Decimals¶
What Are Decimals?¶
Decimals are another way to express fractions using place value. The decimal point separates whole numbers on the left from fractional parts on the right.
| Place | Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|
| Example | 0 | 0 | 3 | . | 4 | 5 | 6 |
In nursing, decimals are everywhere — medication doses, IV rates, lab values, and weight-based calculations.
Patient Safety Rules¶
Leading Zero Rule
Always write a zero before a decimal point. Write 0.5 mg — never .5 mg A missing leading zero can cause a 10x overdose.
Trailing Zero Rule
Never write a zero after a decimal point in medication doses. Write 5 mg — never 5.0 mg A trailing zero can be misread as 50 mg.
Operations with Decimals¶
Addition and Subtraction¶
Line up the decimal points and add or subtract normally.
Multiplication¶
Multiply as whole numbers, then count total decimal places in both numbers and place the decimal point accordingly.
Division¶
Move the decimal point in the divisor to make it a whole number, then move the dividend's decimal point the same number of places.
Comparing Decimals¶
Line up decimal points and compare digit by digit from left to right.
Which is larger — 0.9 or 0.125?
0.900
0.125
Comparing tenths place: 9 > 1, therefore **0.9 is larger**
This matters clinically — misreading decimal size can lead to incorrect dose comparisons.
Clinical Application¶
Example: A patient needs 1.5 mg of a medication. The stock tablet contains 0.5 mg per tablet. How many tablets are needed?
Practice Problems¶
Problem 1
Add: \(2.75 + 0.5\)
Answer
Problem 2
Which is larger — 0.25 or 0.3?
Answer
0.30
0.25
**0.3 is larger.** In tenths place: 3 > 2.
Problem 3
A patient requires 2.5 mg per dose, twice daily for 5 days. What is the total amount of medication needed?
Answer
Problem 4
Which notation is correct for a half milligram dose?
Answer
0.5 mg — always use a leading zero. Never write .5 mg.
Clinical Tip
When in doubt about a decimal dose, say it out loud. "Point five" is easy to mishear as "five." Always confirm unusual doses with a colleague before administering.