Read	Write	Example
<	Less than	The baby weighs < 5 pounds.
>	Greater than	The total cholesterol was high (> 200).
≥	Greater than or equal to	Give the medications if the systolic blood pressure ≥ 160.
≤	Less than or equal to	Hold the medication if his temperature is ≤ 100.
√	Square root	√16 means the square root of 16.

CLINICAL RELEVANCE

Keep in mind the potential effect on a patient receiving a medication that was supposed to be withheld for a pulse <50 because the nurse misinterpreted that symbol as “greater than.” If this results in a patient medication error, remember that ignorance is not a defense.

Mnemonic

Note the “L” in less than and left.

The smaller end of the arrow always points to the smaller number:

5 is> 3 but 5 is < 10

The larger open end of the arrow always faces the larger number.

FAQ

Are these symbols really seen much in medicine and nursing?

ANSWER

Yes. These symbols are frequently seen in printed materials, such as drug and laboratory literature, medication references and medication orders. Misinterpretation has led to medication errors.

Be able to read and interpret them. Do not write them. Write out the meaning. Refer to pp. 101-103 for The Joint Commission and Institute for Safe Medication Practices recommendations for writing out certain abbreviations that are frequently misinterpreted.

RAPID PRACTICE 1-1 Interpreting Symbols

Estimated completion time: 5 minutes Answers on page 481

Directions: Circle the correct definition for the symbols.

TEST TIP:

Keep the initial statement (stem) of the multiple-choice test questions in mind, and as you read each choice, say to yourself, “True or false.”

Put a mark to the right of the incorrect responses as you go through them. Marks on the right are suggested because if the answers are entered on a computer response sheet, any stray marks on the left or within the choices may cause the scanner to read them as a desired response. Eliminating wrong answer choices speeds a second review of the material if time is available.

1. A blood pressure goal for healthy adults is ≤120/80.

1. less than

2. greater than

3. less than or equal to

4. greater than or equal to

2. If the pulse is <50, notify the physician.

1. less than

2. greater than

3. less than or equal to

4. greater than or equal to

3. When a blood pressure is ≥120/80 in an otherwise healthy adult, lifestyle changes need to be instituted.

1. less than

2. greater than

3. less than or equal to

4. greater than or equal to

4. According to the Centers for Disease Control and Prevention (CDC), one of the characteristics of SARS disease is a temperature >100.4°F (38°C).

1. less than

2. greater than

3. less than or equal to

4. greater than or equal to

5. Identify the symbol used for square root.

The square root symbol does not appear in handwritten medical records. It appears in dosage formulas for body surface area.

RAPID PRACTICE 1-2 Writing Math Symbols

Estimated completion time: 5 minutes Answers on page 482

Directions: Write in the appropriate symbol in the space provided.

TEST TIP:

Writing a response is another way to reinforce memory and learning for visual and kinesthetic learners. It is emphasized that the nurse will write out the definition for the symbols in the nursing notations on the medical record to avoid misinterpretation.

1. Inject the medicine in the baby’s thigh if he has walked ______ a year. (less than)

2. Give the patient 1 teaspoon of medicine if his age is _______ 5 years. (less than or equal to)

3. The risk of cancer from smoking is greatly accelerated when the patient has a history of smoking ______ 20 years. (greater than or equal to)

4. If the systolic blood pressure is _______ 180, notify the physician. (greater than)

5. The _________ symbol is used in medication math to determine body surface area for safe dosages for very powerful medicines. (square root)

Whole Numbers

A whole number is a number that is evenly divisible by the number 1.

Multiplying and dividing whole numbers by the number 1

Working with whole numbers is easier than working with fractions and decimals.

Remember that a number divided by or multiplied by 1 will not change in value.

To write a whole number as a fraction, write the whole number as a numerator with the number 1 as the denominator.

The numerator (N), the number above the dividing line, indicates the number of parts out of a total number of equal parts, the denominator (D), designated below the dividing line.

EXAMPLES

Division by 1:

5001NumeratorDenominator=50030=301ND=30101ND=10

Implied Decimal Points and Trailing Zeros

A whole number has an implied decimal point immediately following the whole number (e.g., 1. and 20.).

Do write 1 and 20; do not write 1. and 20.

Implied decimal points, if written, can be misread as commas, zeros, or the number one.

Zeros that follow the last number after a decimal point are called trailing zeros. Do write 1.3; do not write 1.30. Trailing zeros are only appropriate for printed laboratory reports and statistical reports.

Avoid writing implied decimal points and trailing zeros.

EXAMPLES

Do not remove zeros that occur within a number. The number 3.08 would be read as 3.8 if this error was made, resulting in a tentimes error.

Do not remove zeros that occur before a decimal point. They alert the reader to a decimal that follows the zero immediately:

0.040.40.004

Always place a zero in front of a decimal point that is not preceded by a whole number.

Always eliminate implied decimal points and trailing zeros that follow a whole number. Implied decimal points and trailing zeros do not change the value, but they do lead to reading errors and medication dosage errors.

Dividing a number or fraction by itself

A number or fraction divided by itself equals 1.

A number or fraction divided by 1 equals itself.

EXAMPLES

RAPID PRACTICE 1-3 Whole Numbers

Estimated completion time: 5 minutes Answers on page 482

Directions: Circle the correct equivalent for the whole number supplied.

1. Identify the correct location of an implied decimal point for the whole number 10. _______

2. Identify the correct editing of decimals and trailing zeros for the number 350.000. _______

3. When a whole number such as 30 is divided by itself, the numerical result is _______

1. 1

2. 3

3. 30

4. 900

4. Which fraction retains the value of the whole number 30? _______

5. What is the numerical value of 50 multiplied or divided by 1? _______

1. 1

2. 5

3. 10

4. 50

RAPID PRACTICE 1-4 Whole Numbers

Estimated completion time: 5 minutes Answers on page 482

Directions: Fill in the answers pertaining to whole numbers in the space provided.

1. Write the whole number 100 as a fraction without changing the value of the whole number. _______

2. Write the whole number 100 with a decimal point in the implied decimal place. _______

3. Edit the number 125.50 to eliminate any trailing zeros. _______

4. Why is it necessary to remove decimals and trailing zeros after whole numbers? _______

5. Write a fraction that equals 1 with 100 in the numerator. _______

Sum

A sum is the result of addition.

EXAMPLES

The sum of 3 and 6 is 9.

The sum of 2 and 2 is 4.

Product

A product is the result of multiplication of numbers, decimals, fractions, and other numerical values.

EXAMPLES

Factor

A factor is any whole number that can divide another number evenly without a remainder. For example, in addition to 1 and 18, the numbers 2, 3, 6, and 9 are factors of 18. Seventeen only has factors of 1 and 17. No other whole numbers divide 17.

EXAMPLES

3 has factors of 1 and 3.

25 has factors of 1, 5, and 25.

60 has factors of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

A factor can only be less than or equal to a given whole number. One and the number itself are always factors. “Factoring” the number 9 gives you 1, 3, 9.

Factor also has other meanings. It also can be used as a general term to describe relevant data. For example, “He examined all the factors in the case” or “A dimensional analysis equation permits all the factors to be entered in one equation.”

Common Factors

A common factor is a whole number that divides every number in a pair or group of numbers evenly. The number 1 is always a common factor of whole numbers.

Common factors other than 1

EXAMPLES

5 and 10 have the common factor: 5. (It helps to see first whether the smaller or smallest number divides the other number or numbers evenly.)

4 and 16 have common factors of 4 and 2. (8 is not a common factor because the fraction ½ will be the result of dividing 8 into 4 and the factor must be a whole number.)

12 and 8 have common factors of 2 and 4.

A common factor can never be greater than the smallest number in the group. First, try to divide the numbers in the group by the smallest number. If that does not work, try to divide them by 2, 3, and so on.

Mnemonic

Multiply factors to arrive at a multiple (MM).

A multiple must be greater than or equal to the given numbers.

A multiple is a product, but it is a specific kind of product.

Multiple

A multiple is the product of a whole number multiplied by two or more factors (whole numbers).

EXAMPLES

Five multiples of the number 5 are 5 (5 × 1), 10 (5 × 2), 15 (5 × 3), 20 (5 × 4), and 25 (5 × 5).

50 is a multiple of factors 10 and 5, 25 and 2, and 50 and 1.

Factors Versus Multiples

EXAMPLES

5 has factors of 1 and 5. 5 has multiples of 5, 10, 15, …

8 has factors of 1, 2, 4, and 8. 8 has multiples of 8, 16, 24, …

Multiplier

A multiplier is the number used to multiply; it immediately follows the times sign.

EXAMPLES

A multiplier does not need to be a whole number.

RAPID PRACTICE 1-5 Multiplication Terms

Estimated completion time: 10 minutes Answers on page 482

Directions: Multiply or factor the numbers as requested.

1. Write the product of 10 and 4. _______

2. Write four factors of the number 12 (excluding 1 and 12). _______

3. Write the two common factors of 8 and 12 (excluding 1). _______

4. Write the product of 3 and 4. _______

5. Write the first three multiples of the number 5. _______

Divisor, Dividend, Quotient, and Remainder

A divisor is the opposite of a multiplier. It is the number used to divide another number into smaller parts.

A dividend is the number being divided up, or the number the divisor is dividing.

A quotient is the result of division, or the answer.

The remainder is the amount left over in the answer when a divisor does not divide a dividend evenly.

EXAMPLES

RAPID PRACTICE 1-6 Division Terms

Estimated completion time: 5 minutes Answers on page 482

Directions: Identify the division terms requested:

1. Circle the divisor: 20 ÷ 5 = 4.

2. Circle the quotient: 10040 = 2.5

3. Circle the dividend: 502000

4. Circle the divisor: 50050 = 10.

5. Circle the remainder.456=712

Square

The square is the product of a number multiplied by itself one time.

2×2=22=44×4=42=1610×10=102=100

Squares can also can be written and spoken as follows:

“4 squared (4²) = 16; 16 is the square of 4.”

“10 squared (10²) = 100; 100 is the square of 10.”

Think of the dimensions of a square box. To be a square, the sides must all be of equal size.

FAQ

When are squares used in medication administration?

ANSWER

Squares are used to denote square meters of body surface area (BSA). The most appropriate dosage for powerful drugs for pediatric and patients with cancer may be determined by milligrams per square meter (m²) of body surface area rather than by weight. Nurses encounter the symbol when investigating the safe dosage ranges in a pharmacology reference. The symbol may also be on a record sent from the agency pharmacy on the patient’s medical chart.

Large medication errors may occur if the nurse does not understand the difference between m² and milligram (mg).

Square Root

The square root is the (root) number used to arrive at a square when multiplied by itself. It is the inverse of a square.

EXAMPLES

2 is the square root of 4.

10 is the square root of 100.

The square root symbol (√) is used to reduce writing and increase comprehension:

4=2,9=3,100=10

To obtain a square root on a calculator, enter the number followed by the square root symbol.

RAPID PRACTICE 1-7 More Multiplication Terms

Estimated completion time: 5 minutes Answers on page 482

Directions: Select the number of the correct answer. Narrow your choices by eliminating the obviously wrong answers with a lightly penciled mark on the right of the paper.

TEST TIP:

Create a different type of penciled reminder if you wish a reminder to revisit a question or response.

1. Which is a common factor of the numbers 8 and 10? ______

1. ⅘

2. 2

3. 5

4. 80

2. Which is a multiple of 36? ______

1. 6

2. 12

3. 18

4. 72

3. What is the square of 4? ______

1. 2

2. 4

3. 8

4. 16

4. Which is the multiplier of 8 ×¼? ______

1. ¼

2. 2

3. 8

4. 32

5. What is the square root of 25? ______

1. 2

2. 4

3. 5

4. 625

RAPID PRACTICE 1-8 Multiplication, Squares, and Division

Estimated completion time: 5 minutes Answers on page 482

Directions: Fill in the answers to the multiplication and division problems in the space provided.

1. Write the product of 3 × 4. _____________

2. Write the square of 7 (7²)._________________

3. Write the divisor of 10 ÷ ½.__________________

4. Identify the dividend in 100 divided by 10.__________

5. Write the product of 3 and 5. ____________

Bases and Exponents

Bases and exponents are numbers written with two parts:

Mnemonic

The base is a bigger size. The exponent is tiny but it is very powerful. It indicates repeated multiplication.

The base is the number that must be multiplied by itself. The exponent, also known as power, is the small superscript number that indicates how many times the base must be multiplied by itself. Some examples were given in the section on squares. The expression 2³ is a type of shorthand for 2 × 2 × 2. Writing powers saves a lot of math time.

EXAMPLES

Multiply the base the specified number of times by itself.

Read and/or say 2³ as, “2 to the third power” or, alternatively, “the third power of 2.”

Note: The exponent is accompanied by the word “power”.

Read or say

You would say or read 2³ as, “2 to the third power” or, alternatively, “the third power of 2.” The exponent is read as “power.”

Powers of 10 Calculations

When working with powers of 10, such as 10², 10³, 10⁴, and so on, note the number of zeros in the answers.

EXAMPLES

102=10×10=100103=10×10×10=1000104=10×10×10×10×10=10,000

The number of zeros in the result is equal to the number in the exponent.

FAQ

How are powers and exponents used in medication administration?

ANSWER

Using powers of 10 and exponents makes it much easier to understand decimals and metric system conversions. The metric system is a decimal system based on powers of 10. Most medications are delivered in milligrams and grams, which are converted using powers of 10. The nurse who understands these conversions will be less likely to make medication errors. It only takes a few minutes to comprehend powers and exponents of 10.

RAPID PRACTICE 1-9 Powers

Estimated completion time: 5-10 minutes Answers on page 482

Directions: Use your understanding of powers and exponents to answer the following questions:

1. Write 10² out in the sequence to illustrate the process you would use to arrive at the answer. _____________

2. Write 2⁵ out in the sequence to illustrate the process you would use to arrive at the answer. _____________

3. Write in numerical shorthand: 10 to the eighth power. _____________

4. Which number is the base in 10⁴? _____________

5. Which number is the exponent in 10⁴? _____________

Multiplying and Dividing by 10, 100, and 1000

Dividing and multiplying by a multiple of 10—such as 10, 100, and 1000—involves moving the decimal place to the left or right by a number of places that is equal to the number of zeros in the divisor or multiplier: 10, 100 or 1000, and so on. These three numbers are the most frequently used numbers in metric medication calculations. They are powers of 10: 10¹, 10², and 10³.

• To divide, examine the divisor—10, 100, or 1000—for the number of zeros. In the dividend, move the decimal point (real or implied) to the left by a number of places that is equal to the number of zeros:

1000÷10=100

• To multiply, examine the multiplier—10, 100, or 1000—for the number of zeros. In the number being multiplied, move the decimal point to the right by a number of places that is equal to the number of zeros:

Verify your answer.

EXAMPLES

Whole		Whole
Number × Multiplier = Answer		Number ÷ Divisor = Answer
50 × 10	= 500	500 ÷ 10	= 50.0 = 50
400 × 100	= 40,000	40 ÷ 100	=. 40 =0.4
10 × 1000	= 10,000	4 ÷ 1000	=. 004 = 0.004

Whenever there are more than four numbers in a group, insert a comma in front of every three digits from right to left to ease the reading: e.g., 1000000 becomes 1,000,000 (1 million), and 20000 becomes 20,000 (20 thousand).

Insert zeros in front of decimals, and avoid trailing zeros after whole numbers.

RAPID PRACTICE 1-10 Multiplying and Dividing by 10, 100, and 100

Estimated completion time: 5-10 minutes Answers on page 483

Directions: Select the correct notation for multiplication and division using mental arithmetic and moving decimal places. Narrow the field of choices by quickly eliminating the obviously wrong answers.

TEST TIP:

Since only the multiplier or divisor determines the number of places to move the decimal point, first identify the multiplier or divisor and the number of zeros in it. Then move the decimal point to the left or the right.

1. 30 multiplied by 100 = ______.

2. 0.4 multiplied by 1000 = ______.

1. 0.004

2. 4

3. 400

4. 4000

3. 5000 divided by 100 = ______.

1. 5

2. 50

3. 100

4. 500

4. 250 divided by 1000 = ______.

5. 1500 divided by 100 = ______.

RAPID PRACTICE 1-11 Multiplying and Dividing by 10, 100, and 1000

Estimated completion time: 10 minutes Answers on page 483

Directions: Fill in the answer in the table by moving decimal points to the left for division and to the right for multiplication.

Decimal Fractions

A decimal fraction is any fraction with a denominator that is a power of 10. It is easier to read and write decimal fractions in abbreviated form with a decimal point to replace the denominator, for example, 0.1 for 110 and 0.06 for 6100. In this abbreviated form, these decimal fractions are called decimals. Our money system is based on decimals.

EXAMPLES

Decimals replace the division bar and the denominator of a fraction with a decimal point in the specified place that identifies power of 10 in the denominator. Zeros are used to hold the place values.

FAQ

How does the denominator of a decimal fraction differ from the denominators of other fractions?

ANSWER

The decimal fraction has a denominator that is a power of 10. Other fractions, such as ⅔, ⅚, and ⅕, do not have a power of 10 in the denominator.

Fractions with denominators other than powers of 10 are covered in more detail on p. 23.

Like other fractions, decimal fractions—or decimals—are numbers that indicate less than a whole unit.

Observe the number line below, which represents numbers as points on a line. The numbers to the left of the decimal point are whole numbers. The numbers to the right of the decimal point are decimal fractions.

Read the number to the right of the decimal point as the numerator.

The number of places to the right of the decimal point determines the power of 10 in the denominator. One place denotes tenths, two places denote hundredths, three places denote thousandths, and so on.

EXAMPLES

1 Decimal Place	2 Decimal Places	3 Decimal Places	4 Decimal Places
0.5	0.12	0.375	0.0005
5 tenths	12 hundredths	375 thousandths	5 ten-thousandths

A leading zero should always precede a decimal expression of less than 1 to alert the reader to the decimal.

Reading Numbers and Decimals

Decimals are read as fractions. Decimal points separate whole numbers from fractional parts of a number. The fractional part follows to the immediate right of the decimal point.

Read the number or numbers that appear to the left of the decimal point out loud.

Read the decimal point as “and” or “point.”

Read the decimal in fraction form.

EXAMPLES

Written	Read and Spoken as a Fraction
0.5	“five tenths”
1.5	“one and 5 tenths” “or one point 5”
1.06	“one and 6 hundredths” or “one point zero 6”
42.005	“42 and 5 thousandths”
2.0008	“2 and 8 ten-thousandths” or “2 point zero, zero, zero, 8”