Review of Mathematics (Pharmacology and Administration of Medications) (Nursing) Part 3

Decimal Fractions

Decimal fractions are fractions in which 10 is always the denominator. The 10 is sometimes omitted when fractions are written, and a decimal point is inserted in the numerator as many places from the right as there are ciphers (zeros) of 10 in the denominator. Therefore, 1/10 = 0.1 and 1/100 = 0.01.

A fraction like 3/4 can also be written as a decimal by converting it to tenths, or in this case, hundredths: 4 goes into 100 25 times and 25 X 3 is 75. Therefore, 3/4 = 75/100ths or 0.75.

Nursing Alert When writing decimals in nursing, follow these rules:

•    Do not use a "trailing zero" after a decimal point (when dosage is expressed as a whole number). For example, if the dosage is 2 mg, do not insert the decimal point or the trailing zero. This is confusing and could be mistaken for "20" if the decimal point is not seen.

•    Do not leave a "naked" decimal point. For example, if the dosage is 2/10 of a milligram, it should be written as 0.2 mg. In other words, if a number begins with a decimal, it should be written with a zero and a decimal point in front of it. If it is not written that way it could be mistaken for 2, instead of 2/10.

The Formula Method

When the prescribed or desired dosage is different from what is available or “what is on hand,” a dosage calculation is necessary to determine the quantity of drug to give. Use ratio and proportion to solve dosage calculations. Because the calculations are in fractions, follow the rules for working with fractions (see the section on fractions in this topic).

The formula method can be used when calculating dosages in the same system and the same units of measurement. The following formula can be used to calculate the amount of medication needed

1. EXAMPLE: The prescribed dose is 1¼ mg clonazepam (Klonopin), and the medication is supplied as /2 mg tablets. Known factors:

•    Desired amount: 1/4 mg (or 5/4)

•    Available dosage:    mg

•    In what Quantity: 1 tablet

Set up the problem:

Use the rules for calculating fractions:

1. Write the problem.

2. Invert the divisor.

3. Multiply the numerators and denominators.

4. Reduce the fraction to its lowest terms.

The nurse would give 2½ tablets. Because the tablets are scored, the nurse can give medications in ^ tablet increments. (Remember, some tablets cannot safely be split.)

2. EXAMPLE:

Nitroglycerin is ordered for a client. The prescribed dose is 6/10 mg. The medication is supplied as 3/10 mg sublingual tablets. (Remember, 6/10 means 6 parts out of 10 and 3/10 means 3 parts out of 10.)

Known factors:

•    Desired amount: 6/10 mg

•    Available dosage: 3/10 mg

•    In what Quantity: 1 tablet

Set up the problem.

Use the rules for calculating fractions:

1. Write the problem.

2. Invert the divisor.

3. Multiply the numerators and the denominators.

4. Reduce the fraction to its lowest terms.

The nurse would give 2 tablets.

* Key Concept In a fraction, a larger denominator denotes that the item is divided into more pieces. Therefore, 1/10 is half as much as 1/5.

Significant Figures

The term significant figure refers to numbers that have practical meaning or dosages that can be measured. For example, a dosage prescribed is 1.325 mL. When measured with a syringe that has markings of 1.3 mL, 1.4 mL, and 1.5 mL, the last two numbers (the “25”) cannot be measured. Therefore, the amount given is 1.3 mL, because this amount is closer to the prescribed dosage than it is to 1.4 mL. (The dosage that can be measured, 1.3 mL, is the significant figure.) When rounding, the dosage is rounded to the closest amount. Therefore, using the example, values ranging from 1.301 to 1.349 are rounded down to 1.3, and values from 1.350 to 1.399 are rounded up to 1.4.

Key Concept In some cases, a liquid medication is ordered in a dose that is too small to be measured accurately in a medication cup. In this situation, a syringe can be used to draw up the correct amount of medication, and then the medication can be transferred to a medication cup for administration.

Percentages

The term percentage refers to the number per hundred. Therefore, 20% equals 20 per hundred. Percent has no specific units of measure. It is actually a ratio. To convert from percentage to a fraction, the percent number becomes the numerator, and 100 is always the denominator. Example:

20% = 20/100

Fraction to Percent

To convert a fraction to a percent, multiply both the numerator and the denominator by the number required for the denominator to equal 100. The numerator becomes the percentage.

Alternatively, looking at the original equation, 20 goes into 100 5 times.

9 X 5 = 45 Another way to look at it is: 9/20 = 4.5/10

4.5/10 X 10 = 45/100 or 0.45 or 45%.

Percent to Fraction

You can also determine the percentage designated by any fraction by dividing the numerator by the denominator.

Key Concept Use reference topics or tables for any questions about dosage conversions. It is a good idea to have another nurse double-check all calculations of medication dosages. You can also find dosage calculation quizzes on the Foil%

KEY POINTS

•    The metric system is the most commonly used measurement system in the world; it is used for most measurements and dosages in medicine.

•    The nurse must understand how to convert between systems of measurement in the event that a drug order is stated in a different unit of measurement than what is available for administration.

•    Many symbols and abbreviations are used in medication orders.

•    Some abbreviations and symbols are too similar to be used safely (and are not recommended).

•    The nurse must be proficient in the use of ratios, proportions, and fractions.

•    It is vital to ask if any questions arise about a medication or a dosage. A pharmacist is an excellent resource.

•    Weights may be converted to pounds and ounces for the client’s benefit, but are usually recorded in grams and kilograms in the medical record.