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Review of Key Medical Math Fundamentals: Decimals

OBJECTIVES

The student will be able to:

1. accurately communicate decimal numbers in writing and speaking,
2. add and subtract decimals,
3. multiply and divide decimals,
4. apply scientific notation, and
5. round numbers.

Drug dosages, concentrations of drugs in vials, and drug units are commonly expressed as decimal numbers. Therefore, it is imperative that the veterinary professional be able to accurately add, subtract, multiply, and divide using decimal numbers. It is assumed the reader has a working knowledge of using decimals; therefore, this chapter will focus on a quick review with an emphasis on where common dosage calculation errors occur.

2.1 Relative Values of Decimal Numbers

The decimal point, or "point," orients the reader to the values of the decimal number. Each space to the left of the decimal point increases by a power of 10. Therefore, the first space to the left of the decimal point is "ones," the next space to the left is "tens," the next is "hundreds," and so on.

Each space to the right of the decimal point decreases by a power of 10 starting with "tenths." The second space to the right of the decimal point is the "hundredths," the next is "thousandths," and so on. Note that there are no "oneths" to the right of the decimal point and the first place to the right starts with "tenths." The numerals to the left of the decimal point are whole numbers (5, 62, 379) and the numerals to the right of the decimal point represent decimal fractions (e.g. one tenth, four hundredths).

Notice how all decimal fractions end in "th(s)," such as "four tenths" or "one thousandth." Thus, the number 12.35 would contain the whole number "12" and the decimal fraction of "thirty-five hundredths."

The number shown in Figure 2.1 is 7842.125 and illustrates each of the places in the number.

Figure 2.1 The location of whole numbers and decimal fractions in a decimal number

2.2 Properly Communicating Decimal Numbers

When reading a decimal number aloud, there are two ways to communicate the number. The number in Figure 2.1 can be read as either "seven thousand, eight hundred forty-two and one hundred twenty-five thousandths" or as "seven eight four two point one two five."

The first method is more formal and uses the word "and" to represent the decimal point. All units to the right of the decimal point are read as units of the farthest right place. Therefore, in the number above, there are "125 thousandths." For the number "1.12," the value to the right of the decimal point would be read aloud as "twelve hundredths" because the farthest right place that has a number is the hundredths place. When the value of a decimal number is less than 1, such as 0.5, the number would be read only as "five tenths" without stating the zero in the ones place.

The second method for communicating decimal numbers tends to convey the information in a shorter and more concise manner. The numbers are read left to right with the decimal point being spoken as "point." No place values (hundreds, tenths, thousandths, etc.) are stated in this method. Therefore, "234.56" would simply be read aloud as "two three four point five six." In contrast to the first method above, where the zero is not read for numbers with a value less than 1, in this second method the zero is communicated along with the "point." Thus 0.5 would be read as "zero point five." There are additional examples in Table 2.1.

Table 2.1 The correct way to read decimal numbers

Regardless of which method is used when a number is verbally communicated, it is essential that the number be communicated accurately. This can be a challenge when numbers are being communicated while masked for surgery or other procedures because the voice becomes muffled. It also becomes a challenge when communicating numbers by phone, particularly as cell phone reception can garble clear communication. In addition to the physical challenges with communicating numbers, some numbers sounds very similar to others, and the veterinary technician needs to be especially precise in communicating these numbers. It is a good practice to repeat any number that may be confusing, or to emphasize a key feature of the number, such as "One five POINT three," to make sure the recipient correctly receives the number. If there is ever a question about what number was stated by another staff member or the veterinarian, the veterinary technician is ethically and morally obligated to ask that the number be repeated. Reluctance to ask because of perceived irritation or frustration of the person stating the number is absolutely no reason not to be crystal clear on what number was being communicated. The veterinary technician is the advocate for the patient, and therefore it is essential all numeric communications be accurately communicated 100% of the time.

Commonly miscommunicated numbers

There are several numbers that, when read, sound very similar. It is important that the veterinary professional clearly enunciate these to prevent accidental miscommunication of a spoken value. It is also important that, if any question arises of what value is being communicated, the receiver of the spoken value ask for the value to be repeated. A patient's life could hang in the balance.

• Thirteen sounds like thirty.
• Fourteen sounds like forty.
• Fifteen sounds like fifty.
• Sixteen sounds like sixty.
• Seventeen sounds like seventy.
• Eighteen sounds like eighty.
• Nineteen sounds like ninety.

While all of the decimal fractions sound like their counterpart in the whole numbers (e.g. "tenth" and "ten," "hundredth" and "hundred"), generally, the context in which the number is spoken prevents it from being confused (e.g. "three hundred and twenty-three hundredths" for the number 300.23). If there is any doubt, however, the number needs to be repeated to confirm all parties understand the actual number communicated.

2.3 The Rules for the Use of Zero in Decimal Numbers

Rule 1: Whole numbers (e.g. 2, 45, 789) have implied decimal points and trailing zeroes to the right of the decimal point that are usually not written or spoken. "25" and "25.00" both represent the same value of 25 and therefore would be communicated as "twenty-five" unless greater precision is required. For example, a patient's blood chemistry value may always be printed out or displayed on the laboratory equipment with a number in the 1/10ths slot. In those situations, "25.0" would be communicated as "twenty-five point zero" or "two five point zero" to emphasize that there is no other number in the 1/10ths slot. Another example may be that a dose of a toxic drug is required to be calculated to the nearest 1/10th. In that situation the digit in the 1/10th slot would always be written or communicated, even if the digit was zero.

Another reason for leaving off the trailing zeros is because the decimal point could potentially be mistaken as a comma. For example, at quick glance, the numbers "25.000" and "25,000" look very similar, especially if the numbers are handwritten by a doctor or a veterinary technician in a hurry. A mistake made by not correctly interpreting the comma or decimal point can result in a dose miscalculation of a thousand times more than what was intended! To avoid this problem with handwritten numbers, commas should not to be used in written calculations.

In our global economy it is important to remember that a comma is used in place of the decimal point in many non-English speaking countries in continental Europe and Latin America (except Mexico) and also in South Africa. In these countries the decimal point is used like the comma to separate the digits in large numbers and the comma is used to separate the ones from the 1/10ths in the number. Thus, one may see "2.64?mg" written as "2,64?mg" in France, Germany, Austria, and many other countries around the world. The period as the decimal separator is used predominantly in North America (with the exception of French-speaking Canada) and in the UK, Australia, and other countries where English is commonly used in business or medical...