EXAMPLE 2

 

In a typical person, the level of glucose (also known as blood sugar) is about 85 mg/100 mL of blood. If an average body contains about 11 pints of blood, how many grams and how many pounds of glucose are present in the body?

 

To solve this problem, you want to first identify what you are given in the problem. For this question, this is two parts: 1) 85 mg of glucose /100 mL of blood and 2) 11 pints of blood. Next, identify what you are asked to find: 1) how many grams of glucose and 2) how many pounds of glucose in the body. This information can be easily summarized in a table, as shown below:

 

Knowns

Unknowns

85 mg of glucose /100 mL of blood

how many grams of glucose in the body

11 pints of blood.

how many pounds of glucose in the body

 

 

Next, we need to find a starting point for our unit conversion. This point is generally with the known value thats not part of a fraction. In this case, it's the 11 pints of blood. Now we need to start thinking of relationships between pints and mL in order to convert over to another unit used in our known column above. With some thinking, we can remember, there are 2 cups in a pint, 2 pints in a quart. Consulting with any chemistry textbook will give a relationship between quarts and liters, so we'll go in that direction and add this information to our list of known information:

 

Knowns

Unknowns

85 mg of glucose /100 mL of blood

how many grams of glucose in the body

11 pints of blood

how many pounds of glucose in the body

2 pints = 1 quart

 

1 liter = 1.057 quarts

 

 

Now we can start building our unit conversion using some math. Again, start with the value thats not part of a fraction:

 

We need to have units cancel out, so our next step is to use a unit converstion / relationship that relates to pints and another unit. Looking back at our list of Knowns in our table, we can see we identified 2 pints = 1 quart will put us into the next unit. Lets add that into our calculation. Remember, you want to have units cancel each other out, so pints will need to go on the bottom.

  

So ask yourself and check back to our table, is the unit were in now the same unit as we need to be in? Well, we're in units of quarts of blood, but the question asks about the grams of glucose. Since were not, we have to keep going.

 

The next relationship we identified was between quarts and liters (1 liter = 1.057 quarts).Again, setting the problem up for unit cancelation, we'll put the quarts on bottom and liters on top:

  example 2_3.jpg

Again, checking to see if were in the unit we need for the solution, we find that we have to keep going. You may have also noticed, we haven't used another piece of information given us in the original problem. We will need to start aiming our next conversions toward that. Hopefully you noticed that our other known (85 mg of glucose /100 mL of blood) has blood in units of milliliters, while our problem currently as blood in terms of liters. We can quickly switch to milliliters using the metric system prefixes relationships.

example 2_4.jpg  

Since we're now in a unit of the 85 mg of glucose /100 mL of blood, we can apply it, again, watching for the common units to cancel out:

  

example 2_5.jpg

Again, checking to see if were in the unit we need for the solution, we find that we're much closer than weve been before now! We've managed to get milligrams of glucose into our problem and we need to find grams of glucose. Were close! We've gotten the right base unit, the gram! Recalling our metric prefix relationships, we can quickly convert mg of glucose into grams of glucose:

example 2_6.jpg   

Now we just multiply everything on top together, and multiply everything on bottom together, cancel out the units and then divide:

example 2_7.jpg

Looking back at our table of knowns and unknowns, we found that we really knew more than we've let on, when we account for the metric prefix relationships that we know:

 

Knowns

Unknowns

85 mg of glucose /100 mL of blood

how many grams of glucose in the body

11 pints of blood

how many pounds of glucose in the body

2 pints = 1 quart

  

1 liter = 1.057 quarts

  

1 base unit = 1000 milli(base units) where the base unit is liters or grams

 

 

 

Let's work on the second unknown listed in our table. We've got a couple of options with it. We can start back from the beginning of the first calculation, or we can pick up where we left off. As chemists are lazy, were going to pick up where we left off in the last step:

  example 2_8.jpg 

We need to figure out a relationship between grams and pounds. Consulting a textbook and looking at their tables of units generally in the measurement chapter, we find a couple of relationships between grams and pounds:

 

Either of these two relationships will work for our calculation. If you look at our starting unit, grams glucose, we can quickly see that there is a relationship that already uses grams when converting to pounds. Using the 2nd relationship will result in us having to add fewer steps.

 example 2_9.jpg

Or

  example 2_10.jpg

Just like before, once we're in the unit the question asks about, we can do the multiplication and division.

 example 2_11.jpg

We can put this value in scientific notation:

example 2_12.jpg

 


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