Converting 750 Grams to Cups: How-to & Steps

Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

Converting 750 grams of water to cups sounds tricky at first, but once you find out how to convert this mass measurement to a volume measurement it won't seem difficult at all.

Steps to Solving the Problem

When you first see this question you might ask, 'Wait, is it even possible to change grams to cups? Grams is a unit of mass and cups is a unit of volume.'

And, if you did ask that question, you would be making a very interesting point. It is true that 750 grams of liquid mercury, which is very dense, would take up a lot less volume than 750 grams of water vapor, which is hardly denser than air. This is why we need to specify that we are converting 750 grams of water to some number of cups of water. If we chose a different substance, we'd get a different answer because each substance requires a different conversion factor from mass to volume. The conversion factor is simply a ratio that allows you to convert from one type of unit to another type of unit.

Now that we have that confusing bit of information out of the way, let's get on to working our problem!

Step 1 - Convert mass to volume

This conversion becomes easier when we consider the fact that one gram of water at a specific pressure and temperature takes up exactly one milliliter (ml) of water volume. A milliliter is a volume defined as the amount of space taken up by a cube measuring exactly one centimeter on a side. Another term for this volume is a cubic centimeter. This definition of metric volume also explains why we assume we are talking about converting grams of water to a volume.

1 gram of water = 1 ml

Since we have 750 grams of water, this becomes 750 ml of water.

Step 2 - Convert milliliters to fluid ounces

The conversion factor for milliliters to fluid ounces is (1 fluid ounce / 29.57 ml). So now we have:

(750 ml) (1 fluid ounce / 29.57 ml) = 25.36 fluid ounces

We know we have this step correct because the units are correct. If we got anything besides fluid ounces, we would know there was a mistake somewhere.

Step 3 - Convert fluid ounces to cups

Now that we have fluid ounces, we can convert to cups using another conversion factor - 1 cup is 8 fluid ounces:

(25.36 fluid ounces)(1 cup / 8 fluid ounces)

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