Decimals

Decimals

After reviewing this chapter, you should be able to:

1. Read decimals

2. Write decimals

3. Compare the size of decimals

4. Convert fractions to decimals

5. Convert decimals to fractions

6. Add decimals

7. Subtract decimals

8. Multiply decimals

9. Divide decimals

10. Round decimals to the nearest tenth

11. Round decimals to the nearest hundredth

Medication dosages and other measurements in the health care system use metric measures, which are based on the decimal system. An understanding of decimals is crucial to the calculation of dosages. In the administration of medications, nurses calculate dosages that contain decimals (e.g., levothyroxine 0.075 mg).

Decimal points in dosages have been cited as a major source of medication errors. A misunderstanding of the value of a dosage expressed as a decimal or omission of a decimal point can result in a serious medication error. Decimals should be written with great care to prevent misinterpretation. A clear understanding of the importance of decimal points and their value will assist the nurse in the prevention of medication errors.

Example 1:

Digoxin 0.125 mg

Example 2:

A decimal is a fraction that has a denominator that is a multiple of 10. A decimal fraction is written as a decimal by the use of a decimal point (.). The decimal point is used to indicate place value. Some examples are as follows:

Fraction	Decimal Number
310	0.3
18100	0.18
1751000	0.175

The decimal point represents the center. Notice that the numbers written to the right of the decimal point are decimal fractions with a denominator of 10 or a multiple of 10 and represent a value that is less than one (1) or part of one (1). Numbers written to the left of the decimal point are whole numbers, or have a value of one (1) or greater.

The easiest way to understand decimals is to memorize the place values (Box 3-1).

BOX 3-1 Decimal Place Values

The decimal value is determined by its position to the right of the decimal point.
(100,000)	(10,000)	(1000)	(100)	(10)	(1)	Decimal point	(0.1)	(0.01)	(0.001)	(0.0001)	(0.00001)
Hundred-thousands	Ten-thousands	Thousands	Hundreds	Tens	Ones (Units)		Tenths	Hundredths	Thousandths	Ten-thousandths	Hundred-thousandths
6	5	4	3	2	1	.	1	2	3	4	5
Whole Numbers to the Left							Decimal Numbers to the Right

The first place to the right of the decimal is tenths.

The second place to the right of the decimal is hundredths.

The third place to the right of the decimal is thousandths.

The fourth place to the right of the decimal is ten-thousandths.

In the calculation of medication dosages it is necessary to consider only three figures after the decimal point (thousandths) (e.g., 0.375 mg).

When there is no whole number before a decimal point, it is important to place a zero (0) to the left of the decimal point to emphasize that the number is a decimal fraction and has a value less than 1. This will emphasize its value and prevent errors in interpretation and avoid errors in dosage calculation. This has been emphasized by the Institute for Safe Medication Practices (ISMP) and is a requirement of The Joint Commission (TJC). The Joint Commission’s official “Do Not Use” List (2005) prohibits the writing of a decimal fraction that is less than 1 without a leading zero preceding a decimal point.

The source of many medication errors is misplacement of a decimal point or incorrect interpretation of a decimal value.

READING AND WRITING DECIMALS

Once you understand the place value of decimals, reading and writing them are simple.

To read the decimal numbers, read:

1. The whole number,

2. the decimal point as “and,” and

3. the decimal fraction.

Notice that the words for all decimal fractions end in th(s).

Example 1:

The number 0.001 is read as “one thousandth.”

Example 2:

The decimal 4.06 is read as “four and six hundredths.”

Example 3:

The number 0.4 is read as “four tenths.”

When there is only a zero (0) to the left of the decimal, as in Example 3, the zero is not read aloud.

Tips for Clinical Practice

An exception to this is in an emergency situation when a nurse must take a verbal order over the phone from a prescriber. When repeating back an order for a medication involving a decimal, the zero should be read aloud to prevent a medication error.

“Zero point 4” would be the verbal interpretation of Example 3. In addition to repeating the order back, the receiver of the order should write down the complete order or enter it into a computer, then read it back, and receive confirmation of the order from the individual giving the order.

To write a decimal number, write the following:

1. The whole number (If there is no whole number, write zero [0].)

2. The decimal point to indicate the place value of the rightmost number

3. The decimal portion of the number

Example 1:

Written, seven and five tenths = 7.5

Example 2:

Written, one hundred twenty-five thousandths = 0.125

Example 3:

Written, five tenths = 0.5

When writing decimals, placing a zero after the last digit of a decimal fraction does not change its value.

Example:

0.37 mg = 0.370 mg

When writing decimals, unnecessary zeros should not be placed at the end of the number to avoid misinterpretation of a value and the overlooking of a decimal point. This is also a recommendation of the Institute for Safe Medication Practices (ISMP) and is a part of The Joint Commission (TJC) official “Do Not Use” List (2005). TJC forbids the use of trailing zeros for medication orders or other medication-related documentation. Exception: A trailing zero may be used only when required to demonstrate the level of precision of the value being reported, such as for laboratory results, imaging studies that report the size of lesions, or catheter/tube sizes.

Because the last zero does not change the value of the decimal, it is not necessary. The preferred notation, as in the example shown on p. 23, is 0.37 mg, not 0.370 mg, and 30, not 30.0, which could be interpreted as 370 and 300, respectively, if the decimal point is not clear or is missed.

Practice Problems

Write each of the following numbers in word form.

1. 8.35 _______________________

2. 11.001 _______________________

3. 4.57 _______________________

4. 5.0007 _______________________

5. 10.5 _______________________

6. 0.163 _______________________

Write each of the following in decimal form.

7. four tenths _______________________

8. eighty-four and seven hundredths _______________________

9. seven hundredths _______________________

10. two and twenty-three hundredths _______________________

11. five hundredths _______________________

12. nine thousandths _______________________

Answers on p. 602

COMPARING THE VALUE OF DECIMALS

Zeros added before or after the decimal point of a decimal number change its value.

Example 1:

0.375 mg is not equal to 0.0375 mg

Example 2:

2.025 mg is not equal to 20.025 mg

Example 3:

However, .7 = 0.7 and 12.6250 = 12.625; but you should write 0.7 (with a leading zero) and 12.625 (without a trailing zero).

Understanding which decimal is of greater or lesser value is important in the calculation of dosage problems. This helps to prevent errors in dosage and gives the nurse an understanding of the size of a dosage (e.g., 0.5 mg, 0.05 mg). Understanding the value of decimals prevents errors of misinterpretation. There is an appreciable difference between 0.5 mg and 0.05 mg. In fact, 0.5 mg is 10 times larger than 0.05 mg. A misinterpretation of the value of decimals can result in serious consequences in dosage calculations.

When decimal numbers contain whole numbers, the whole numbers are compared to determine which is greater.

Example 1:

4.8 is greater than 2.9

Example 2:

11.5 is greater than 7.5

Example 3:

7.37 is greater than 6.94

If the whole numbers being compared are the same (e.g., 5.6 and 5.2) or if there is no whole number (e.g., 0.45 and 0.37), then the number in the tenths place determines which decimal is greater.

Example 1:

0.45 is greater than 0.37

Example 2:

1.75 is greater than 1.25

If the whole numbers are the same or zero and the numbers in the tenths place are the same, then the decimal with the higher number in the hundredths place has the greater value, and so forth.

Example 1:

0.67 is greater than 0.66

Example 2:

0.17 is greater than 0.14

Example 1:

0.2 is the same as 0.2000, 0.20

Example 2:

4.4 is the same as 4.40, 4.400

Practice Problems

Circle the decimal with the largest value in the following:

13.	0.5	0.15	0.05
14.	2.66	2.36	2.87
15.	0.125	0.375	0.25
16.	0.175	0.1	0.05
17.	7.02	7.15	7.35
18.	0.067	0.087	0.077

Answers on p. 602

ADDING AND SUBTRACTING DECIMALS

To add or subtract decimals, place the numbers in columns so the decimal points are lined up directly under one another and add or subtract from right to left. Zeros may be added at the end of the decimal fraction, making all decimals of equal length, but unnecessary zeros should be eliminated in the final answer.

Eliminate unnecessary zeros in the final answer to avoid confusion and prevent errors of misinterpretation.

Example 1:

Add 16.4 + 21.8 + 13.2

16.421.8+13.251.4=51.4

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Feb 11, 2017 | Posted by admin in PHARMACY | Comments Off

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