Week 9 Module Lessons

Weight per Gram

* The rule of multiplying or dividing by 10 to change to the next smaller basic unit does not apply to micrograms: 1 milligram (1 mg) equals 1000 micrograms (1000 mcg).

Example Problems: Changing Percentages to Fractions, Decimal Numbers, and Ratios

As needed, a percentage can be changed to a fraction, a decimal number, or a ratio. Remember ratios? They indicate a relationship between two numbers, which are separated by a colon, such as 2:3. Because the colon indicates division, a ratio is a fraction. The numbers (terms) in a ratio are the numerator (to the left of the colon) and denominator (to the right of the colon). Like fractions, ratios must be reduced to their lowest terms. Select to view how to change percentages to fractions, decimal numbers, and ratios.

Trailing Zero

Don't place unnecessary zeros at the end of a decimal number. Although these trailing zeros don't change the number's value (for example, 2.350 is the same thing as 2.35), they: Are linked to an increased risk of misinterpretation of values. May lead to the decimal point being completely overlooked. The Joint Commission's official "Do Not Use" List (2013) and the Institute of Safe Medication Practices prohibits the use of trailing zeros in medication prescriptions and other medication-related documentation.

Leading Zero

For dosages of less than 1 (with no whole number before the decimal point), write a 0 before the decimal point to avoid confusion. This is called a leading zero. For example, write .25 as 0.25.

Units of the Metric System

IV bags commonly hold 1000 mL (1 L). Medication cups typically hold 30 mL. Tables of equivalents help demonstrate the relationships among units of measure in the metric system.

Roman & Arabic Numbering Introduction

In health care, nurses commonly use Arabic numbers and occasionally use Roman numerals. In the Arabic system, the nurse typically sees fractions, decimal numbers, and percentages in medical records and medication documentation. On the job, these numbers are likely to appear on such things as: -Medication dosages and containers -Controlled substance schedules -Intravenous solutions -Patient care charting -Burn assessments

Converting Other Numbers in the Roman System

In the Roman system, the Roman numerals i/I, v/V, x/X, l/L, c/C, and m/M correspond to the Arabic numbers 1, 5, 10, 50, 100, and 1000. When combined according to certain rules, these six Roman numerals can represent whole Arabic numbers (1 and higher) as well as fractions of 1. Some Roman numerals, such as i/I and v/V, convert directly to Arabic numerals. Converting other Roman numerals, such as iv/IV and xxiii/XXIII, requires the addition or subtraction of the numerals, depending on their values and relative positions.

Apothecary System Equivalents

In the apothecary system, the basic units of measure are the: Grain (gr), which is used to measure weight Minim, which is used to measure volume These are the smallest units in the apothecary system. Larger units include the dram (dr) and the ounce (oz). The terms fluid dram and fluid ounce are only for measuring a liquid. The terms dram and ounce are for fluids or solids. The apothecary system expresses whole numbers as lowercase Roman numerals and expresses the fraction ½ as the symbol ss. The Roman numerals appear after the abbreviation. For example, the apothecary system expresses "10 grains" as "gr x." This table shows the equivalents of volume and weight measures within the apothecary system.

Converting Time & Temperature Introduction

No matter what setting you work in, you should be prepared to perform two more mathematical conversions: time and temperature. Primarily for documentation, you may need to convert from standard time to military time. To avoid misinterpretation of AM and PM times, most facilities use military time. With this 24-hour system of timekeeping, a 24-hour time cycle replaces the two 12-hour cycles in standard time. This helps prevent errors in patient care. Although most facilities require temperatures to be documented in degrees Celsius, others require documentation in degrees Fahrenheit. You must be familiar with the temperature documentation requirements of your facility and, when needed, convert accurately between the two scales. Most thermometers measure temperature using the Celsius or Fahrenheit scale. Some electronic thermometers convert between the two scales with a simple press of a switch. In other cases, you can perform the conversion yourself with a simple calculation.

Example Problems: Changing a Fraction to a Decimal Number

Nurses commonly convert fractions to decimals. To do this, follow these steps: Divide the numerator by the denominator. Round off, if needed. These examples show how to work through conversions.

Metric and Household Length Conversions

Nurses commonly record length measurements, including: Linear laceration or lesion Size of the pupil of an eye Infant's head circumference Abdominal girth Measurements for edema In various healthcare settings, the most commonly used metric units of measure for length are the centimeter and the millimeter. Plan to use these conversion factors: 1 cm = 10 mm 1 in = 2.54 cm

What Is a Percentage?

Percentages are commonly used in the: Administration of medications and intravenous solutions Assessment of burns An understanding of percentages forms the basis for preparing and calculating medication dosages. The term percent (represented by the % symbol) means "parts per hundred." A percentage is the same as a fraction with a denominator of 100, with a numerator that reflects the part of 100 being considered. A percentage may be expressed as a decimal number or a fraction. These examples show different ways of expressing percentages: 5% = 5 percent = 51005100 = 5 per 100 = 0.05 60% = 60 percent = 6010060100 = 60 per 100 = 0.6

Decimals

Primary healthcare providers prescribe most medications in metric measures that include decimal numbers. To understand decimal numbers, remember that: Numbers to the right of the decimal point are decimal fractions with a denominator of 10 or a multiple of 10. They have a value of less than—or part of—1. Numbers to the left of the decimal point are whole numbers. They have a value of 1 or greater. These example medications have dosages written with decimal numbers: Carvedilol (Coreg) 3.125 mg Digoxin (Lanoxin) 0.25 mg Levothyroxine (Synthroid) 0.2 mg Valacyclovir (Valtrex) 0.5 g

Percentage to Ratio

Remove the percent sign. Change the number to a fraction. (Use the number as the numerator and use 100 as the denominator.) Reduce the fraction to its lowest terms. Use the numerator as the first term of the ratio. Use the denominator as the second term. Put a colon (:) between the two terms. Example: To change 75% to a ratio, apply the steps. 75%=7510075100which equals 75:100 or 3:4.

Percentage to Fraction

Remove the percent sign. Make the number be the numerator (top number of a fraction). Use 100 as the denominator (bottom number of a fraction). Reduce the fraction to its lowest terms. Example: To change 75% to a fraction, apply the steps. 75%= 7510075100 which equals 3434 Percentage to Decimal Number Substitute a decimal point for the percent sign. Divide the number by 100. (In other words, move the decimal point two places to the left.) Example: To change 75% to a decimal number, apply the steps. 75% = 0.75

Celsius and Fahrenheit Conversions

The Celsius (centigrade) scale is the metric form of temperature measurement. Although this scale is increasingly being adopted, most patients in the United States know and use the Fahrenheit scale. A universal temperature scale has not been agreed upon yet. The nurse needs to: Know the difference between the Celsius and Fahrenheit scales. Be prepared to teach patients and families how to convert readings from one scale to the other, if needed. Always identify the scale being used by placing an "F" (Fahrenheit) or a "C" (Celsius) after the reading. On the Fahrenheit scale, the freezing point of water is 32˚ F and the boiling point is 212˚ F. On the Celsius scale, the freezing point of water is 0˚ C and the boiling point is 100˚ C. Conversions from Celsius to Fahrenheit measurements rely on two factors: The 32-degree difference between the freezing points on the Celsius and Fahrenheit scales The 180-degree difference between the boiling point and freezing point on the Fahrenheit scale versus the 100-degree difference on the Celsius scale The difference between the scales' freezing and boiling points forms a ratio of 180:100. This difference can be expressed as the fraction 9/5 or the decimal number 1.8. This number is the basis of the conversion formula and reflects the fact that each degree Celsius is 1.8 times greater than each degree Fahrenheit.

Decimal numbers

The Joint Commission prohibits the writing of a decimal fraction that: Is less than 1 without a leading zero preceding the decimal point. Includes a trailing zero after the decimal point. Examples of correct and incorrect use of zeros include: [image] The tabs provide details about leading and trailing zeros.

Using Roman Numerals

The Roman numeral system uses letters to designate amounts. Roman numerals commonly identify: Controlled substances, which can lead to abuse or dependence (These medications are labeled by the Drug Enforcement Agency (DEA) as Schedule I through V and are indicated on the label with the Roman numeral within a large C.) Clotting factors in blood, such as factor I (fibrinogen) and factor III (thromboplastin) Time, as on watches and clocks Football games (Super Bowl XXVII), movies (Godfather II), or cars (Mach V) Common Roman numerals used in the Roman numeral system are: I - One V - Five X - Ten L - Fifty C - One hundred D - Five hundred M - One thousand

Converting Among Systems Introduction

The ability to convert accurately among different systems of measurement—metric, household, and apothecary—is a critical nursing skill. Expect to use this skill regularly for tasks involving volume, weight, and length measurements, including: Dosage calculations Medication measurement and administration Assessments, especially related to weight, height, and length Fluid intake and output measurements

Apothecary System

The apothecary system of measurement dates back to the Middle Ages, however, it can be confusing and may increase the risk of medication errors. As a result: The Institute for Safe Medication Practices (ISMP) recommends that all medications be prescribed and calculated with metric measures. The Joint Commission (TJC) recommends not using this system and is likely to include apothecary terms and measures as part of its official Do Not Use list in the future. TJC also recommends using the metric system exclusively for medications. In the United States, all medications are labeled with metric units. However, the nurse may see apothecary system measurements on: Certain medication labels—mostly for older drugs, such as aspirin (Bayer), atropine, nitroglycerin (NitroQuick), and phenobarbital (Luminal). These labels list the apothecary unit grains in parentheses near the metric unit. Household measuring devices for ounces, which originated in the apothecary system. Today, ounces are part of the household system. Do not use the apothecary symbol for ounce (℥). Although apothecary system use is discouraged, you should be familiar with it because it is still used in rare cases. You also must differentiate it from acceptable units of measure because safe medication administration depends on understanding the information on medication labels and prescriptions. Safety Focus!! Do not misread grains (gr) as grams (g). Because their names and abbreviations are similar, they are easily confused. A grain is a unit of measure in the apothecary system; a gram is a unit in the metric system. When a label includes apothecary and metric units, always use the metric unit for dosage calculations. To avoid causing harm, do not use these error-prone abbreviations and symbols, which are part of the apothecary system: gr (grains, a unit of weight), which is easily confused with metric grams (g) m (minim, a unit of volume), which can be mistaken for mL ʒ (dram, a drop), which may be misread as the number 3 ℥ (ounce symbol), which is now considered obsolete ss, (one-half or ½ ), which can be misread as the number 55

Household System

The household system of measurement is used primarily in the home setting. The basic units of measurement are the teaspoon, the tablespoon, and the cup (measuring cup). Household system measurements aren't as accurate as metric system measurements because spoons, cups, glasses, and droppers hold slightly different amounts. For example, the teaspoon a patient uses to measure medication at home may hold 4, 5, or 6 mL. This is why the household system is the least accurate system of measurement. Even so, this system is increasingly used for medication administration because of the trend toward outpatient procedures, early discharge from acute care, and increased use of skilled nursing care in the home setting. Nurses must: Be familiar with household measures because patients commonly use utensils in the home to take prescribed medications. Be able to calculate equivalents for use in the home because patients may not have calibrated medication administration equipment, such as metric-calibrated spoons, droppers, and medication cups. To help ensure the consistency of household system dosages, follow these recommendations: Encourage the patient to use the same teaspoon to measure every dose. That way, the patient will receive the same dose each time. When measuring devices are dispensed with medications, teach patients, family members, and other caregivers to always use the dedicated measuring device.

Metric System Overview

The metric system has three basic units of measurement for volume, weight, and length. Each of these units has a set of related abbreviations: The liter is the basic unit of measurement for volume of a liquid or capacity. Its abbreviation is "L." The gram is the basic unit of measurement for weight. Its abbreviation is "g." The meter is the basic unit of measurement for length. Its abbreviation is "m." Nurses typically use liters and grams to calculate doses. They use meters to measure a patient's height and help assess growth patterns *Do not use the former abbreviation for microgram, which was µg. The Joint Commission has placed µg on its Do Not Use list because this abbreviation is easily confused with the one for milligram (mg) and can lead to serious dosage calculation errors.

Volume, Weight, and Length in the Household and Apothecary Systems

The metric system is the most commonly used system of measurement for medication administration. Some prescriptions, however, are still written in the household and apothecary systems. The nurse must be prepared to use all three systems and to recognize, convert, and calculate medication dosages with them. Keep in mind that: Dosages may be prescribed in one system, but available in a different system. Conversions and calculations can be confusing because the household and apothecary systems use Roman numerals, fractions, and unusual notations. The labels on some older drugs still list an apothecary measurement, but give the metric equivalent—usually in larger print—as the preferred measurement.

Metric, Household, & Apothecary Systems Introduction

The nurse may use three measurement systems—metric, household, and apothecary—when calculating drug dosages. The metric system is a decimal system based on multiples and fractions of 10. It is widely used in the United States, and the Metric Conversion Act of 1975 legislated a move toward the metric system as the standard of measurement. The apothecary system, in contrast, is rarely used in healthcare. No matter which measurement system is used, remember that every system has these key features: Standard or basic units of measurement Principles for converting from one basic unit to another Memorize the basic units of measurement for each measurement system. To calculate medication dosages, you'll use those basic units of measurement, along with the principles of conversion, which are covered in the next module.

Metric and Household Weight Conversions

The nurse must be able to use body weight to calculate medication doses for adults, children, and especially infants and neonates. Because their body systems are immature, infants and neonates require precise dosage calculations to prevent harmful or even fatal errors. To perform household-to-metric weight conversions, remember this conversion factor: 2.2 lb = 1 kg

Overview of Fractions

The nurse needs to know how to handle fractions because they are commonly used in: Calculations of dosages and solutions Medical orders Charting related to patient care A fraction is a way to express one or more parts of a whole. Every fraction is composed of a numerator and a denominator. The numerator is always on the top of the fraction. It represents the number of parts that are present. The denominator is always on the bottom. It represents the total number of parts in the whole. For example, in the fraction 1/6, the whole is divided into six parts (the denominator), and one part (the numerator) is present. The fraction can be read as "one sixth" or as "one of six parts of the whole.

Traditional and 24-Hour Clock Conversions

The outer circle indicates military time on a 24-hour clock, and the inner circle indicates standard time on a 12-hour clock. At work, nurses regularly perform time conversions, especially when documenting patient care. Instead of the traditional 12-hour clock, nurses commonly use the 24-hour clock. Unlike the 12-hour clock, the 24-hour clock: Uses military time (international time) rather than standard time. Does not differentiate between AM (ante meridiem, or before noon) and PM (post meridiem, or after noon). Does not use colons in expressing the time. Never repeats a time in a 24-hour period. Is widely used in various healthcare settings. The 24-hour clock offers two main advantages: The use of military time removes confusion about whether a time is in the morning (AM) or the evening (PM). Military time uses four digits to identify all 24 hours with a unique number, eliminating the need for AM and PM designations. Military time helps prevent errors in documentation and medication administration because no numbers are repeated. Each time occurs only once per day. Military time is easy to use. Simply write the four-digit number without a colon and omit the AM and PM. The first two digits reflect the hour. The last two digits reflect the minutes.

Converting from Larger to Smaller Units

Three methods are available for converting a number from a larger unit of measurement to a smaller one are: Multiply by 10s. Multiply by the metric equivalent. Move the decimal point to the right. Example Convert 3 g to mg. Multiply by 10, three times. 3 g×10×10×10=3,000 mg -- OR -- Multiply by the metric equivalent, 1000. 3 kg × 1000 = 3,000 mg

Example Problems: Adding Fractions

To add fractions with the same denominator, follow these steps: Add the numerators together. Place the numerator sum over the denominator. Reduce this new fraction to its lowest terms. To add fractions with different denominators, follow these steps: Find the lowest common denominator. Convert each fraction to its equivalent fraction, using the lowest common denominator. Add the numerators together. Place the numerator sum over the common denominator. Reduce this new fraction to its lowest terms.

Converting Other Numbers in the Roman System

To convert Roman numerals to Arabic numerals, follow two simple rules: Add the Arabic values of the numerals when the first Roman numeral is higher than the following numerals. Subtract the Arabic values of the numerals when the first Roman numeral is lower than the following numerals. Examples of these conversions are: First Numeral is Higher Example: XIII (or xiii) The X represents the Arabic number 10. The III represents the Arabic number 3. To convert XIII from the Roman system to the Arabic system, add X (10) and III (3) to get the Arabic equivalent (13). First Numeral is Lower Example: IV (or iv) The I represents the Arabic number 1. The V represents the Arabic number 5. To convert IV from the Roman system to the Arabic system, subtract I (1) from V (5) to get the Arabic equivalent (4).

Ounces to Milliliters

To convert a liquid volume measurement from the household system (ounces) to the metric system (milliliters) or vice versa, use this conversion factor: 1 oz = 30 mL To convert ounces to milliliters, multiply the number of ounces by the conversion factor 30. When calculating dosages, remember that liters and quarts can be used interchangeably.

Metric and Household Volume Conversions

To convert a liquid volume measurement from the metric system (liters) to the household system (ounces) or vice versa, use this conversion factor: 1 L = 32 oz Note: When calculating dosages, consider liters and quarts to be interchangeable.

PM Conversions

To convert a standard evening (PM) time to military time: Remove the colon and the PM designation. Add 1200 to the time.

AM Conversions

To convert a standard morning (AM) time to military time: Remove the colon and the AM designation. Add a zero at the beginning, if needed, to create a four-digit number.

Celsius to Fahrenheit

To convert a temperature from Celsius to Fahrenheit: Set up the formula °F = 1.8 × °C + 32 Multiply the Celsius temperature by 1.8. Add 32 to that sum. Round to the nearest tenth, if needed.

Fahrenheit to Celsius

To convert a temperature from Fahrenheit to Celsius: Set up the formula °C = °F − 32 1.8 Subtract 32 from the Fahrenheit temperature. Divide that number by 1.8. Round to the nearest tenth, if needed.

Grains to Milligrams

To convert grains to milligrams, multiply the number of grains by the conversion factor of either 60 or 65.

Kilograms to Pounds

To convert kilograms to pounds, multiply the number of kilograms by the conversion factor 2.2. If needed, round off to the nearest tenth.

Liters to Ounces

To convert liters to ounces, multiply the number of liters by 32. Because liters and quarts are essentially interchangeable, you can convert quarts to ounces the same way. Just multiply the number of quarts by 32.

Milligrams to Grains

To convert milligrams to grains, divide the number of milligrams by the conversion factor 60.

Milliliters to Ounces

To convert milliliters to ounces, divide the number of milliliters by the conversion factor 30.

Ounces to Liters

To convert ounces to liters, divide the number of ounces by 32. You can convert ounces to quarts similarly. Just divide the number of ounces by 32.

Pounds to Kilograms

To convert pounds to kilograms, divide the number of pounds by the conversion factor 2.2. If needed, round off to the nearest tenth.

Example Problem: Dividing Decimal Numbers

To divide decimal numbers, follow these steps: Set up the divisor and dividend in the standard equation. Make the divisor a whole number by moving the decimal point to the right. Move the decimal point in the dividend and quotient to the right the same number of places. Do the division and solve the problem. Round off the answer, as needed. Note: When calculating a dosage, decide how many places to carry the division based on the equipment available and the medication dosage. To ensure accuracy, expect to carry the division to at least two decimal places (to the hundredth place) and then round to the nearest tenth.

Dividing Decimal Numbers

To divide decimal numbers, use the standard equation and keep these three terms in mind: The divisor is the number to divide by. The dividend is the number to be divided. The quotient is the answer (product). If the divisor is a decimal number, follow these steps: Move the decimal point in the divisor to the right to produce a whole number. Move the decimal point in the dividend to the right the same number of places. Move the decimal point in the quotient to the right the same number of places.

Example Problems: Dividing Fractions

To divide fractions, follow these steps: Invert the divisor. In other words, turn the second fraction upside down. Change ÷ to ×. Cancel terms, if possible. Multiply the fractions. Reduce the resulting fraction to its lowest terms, if needed.

Decimal Numbers as Fractions

To express decimal numbers as fractions, use a denominator of 10 (or a multiple of 10, such as 100 or 1000). These examples show decimal numbers expressed as fractions: 0.35 is 35 hundredths ( 35 100 ) 2.75 is 2 and 75 hundredths ( 2 75 100 ) 0.9 is 9 tenths ( 9 10 ) 0.062 is 62 thousandths For accurate dosage calculations, the nurse must recognize the place values (number of positions to the right of the decimal point) in decimal numbers. Remember that the place of the last number after the decimal point indicates the number of parts into which the whole is divided (tenths, hundredths, thousandths, and so on). Examples of place values in decimal numbers are:

Example Problems: Multiplying Decimal Numbers

To multiply decimal numbers, follow the same steps used to multiply numbers without decimal points. But remember that the correct answer depends on the total number of decimal places in the original numbers. This example demonstrate how to multiply decimal numbers.

Example Problems: Multiplying Fractions

To multiply fractions, follow these steps: Cancel terms, if possible. Multiply the numerators. Multiply the denominators. Reduce the resulting fraction to its lowest terms, if needed.

Example Problems: Reducing Fractions

To reduce a fraction to its lowest terms, divide the numerator and denominator by the largest number by which they can both be evenly divided. This example shows how to reduce a fraction step by step.

Example Problems: Subtracting Fractions

To subtract fractions with the same denominator, follow these steps: Subtract the numerators. Place the difference between the numerators over the denominator. Reduce this new fraction to its lowest terms. To subtract fractions with different denominators, follow these steps: Find the lowest common denominator. Convert each fraction to its equivalent fraction, using the lowest common denominator. Subtract the numerators. Place the difference between the numerators over the common denominator. Reduce this new fraction to its lowest terms.

Converting from Smaller to Larger Units

Two methods are available for converting a number from a smaller unit of measurement to a larger one in the metric system: Divide by the metric equivalent. Move the decimal point to the left. Example Convert 1,500 mL to L Divide by the metric equivalent, 1000. 1500 mL ÷ 1000 = 1.5 L

Identifying Types of Fractions

Types of fractions include proper, improper, mixed number, complex, and whole number fractions. Proper The numerator is less than the denominator. The value is always less than 1. Examples include 1 3 , 5 8 , 11 16 Improper The numerator is greater than or equal to the denominator. The value is always greater than or equal to 1. Examples include 4 3, 11 8, 5 5, 15 10 Mixed Number A whole number precedes a fraction. The value is always greater than 1. Examples include 3 1 3, 5 1 2, 7 1 8 Complex The numerator, the denominator, or both are fractions. The value may be less than, greater than, or equal to 1. Examples include 1 3 7 8, 3 5 11 3, 5 8 12 Whole Number A whole number is expressed as a fraction with a denominator of 1. The value is always greater than or equal to 1. Examples include 2 1, 8 1, 15 1,

Household System Equivalents

When you need to convert between household measurements, use a table of equivalents, such as these for volume, weight, and length. Memorize the most common equivalents, which are featured.

Metric-to-Apothecary Conversions for Volume and Weight

Whenever you see a volume or weight measurement in the apothecary system, expect to convert it to the metric system. Many other apothecary systems exist, but we are going to focus only on grains (gr). To convert grains (gr) to mg, use this conversion factor: gr I = 60 mg - 65 mg Right now, these are just math. When we incorporate medication dosing, you will choose the conversion option that gets you closest to a full tablet (or dose) of medication.

Example Problems: Converting from Standard to Military Time

Whether you need to convert a standard morning (AM) or evening (PM) time to military time, begin by removing the colon and the AM or PM designation. Then continue with the conversion.

Decimal Place Values

Whole number values are to the left of the decimal point and decimal number values are to the right of the decimal point. (Drug Calculations Online for Calculation of Drug Dosages, 8th Edition, St. Louis, 2008, Mosby.) The decimal value depends on the number's position to the right of the decimal point. Numbers to the right of the decimal point are fractions of less than 1. They are expressed as tenths, hundredths, thousandths, and so on. Important Note: Many medication errors result from: Decimal point misplacement Incorrect interpretation of a decimal value