Fundamentals of Healthcare Professions - HCT 101, Topic 5 - Medical Math PDF

Fundamentals of Healthcare Professions HCT 101 Topic 5 - Medical Math Section 1, 2 and 4: Maya Tannoury, MS; Lecturer; College of Healthcare Technologies [email protected]....

Fundamentals of Healthcare Professions HCT 101 Topic 5 - Medical Math Section 1, 2 and 4: Maya Tannoury, MS; Lecturer; College of Healthcare Technologies [email protected]  Learning outcomes Perform math calculations on whole numbers, decimals, fractions, percentages, and ratios. Convert between the following numerical forms: decimals, fractions, percentages, and ratios. Round off numbers correctly. Solve mathematical equivalency problems with proportions. Express time using the 24-hour clock (military time). Express numbers using Roman numerals. Estimate angles from a reference plane. Use household, metric, and apothecary units to express length, volume, and weight. Know equivalencies for converting among the household, metric, and apothecary systems of measurement. Convert between Fahrenheit and Celsius temperature scales. 2  The Importance of Medical math 3 Taken from Dakota Mitchell and Lee Haroun 2021, Introduction to Health Care, 5th Edition, Cengage.  Medical math Health care work requires the use of math skills to measure and perform calculations: o Calculating medication dosages o Measuring the amount of intake (fluids consumed or infused) and output (e.g., urine, vomit) o Performing billing and bookkeeping tasks o Performing lab tests o Mixing solutions Health care professionals must strive for 100% accuracy – errors in math can have significant effects on patients. People feel fear when confronted with mathematics = math anxiety. 4  Basic Calculations To work safely in health care, it is essential to be able to add, subtract, multiply, and divide whole numbers, decimals, fractions, and percentages. Learn basic functions by “longhand” (without calculators). Some professional exams required for licensure or certification do not allow the use of calculators. An easy way to remember how to convert decimals, percentages, and fractions is to think of this humorous cartoon. 5  Basic Calculations Whole numbers Whole numbers are what we traditionally use to count (1, 2, 3,...). They do not contain fractions or decimals. E.g.: 50, 23, 101 For example, 30 is a whole number, whereas 30½ and 30.5 are not. 6  Basic Calculations Decimals (1/6) Decimals are used to express parts of numbers or anything else that has been divided into parts. Parts are expressed in units of 10. That is, decimals represent the number of tenths, hundredths, thousandths, and so on. E.g., 0.7 represents 7 of the 10 parts into which something has been divided. 7  Basic Calculations Decimals (2/6) The position of the number to the left or the right of the decimal point is its place value. The value of each place to the left of the decimal point is 10 times that of the place to its right. The value of each place to the right of the decimal point is one-tenth the value of the place to its left. 8  Basic Calculations Decimals (3/6) When reading decimals verbally, it is necessary to know the placement values for the decimals (digits to the right of the decimal point) and that the decimal point is read as “and.” o 0.5 is read “five tenths” o 1.5 is read “one and five tenths” o 1.50 is read “one and fifty hundredths” o 1.500 is read “one and five hundred thousandths” o 1.5000 is read “one and five thousand ten thousandths” 9  Basic Calculations Decimals (4/6) Practice in order to reduce errors. Decimals are added, subtracted, multiplied, and divided in the same way as whole numbers. The most common mistake is incorrect placement of the decimal point. The Joint Commission requires the following designations when writing decimals: o Never use a trailing zero (e.g., write 1 mg, not 1.0 mg because the decimal point can be missed and read as 10 mg. This would result in a tenfold error in dosage.). o Always use a leading zero if less than 1 (e.g., write 0.1 mg, not.1 mg because the decimal point can be missed and read as 1 mg. This would result in a tenfold error in dosage.). 10  Basic Calculations Decimals (5/6) The table below shows tips to reduce medication errors: 11  Basic calculations Decimals (6/6) The table below shows how to work with decimals: 12  Basic calculations Fractions Fractions are another way of expressing numbers that represent parts of a whole. A fraction has a numerator (top number) and a denominator (bottom number): o E.g.: In the fraction 3/10, 3 is the numerator and 10 is the denominator. o The fraction 3/10 is read as “three tenths.” o The denominator (bottom number) defines how many parts make a whole. o The numerator (top number) is the actual number of parts of this whole. Numerator 3 Denominator 10 13  Basic calculations Percentages Percentages are used to express either a whole or part of a whole. The whole is expressed as 100% (percent). The 10 slices together equal the whole, or 100%, of the pie. One hundred divided by ten equals ten → each slice represents 10% of the pie. If each slice is 10%, then three slices represent 30% of the pie. When working with percentages, it is easier to convert the percentage to a decimal and then to perform the addition, subtraction, multiplication, and division 14  Basic calculations Ratios Ratios show relationships between numbers or like values: How many of one number or value is present in comparison to the other. For example, a 1:3 bleach to water solution is one part of bleach added for every three parts of water. The whole quantity in this case is four parts. To determine the strength of the bleach solution, the amount of bleach (1 part) is divided by the whole (4 parts). It can then be stated that this is a 25% bleach solution. 15  Basic calculations Converting decimals, fractions, percentages, and ratios Steps involved in converting among numerical forms 16  Basic calculations Rounding numbers (1/2) Rounding a number means changing it to the nearest ten, hundred, thousand, and so on. Deciding to round depends on the degree of accuracy required. Rounding up or rounding down depends on the digits (numbers) located to the right of the value chosen for rounding. Rules of rounding: o When rounding to the nearest 10, look at the digit to the right of the tens place - if the number is 5 or above, round up. If it is less than 5, round down. E.g.: 88 rounds up to 90; 83 rounds down to 80. o When rounding to the nearest 100, look at the digit to the right of the hundreds place (the tens place). If the number is 5 or above, round up. If it is less than 5, round down. E.g.: 67 rounds up to 100; 133 rounds down to 100; 668 rounds up to 700; 621 rounds down to 600. o When rounding to the nearest 1000, look at the digit to the right of the thousands place (the hundreds place). If the number is 5 or above, round up. If it is less than 5, round down. E.g.: 7777 rounds up to 8000; 7355 rounds down to 7000 17  Basic calculations Rounding numbers (2/2) 18 Classwork Round the following numbers to the nearest... Number Round to the... Answer 86786.1672 Tens 86790 543.468786 Hundredths 543.47 1,327,658.53165 Thousandths 1,327,658.532 8765.1654 Thousands 9000 725.1654 Hundreds 700 1645.1357 Thousandths 1645.136 8765.1654 Tens 8770 32.465 Tenths 32.5 19  Basic calculations Solving problems with proportions A proportion (cross multiplication) is a statement of equality between two ratios. For example, the proportion 2:6 = 3:9 means that 2 is related to 6 in the same way that 3 is related to 9. It is verbalized as “two is to six as three is to nine.” Proportions are useful for converting from one unit to another when three of the terms in the proportion are known. A common application of proportions in health care is to find the value of an unknown when converting medications from one form to another. E.g., a physician orders a patient to have 50 grams of a medication. The nurse notes that the medication is available only in 12.5-gram tablets. How many tablets should she give the patient? x tablets = (50 x 1) /12.5 = 4 tablets of 12.5 grams each ? 20  Estimating Health care professionals must work carefully when performing calculations. Estimating helps check work by anticipating the results. This involves calculating the approximate answer and judging if the calculated results seem reasonable. 21  Military time (1/3) Military time is used in health care to avoid the confusion created by the a.m. and p.m. If the a.m. or p.m. is omitted or misread, an error of 12 hours is made. Military time is also called the 24-hour clock. In military time, all time designations are made with the 24-hour clock. o The twelfth hour is at 12 noon and the twenty- fourth hour is at 12 midnight. 22  Military time (2/3) When using the 24-hour (military) clock, remember the following key points: o Time is always expressed using four digits. E.g.: 0030, 0200, 1200, 1700. o The a.m. hours are expressed with the same numbers as the traditional clock. E.g.: 1 a.m.: 0100; 5:30 a.m.: 0530; 10 a.m.: 1000. o To convert to p.m. hours, add the a.m. time to 1200. E.g.: 1 p.m.: 0100 + 1200 (1:00 p.m. expressed in four digits) = 1300 5:30 p.m.: 0530 + 1200 (5:30 p.m. expressed in four digits) = 1730 10 p.m.: 1000 + 1200 (10:00 p.m. expressed in four digits) = 2200 o When times are verbalized, there is a specific way in which they are expressed: E.g.: 1300 = thirteen hundred hours 1301 = thirteen oh one 1730 = seventeen thirty hours 2200 = twenty-two hundred hours 23  Military time (3/3) Military (24-hour clock) and traditional time conversion chart. 24  Roman numerals (1/3) The traditional numbering system we use every day is referred to as Arabic numerals (1, 2, 3,...). In health care, Roman numerals are used for some medications, solutions, and ordering systems. Some files or materials are organized using Roman numerals. Arabic and Roman numeral conversion chart. 25  Roman numerals (2/3) When using Roman numerals, remember the following key points: 1. All numbers can be expressed by using seven key numerals (table on the right). 2. If a smaller numeral is placed in front of (before) a larger numeral, the smaller numeral is subtracted from the larger numeral. I 1 E.g.: In IV, the 1 is placed before the 5, so it is subtracted (5 − 1 = 4). V 5 3. If a smaller numeral is placed after a larger numeral, the smaller X 10 numeral is added to the larger numeral. L 50 E.g.: In VI, the 1 is placed after the 5, so it is added (5 + 1 = 6). C 100 4. When the same numeral is placed next to itself, it is added. D 500 E.g.: III = 1 + 1 + 1 = 3 M 1000 E.g.: XX = 10 + 10 = 20 E.g.: IXX: this has two of the same numeral preceded by a smaller numeral, but the rules still apply (10 + 10 − 1 = 19 or 10 − 1 + 10 = 19) 26  Roman numerals (3/3) When using Roman numerals, remember the following key points (cont.): 5. The same numeral is not placed next to itself more than three times. E.g.: XXX = 30 E.g.: XL = 40 (XXXX is not correct) 6. When Roman numerals are used with medication dosages, the lowercase (i, v, x, l, c, d, m) may be used rather than uppercase (capital letters). E.g.: ii = 2 E.g.: iv = 4 E.g.: ixx = 19 27  Classwork Write the following Hindu-Arabic numerals in Roman numerals: Number In Roman Numeral 32 XXXII 39 XXXIX 48 XLVIII 288 CCLXXXVIII 28  Angles (1/6) Angles are used in health care when: o Injecting medications o Describing joint movement o Indicating bed positions Angles are defined by comparison to a reference plane. The reference plane is a real or imaginary flat surface from which the angle is measured. The distance between the plane and the line of the angle is measured in units called All angles are expressed in relation to a real degrees. or imaginary reference plane. 29  Angles (2/6) If a flat stick is placed on a table (the reference plane), the angle is at 0 degrees. If the stick is lifted to stand straight up (perpendicular to the table), there is a 90- degree angle to the table. Rotating the stick all the way around the arc and returning to the reference point represents 360 degrees All angles are expressed in relation to a real or imaginary reference plane. 30  Angles (3/6) Examples to illustrate how angles are used in heath care: Example 1: Injecting needles Reference plane is the skin surface. Angles for injecting vary, depending on the type of medication or procedure. 31  Angles (4/6) Example 2: Angles and vectors in Dentistry Ref: Hartmann et. Al. (2018)  Angles (5/6) Example 3: Bed position Sometimes the physician will order that the head of the bed be kept always elevated by 30 to 45 degrees. This is usually ordered to aid in respiration or to prevent aspiration (stomach contents entering the lungs). In this situation, the bed in the flat position is the reference plane. Multiple Bed positions can be adjusted according to the physician recommendation and physical state of Source: Contribution to hospital bed the patient design , Advcances in Ergonomy design (Martelz et. al. 2017) 33  Angles (6/6) Example 4: Describing angle of extremities When describing the angle of extremities (arms and legs), the body in a full upright position is the reference plane. Each joint (e.g., elbow, knee, hip) has a normal range it can move within. Physicians assess the range of a patient’s joint compared to this normal range to chart loss of function or progress of recovery. 34  Systems of Measurement Various systems of measurement are used in health care: o Distance (length) o Capacity (volume) o Mass (weight) The three systems used in health care are: o Household o Metric o Apothecary 35  Systems of Measurement The household measurement system 36  Systems of Measurement Household system Most used method of measurement in the United States. “Ounce” is used as both a measurement of capacity/ volume and mass/weight. Various units of measurements in the household can be converted between each other. For example, volume/capacity is measured in drops, teaspoons, tablespoons, ounces, cups, pints, quarts, and gallons. 37  Systems of Measurement Metric system Familiar outside of the United States and among scientists. More accurate than the household system. Easier to convert between numbers because everything is based on a unit of ten. The nomenclature for the metric units is as follows: o Distance/length: meter (m) o Capacity/volume: liter (l or L) o Mass/weight: gram (g) 38  Systems of Measurement Metric system To express larger or smaller units, the appropriate prefix is added to the meter, liter, and gram. The decimal system is based on multiples of ten. Therefore, conversions within the decimal system are calculated by multiplying by 10, 100, 1000, and so on: Comparison of common metric units used in health care. 39  Systems of Measurement Apothecary system It is the oldest and least used of the three systems of measurement. This system is seldom seen in the modern health care environment. The Joint Commission has advised that the apothecary symbols and measurements should no longer be used, but has not yet added this system to its official “do-not-use” list. 40  Systems of Measurement Apothecary system Apothecary measurement system. 41  Systems of Measurement Power conversion Mass Conversion Table Mass measures the amount of matter in an object or substance. The standard unit of mass in the International System of Units (SI) is the kilogram. This table provides conversions between various units of mass, from the smallest (milligram) to larger units like the metric ton. Unit Equivalent in Grams (g) Milligram (mg) 0.001 g Centigram (cg) 0.01 g Decigram (dg) 0.1 g Gram (g) 1g Decagram (dag) 10 g Hectogram (hg) 100 g Kilogram (kg) 1,000 g Metric ton (t) 1,000,000 g Example: A doctor prescribes 500 mg of a medication. The pharmacist knows that this is equivalent to 0.5 g. 42  Systems of Measurement Power conversion Volume Conversion Table Volume denotes the space an object or substance occupies. In medical scenarios, volume is vital when administering fluids or measuring organ capacities. For example, a nurse might administer medication in milliliters using a syringe. Unit Equivalent in Liters (L) Milliliter (mL or cc) 0.001 L Centiliter (cL) 0.01 L Deciliter (dL) 0.1 L Liter (L) 1L Decaliter (daL) 10 L Hectoliter (hL) 100 L Kiloliter (kL) 1,000 L Example: A patient requires 5 mL of a Atrophine liquid medication. If a nurse has a 10 mL syringe, they know to fill it halfway. 43 Systems of Measurement Power conversion Common prefixes of the metric system 44  Do not memorize Resources: National Institute of Standards and Technology 45 Resources: National Institute of Standards and Technology Do not memorize 46  Systems of Measurement Power conversion 1 kiloliter = 1000 × 1 liter = 1000 liters = 103 liters (10 to the power of three) 1 hectoliter = 100 × 1 liter = 100 liters = 102 liters (10 to the power of two) 1 decaliter = 10 × 1 liter = 10 liters = 101 liters (10 to the power of one) 1 deciliter = 0.1 × 1 liter = 0.1 liter = 10-1 liters (10 to the power of minus one) 1 centiliter = 0.01 × 1 liter = 0.01 liter = 10-2 liters (10 to the power of minus two) 1 milliliter = 0.001 × 1 liter = 0.001 liter = 10-3 liters (10 to the power of minus three) 1 microliter = 0.000001 x 1 liter = 0.000001 liter = 10-6 liters (10 to the power of minus six) 1 liter = 10-3 kiloliter 1 milliliter = 10-3 liter 1 microliter = 10-3 milliliter 1 microliter = 10-6 liter 47  Systems of Measurement Power conversion Pressure Conversion Table Pressure quantifies the force exerted on a surface per unit area. It's a crucial parameter in various scientific and engineering applications. The SI unit for pressure is the Pascal. This table outlines conversions between common pressure units, including atmospheres, bars, and torrs. Unit Equivalent in Pascals (Pa) Atmosphere (atm) 101,325 Pa Bar 100,000 Pa Millibar (mbar) 100 Pa Torr (mmHg) 133.322 Pa Pound per square inch (psi) 6,894.76 Pa Example: A patient's blood pressure reading is 120/80 mmHg. For a research study, this might be converted to Pascals. 48 Thinking It Through Question 1: Use the calculation of proportion (cross multiplication): 1 ft → 12 in 6 ft → a=? ➔ a = 6 x 12 / 1 = 72 in Question 2: Step 1: Convert all values to pounds by using the calculation of proportion (cross multiplication): 1 lb → 16 oz b=?  8 oz ➔ b = 8 x 1 / 16 = 0.5 lb Step 2: Then add all pound values together: 160 lb and 8 oz is equivalent to 160.5lb 49  Systems of Measurement Converting systems of measurement E.g.: Convert 19 inches to centimeters. 50  Systems of Measurement Converting systems of measurement Approximate equivalents between measuring systems. 51  Systems of Measurement Temperature conversion To measure temperature, the Fahrenheit (F) unit is conventionally used in the United States. The Celsius (C) system (centigrade) of measurement is frequently seen outside of the United States and in medical practice worldwide. Boiling points: 212°F = 100°C Freezing points: 32°F = 0°C The formular for conversion between Fahrenheit and Celsius: 5 °𝐹 − 32 ∗ = °𝐶 9 52  Systems of Measurement Comparison of Fahrenheit and Celsius. Fahrenheit- Celsius Conversion Chart. 53  Systems of Measurement Temperature conversion All temperature conversion formulas include parentheses. These are used to indicate that the enclosed calculation must be performed first. E.g.: the steps to solve the formula (°F − 32) × 5/9 = °C are to first subtract 32 from the value for F and then multiply that value by 5/9. Temperature scale 54 conversion formulas.  Classwork Maria is working in the hospital and when taking vital signs, she discovers that a patient has a temperature of 37.6°C. When she checks the orders, she finds the physician has ordered Tylenol gr x to be given every four hours as needed for a temperature above 101°F. Maria notes it is 4 p.m. and the last dose was given at 1300 hours. The Tylenol tablets she has available are marked as 525 mg/tablet. She gives the patient two tablets and charts the time given as 1500. a. Assuming the last dose was given at 1300 hours, when would the next dose of Tylenol be due? If it is now 4 p.m., how much time has elapsed since the medication was given? b. Did Maria note the time correctly? If not, how is 4 p.m. expressed in military time? c. What would be the equivalent of 101°F in the Celsius system? Was the temperature elevated high enough to give the Tylenol as ordered? d. Was the correct amount of medication given? If not, was too much or too little given? 55