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Benjamin and Ethan are calculating how many liters there are in 40 milliliters.
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Benjamin thinks the result is 40000 liters, and Ethan thinks it is 0.04 liters.
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Who is correct?
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In this question, we’re thinking about how many liters there are in 40 milliliters.
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In order to answer this, we should recall the conversion that in one liter, there’s 1000 milliliters.
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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.
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This is the problem that Benjamin and Ethan are having; Benjamin has multiplied by 1000 and Ethan has divided by 1000.
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So, let’s think through this problem logically.
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When we have 1000 milliliters equal to one liter, that means that the numerical value gets smaller when we change from milliliters to liters.
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In other words, we must divide by 1000 when we’re changing a quantity in milliliters into liters.
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We could also think of this in terms of finding out 10 milliliters in liters.
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In order to go from 1000 milliliters to 10 milliliters, we must divide by 100.
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Therefore, we need to do the same with our value in liters.
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One divided by 100 is the fraction one hundredth or the decimal value 0.01 liters.
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In order to find the number of liters in 40 milliliters, we then think how we go from 10 milliliters to 40 milliliters.
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We could do this by multiplying by four, so we must do the same on the other side for our liter value.
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0.01 multiplied by four is 0.04 liters or four hundredths liters.
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Another way to think through this question would have been to think of some real-world examples of quantities of milliliters and liters.
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In terms of measuring quantities, one teaspoon or one small spoon is about five milliliters.
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To get 40 milliliters, we’d have approximately eight teaspoons.
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Compare this to the size of a one-liter bottle, for example, one that’s filled with soda.
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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.
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And it most definitely would not give us 40000 worth of these liter bottles.
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To answer the question then of who got the result correct of 0.04 liters in 40 milliliters, it was Ethan.
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And so, we give this as our answer.