Mathematics Study Guide for the HESI Exam

Additional Math Concepts

These concepts are somewhat less common in comparison to the others, but they are still relevant to this test. Understanding them can be helpful in certain real-world situations, especially in the healthcare and technical fields.

Roman Numerals

Roman numerals come from the ancient number system used in the Roman Empire. In select situations, they are still used as an alternative to the modern numeral system. Roman numerals are based on the idea of adding (and in special cases subtracting) to represent each number. The following table provides a list of the most commonly used Roman numerals today and their meaning.

Roman Numeral	Numerical Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1,000

Roman numerals are written from left to right, moving from the greatest numeral to the smallest. As you read them, add together the symbols for the numeric value.

Let’s try a problem that involves Roman numerals.

Erica is visiting Rome for vacation. She sees an old building with “MCCLIII” written on it. What number is this?

Solution

Looking at our reference chart, we see the first symbol, M, is \(1\text{,}000\). The second two symbols are both C, which is \(100\), so CC is \(100+100\). L is \(50\), and III is \(1 + 1 + 1\). Adding this all together, we get:

\[1\text{,}000 + 100 + 100 + 50 + 1 + 1 + 1 = 1\text{,}253\]

Thus, the number on the building is \(1\text{,}253\), or simply \(1253\) since it probably stands for a year.

There are a few special cases where instead of adding, we subtract to find the meaning of the Roman numeral. These special cases occur when we want to avoid stringing four of the same symbol together (like IIII for \(4\) or VIIII for \(9\)). Instead, we use one of the symbols for a power of ten (I, X, C, M) and place it before a symbol with a greater numeric value.

An example of this is for the value of four. This is written as IV, or “\(5\) minus \(1\).” The next time this occurs is for the number nine, IX, or “\(10\) minus \(1\).” Forty is denoted by XL, or “\(50\) minus \(10\),” while ninety is XC, or “\(100\) minus \(10\).”

Here is another example problem.

Jerome is in class and wants to toss a note inconspicuously to let his friend know that he wants to meet up at \(4\text{:}59\). In case the teacher sees the note, he is going to write the time as \(459\) but in Roman numerals. How would he write this number in Roman numerals?

Solution

First, we break up the number by place value. Written this way, \(459\) becomes \(400 + 50 + 9\) or \((500-100) + 50 + (10-1)\). In Roman numerals, we write this as CDLIX. So, Jerome will write “MEET AT CDLIX!!!” in his note to his friend.

Converting Measurements

Any measurement of an object will be given in a certain unit. Whether it’s the volume of a vial of blood in milliliters, the height of a person in inches, their weight in pounds, or a dose of medicine in grams, there is a unit attached to it so that we have an idea of exactly how much that measurement is.

Very often, however, the unit the measurement is given in is not the unit we need to know. In that case, we must convert to a different unit. In the nursing field, this often applies to units such as time, temperature, length/distance, volume/capacity, weight, and mass. Converting between these units is essential for proper care, such as when calculating medication dosages or measuring patient vitals. For this test, you should familiarize yourself with these conversions, as no formulas will be provided. Memorizing these conversion factors will be key to solving the related problems.

Time

Time conversions are commonly used in healthcare settings to calculate shifts, patient schedules, and treatment intervals. Here are some key time conversions:

\(1\) year \(= 52\) weeks
\(1\) year \(= 365\) days
\(1\) week \(= 7\) days
\(1\) day \(= 24\) hours
\(1\) hour \(= 60\) minutes
\(1\) minute \(= 60\) seconds

Temperature

In healthcare, temperature conversions are critical when interpreting patient body temperature, especially when using different systems, such as Celsius and Fahrenheit. The formula to convert Celsius (\(^{\circ} \text{C}\)) to Fahrenheit (\(^{\circ} \text{F}\)) is:

\[F = \frac{9}{5} C + 32\]

This is the formula to convert Fahrenheit to Celsius:

\[C = \frac{5}{9}(F - 32)\]

Note: Pay attention to the parentheses in the second formula (conversion to Celsius). According to the order of operations, you do the subtraction within the parentheses before multiplying by the fraction.

Let’s see how this would be relevant in a real-world situation.

Nurse Sarah takes a patient’s temperature, which reads \(38^{\circ}\text{C}\). What is the patient’s temperature in Fahrenheit?

Solution

This is a simple problem if you know the conversion formula:

\[\frac{9}{5} \times 38 + 32 = 100.4^{\circ} \text{F}\]

Length/Distance

Knowing how to convert different units of length and distance is useful in all manner of real-world situations. In nursing specifically, length conversions are essential when measuring a patient’s height or the dimensions of wounds or anatomical features. The most common length and distance conversions include:

\(1\) kilometer \(= 0.621371\) miles
\(1\) mile \(= 5\text{,}280\) feet
\(1\) inch \(= 2.54\) centimeters
\(1\) kilometer \(= 1\text{,}000\) meters
\(1\) meter \(= 100\) centimeters
\(1\) meter \(= 1\text{,}000\) millimeters

Volume and Capacity

Volume and capacity conversions are important when administering liquids in medicine or measuring blood volumes. Here are some common conversions:

\(1\) gallon \(= 4\) quarts
\(1\) quart \(= 2\) pints
\(1\) pint \(= 2\) cups
\(1\) cup \(= 8\) ounces
\(1\) cup \(= 16\) tablespoons
\(1\) gallon \(= 3.78541\) liters
\(1\) liter \(= 1\text{,}000\) milliliters
\(1\) cubic centimeter \(= 1\) milliliter

Weight and Mass

Weight and mass conversions are often necessary in the medical field, such as when you’re calculating medication dosages based on patient weight. Here are some key conversions:

\(1\) pound \(= 453.592\) grams
\(1\) ounce \(= 28.3495\) grams
\(1\) kilogram \(= 2.20462\) pounds
\(1\) kilogram \(= 1\text{,}000\) grams
\(1\) gram \(= 1\text{,}000\) milligrams

Conversion Word Problems

Some of these conversion factors might look familiar, while others may be new to you. Usually, people find that the more often they use a conversion factor, the easier it is to recall. There are going to be many times in your career that you will need to do quick conversions, so it’s good to practice now. Let’s try some word-problem examples that require conversions.

Jordan takes a patient’s height and finds they are \(5\) feet, \(8\) inches tall. However, when he goes to mark the chart, he realizes the measurement should have been in centimeters. Convert the patient’s height to centimeters.

Solution

First, we will convert \(5\) feet (\(\text{ft}\)) to inches (\(\text{in}\)), then add it to the remaining \(8\) inches:

\(\require{cancel}\) \(\frac{5\;\cancel{\text{ft}}}{1} \times \frac{12\;\text{in}}{1\;\cancel{\text{ft}}} = \frac{60 \;\text{in}}{1} = 60 \;\text{in}\)

Notice how the feet units on the top and bottom cancel each other out. Think of it like this:

\[\frac{\text{ft}}{\text{ft}} = 1\]

Jordan’s patient is \(68\) inches tall (\(60\) inches + \(8\) inches). Next, we need to do another conversion multiplication to go from inches to centimeters (\(\text{cm}\)):

\(\require{cancel}\) \(\frac{68\;\cancel{\text{in}}}{1} \times \frac{2.54 \;\text{cm}}{1 \;\cancel{\text{in}}} = \frac{172.72 \;\text{cm}}{1} =172.72 \;\text{cm}\)

Again, notice how the inches in the top of the first fraction cancel out with the inches from the conversion factor of the second fraction.

At the end of the problem, we are only left with centimeters, which is what we wanted. Jordan should document that the patient is \(172.72\) centimeters tall.

If there is more than one conversion factor needed to convert a measurement, we can create a conversion chain of multiplication problems using the conversion factors.

Here is an example problem that requires a conversion chain.

Shawna received a container for storing chemicals that measures \(250\) fluid ounces. However, her lab uses the metric system (liters) to measure everything. How many liters should she label the container as being? (Round to three decimal places.)

Solution

This conversion requires the following steps based on the conversion factors pulled from the table above: fluid ounces (\(\text{fl oz}\)) to cups (\(\text{c}\)) to pints (\(\text{pt}\)) to quarts (\(\text{qt}\)) to gallons (\(\text{gal}\)) to liters (\(\text{L}\)). Here is what the conversion chain looks like:

\(\require{cancel}\) \(\frac{250 \;\cancel{\text{fl oz}}}{1} \;\times \;\frac{1\;\cancel{\text{c}}}{8 \;\cancel{\text{fl oz}}} \;\times\; \frac{1 \;\cancel{\text{pt}}}{2 \;\cancel{\text{c}}} \;\times\; \frac{1 \;\cancel{\text{qt}}}{2 \;\cancel{\text{pt}}}\; \times\; \frac{1 \;\cancel{\text{gal}}}{4 \;\cancel{\text{qt}}}\;\times \;\frac{3.78541 \;\text{L}}{1 \;\cancel{\text{gal}}}\)

\[= \frac{250\; \times\; 3.78541 \;\text{L}}{128}\] \[= \frac{946.3525 \;\text{L}}{128}\] \[\approx 7.393 \;\text{L}\]

Note how the fluid ounces on top cross out with the fluid ounces on the bottom, the cups on top with the cups on bottom, etc., until the only unit that is left is liters. So, Shawna should label the \(250\)-fluid ounce container as holding about \(7.393\) liters.