, one that’s filled with soda. If we were to put all the teaspoon measures of water, for example, into this one-liter bottle, it wouldn’t fill up the one-liter bottle. And it most definitely would not give us 40000 worth of these liter bottles.

To answer the question then of who got the result correct of 0.04 liters in 40 milliliters, it was Ethan. And so, we give this as our answer.

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