Relative Value, Addition, and Subtraction of Decimals Flashcards

Healthcare professionals utilize decimal fraction dosages on a daily basis.
A helpful hint for conceptualizing decimals is to consider the United States (U.S.) monetary system of dollars and cents.

The place value system is organized around the decimal point, with specific names for positions to the left (whole numbers) and the right (fractions).
Whole Number Positions (Left of Decimal):
- Ones or units
- Tens
- Hundreds
- Thousands
- Ten-thousands
- Hundred-thousands
- Millions
Decimal Side Positions (Right of Decimal):
- The decimal point separates the whole number from the fractional part.
- Tenths
- Hundredths
- Thousandths
- Note that numbers following the decimal point end in the suffix "-th."
Numerical Representation:
- $0,000,000.000$

In clinical practice, drug dosages measured as decimal fractions typically do not contain more than three digits after the decimal point.
Practitioners should generally consider only three decimal places (tenths, hundredths, and thousandths).
An example of a standard dosage format is $0.025$ .

The relative value is first determined by the whole number, which is located to the left of the decimal point.
The greater the whole number, the greater the overall value.
For example, $5.078$ is greater than $4.997$ because 5 > 4.
In a comparison of $3.3$ , $2.7$ , and $4.5$ , the value $4.5$ is the greatest.

The fraction determines the relative value if the whole numbers are equal or if there are no whole numbers present.
Tenths Comparison: The fraction with a greater number in the tenths place (the first digit after the decimal) has a greater value.
- In a comparison of $0.178$ , $0.521$ , and $0.276$ , the value $0.521$ is the greatest because $5$ is the largest digit in the tenths place.
Hundredths Comparison: When the digits in the tenths place are identical, the fraction with the greater number in the hundredths place has the larger value.
- Example: Comparing $0.23$ and $0.28$ , the value $0.28$ is larger because 8 > 3.
- Example: Comparing $2.25$ , $2.22$ , and $2.28$ , the value $2.28$ is the greatest.
Standardizing Decimal Length: To compare decimals of different lengths, zeros can be added to the end to make them equal in length.
- Example: When comparing $0.4$ and $0.36$ , convert $0.4$ to $0.40$ . It becomes clear that $0.4$ ( $0.40$ ) is larger than $0.36$ .

If a decimal fraction is not preceded by a whole number, a leading zero must be used in front of the decimal point.
Importance of Leading Zeros:
- Emphasizes that the number is a fraction.
- Prevents the decimal point from being overlooked, which could lead to a massive dosing error.

For safety reasons, it is important to develop the habit of eliminating trailing zeros.
Examples of Elimination:
- $0.012000$ should be written as $0.012$
- $4.200$ should be written as $4.2$

Calculator Use: Calculators should be used for most addition and subtraction of decimal fractions. Proficiency with the device is required for accuracy.
Manual Procedure:
1. Line up the decimal points vertically when writing down the numbers.
2. Add or subtract from left to right (after standard vertical alignment).
3. Add placeholder zeros at the end of the numbers to make them an equal length.
Alignment Examples:
- Addition: To add $0.7$ to a thousandths-level decimal, rewrite $0.7$ as $0.700$ .
- Subtraction: To subtract from a value like $0.07$ , rewrite it as $0.070$ to match the length of other three-digit decimal fractions.

Prescription: $0.125\,mg$ tablet
On-Hand: $0.25\,mg$ tablets
Administration: Because $0.25$ ( $0.250$ ) is greater than $0.125$ , the nurse should administer less than 1 tablet.

Consistent practice with decimal calculations leads to:
- Increased proficiency and accuracy.
- Decreased risk of medication errors.
- An increased comfort level with clinical calculations.