Using Conversion Factors

You will demonstrate this skill on every assessment and in most labs -

it's also the one you will use for dosage calculations

Every morning you buy a donut for 55 cents. How much money will you spend on donuts in a year?

Every donut contains 530 calories. How many calories are you eating in donuts every week?

The donut shop is 3 miles out of your way and your car gets 21 miles per gallon. Gas costs 2.69 a gallon. How much are you spending for gas every month to get your morning donut?

You can solve these problems, so why shouldn't you be able to solve scientific ones? One big reason is that people get scared of the unfamiliar units. But the units don't matter. In fact, the units almost all cancel out when you're solving a conversion factor problem. All they are is words that tell you how to arrange the numbers to solve your problem! This is a good thing, because most of us are better at working with words than with numbers. So the UNITS are your friends.

The basic method of doing conversion factor problems: USE THE UNITS!!!

This method may seem like a lot of work for simple problems. However, it will get you through the most complicated problems, so it is worth learning at this point.

1. Make a list of what you know from the question in fraction form– include UNITS. People often have trouble writing the information from a word problem in fraction form. for tips on writing out information in fraction form, click here

I know I drive 6 miles extra a day to get my donut -- 6 miles/day

I know my car gets 21 miles/gallon

I know gas is $2.69/gallon

I know there are 30 days/month

2. Identify what the question is asking you to figure out – include UNITS

I want to know how many dollars I spend each month to drive to the donut shoppe.

3. Set up the question as an equation with the UNITS you want to find out on the right of the equal sign

4. Look in the list of what you know for the UNITS you want in your answer. Put that information on the left of the equal sign.

5. What’s the difference in UNITS between the left and right sides of the equation? Use some of the other pieces of information you know to cancel out the UNITS you don't want to appear in your answer until the UNITS are the same on each side.

6. Estimate your answer!

7. Now solve it with your calculator, if you need to.

For example:

Mr. K takes 15 tablets of aspirin. Each tablet contained 200 mg acetylsalicylic acid. How much acetylsalicylic acid did he take?

Step 1: what do you know? In this case, you know:


Step 2: what do you WANT to know?

You want to know mg of acetylsalicylic acid taken.

Step 3: lay out your setup. Here's how it would look for this example:

Step 4: Figure out how to use what you know to solve the problem. You know that your final answer should tell you how many mg of acetylsalicylic acid he took. Those UNITS are on the top of the equation in the answer; so you know that they should be on the top in the work you do to solve the problem. Take the fraction with those UNITS in it and put it on the left with those UNITS on the top.

Now you have mg of acetylaslicylic acid on each side, but the left side of the equation also has tablets in it. You want to get rid of those UNITS. You'll do that by using the other piece of information with those UNITS to cancel them out:

You know you've set it up correctly when all the UNITS cancel out except the ones you want to have in your answer. Don't even bother doing the math until you have the UNITS set up correctly so they cancel out.

Step 6: estimate your answer. Is it going to be closer to 100 or 1000 or 10,000? You know 200 x 10 = 2000, so you know your answer should be close to 2000 mg.

Step 7. Now solve it: when you take 200 x 15, you should get 3000 mg acetylsalicylic acid.

For lots of simple conversion factor problems, click here

Practice problems from physiology:

1. Mrs. T weighs 79 kg and is taking 5 mg of medicine A per kg per day. The tablets of medicine A contain 100 mg and a bottle of 200 tablets costs $64.

How many tablets will she take a day?

How much will her medication cost her per year?

2. A man weighs 75 kg and has approximately 45 mmol K+ per kg body weight. He has 60 trillion cells (60,000,000,000).

How many cells does he have per kg of body weight?

How many cells does he have per pound of body weight? (1 lb = 454 grams; 1 kg = 1000 grams)

How many millimoles of K+ does he have per pound of body weight?

How many millimoles of K+ are in his whole body?

How many millimoles of K+ are in each cell?

Conversion factors don’t have to make sense…

Here’s a whole bunch of conversion factors for your use in solving the practice problems below:

63 whiggles per flidge
12 googles/snerd
36 quiddits = 54 snips
42 flidges/ milliwhomp
12 snips/whiggle
2.5 cm/in
1 lollop per quiddit
1000 mL/L
15 snerds = 1 lollop

EXAMPLE: Mr. X has 15 snips. How many milliwhomps does he have?

YOU KNOW: 15 snips and all the conversion factors above.

YOU WANT TO KNOW: milliwhomps

Set it up as an equation:

Now line up the conversion factors to cancel out the units until you end up with milliwhomps:

Solve the problems:

61 flidges = ??? lollops

52 snerds = ??? quiddits

2 snips = ??? lollops

17 quiddits = ??? googles

61 snerds/ 1 inch = ??? googles/cm

think my units are silly? Try using these...