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The Unit Factor Method for Physiology Questions

Many laboratory questions in this physiology course will require you to perform a mathematical calculation. For example, “Dr. Gomez orders 0.08 grams of medication for a patient. Each pill contains 0.003 grams of the medicine. How many pills will the patient need?” This problem may seem difficult at first but there is a problem-solving method called the unit factor method that will guide you, step by step, to the correct answer. This method is sometimes also called the “dimensional analysis” method.

A) Numbers and units

Any value or quantity in a problem has two parts: A number and a unit. For example,

0.08 grams

You can think of the word “per” as meaning “a fraction line” or “divided by.” In fact, the unit conversion factor written above is read aloud by saying “60 seconds per minute.”

Also notice the number 1 was put before the minute unit. Each unit must always have a number in front of it. If the phrase doesn’t tell you the number for a unit, assume the number is one.

The word “equals” works the same way as the word “per.” For example, you know the phrase “12 inches equals one foot.” From this you can make a conversion factor:

12 inches

1 foot

Just like the word “per,” the word “equals” means you should draw a fraction line. What comes before the word “equals” always goes above the fraction line and what comes after the word “equals” always goes below the fraction line.

Often the unit conversion factor you need to solve a problem is not given to you directly in the problem. So where does it come from? From you. You can make a unit conversion factor from any phrase you know that contains the word “per” or the word “equals.” You can even make unit conversion factors out of phrases that don’t contain the words “per” or “equals.” Any phrase that relates one quantity to another is a unit conversion factor. Some examples are given below:

Gasoline costs $1.90 a gallon. 1.90 dollars

(“1.90 dollars per gallon”) 1 gallon

Nickels weigh 4.5 grams each. 4.5 grams

(“4.5 grams per nickel”) 1 nickel

Every day the cat eats 3 cups of catfood. 3 cups catfood

(“3 cups catfood per day”) 1 day

When you look at a written unit conversion factor, whatever value is on top of the fraction line is called the numerator. Whatever value is below the fraction line is called the denominator. In the previous example, 3 cups catfood is the numerator and 1 day is the denominator.

The last thing you need to know about unit conversion factors is that you are always free to flip them upside down whenever you need to. This is called inverting them.

12 inches can become… 1 foot

1 foot 12 inches

So unit conversion factors always come in pairs. Each member of the pair is made by inverting the numerator and denominator of the other.

Exercise 1: For each unit below, write a pair of unit conversion factors that relate it to some other unit. The first one is done for you as an example. If you get stuck, ask your instructor for help.

a) Days 7 days and 1 week b) Pennies

1 week 7 days

c) Yards d) Quarts

Show your instructor your answers to this exercise before moving on to the next section.

C) The unit factor conversion method of problem solving

As an example of how to use the unit conversion factor method to solve a problem, we will use the following problem: “An experiment is done to see the health effect of large amounts of aspirin on rats. Each rat gets 22 grams of...

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