Decimal Operations

Why This Matters for Nursing: Most medication doses, lab values, and vital signs use decimals. A patient's temperature of 98.6°F, a dose of 0.25 mg, or a lab value of 3.7 mEq/L—you'll work with decimals daily.

What You Need to Know

Decimals are another way to represent fractions and parts of whole numbers. The decimal point separates the whole number from the fractional part.

Place Values (Right of Decimal)

In 3.458:

• 3 = ones
• 4 = tenths (4/10)
• 5 = hundredths (5/100)
• 8 = thousandths (8/1000)

🧠 Memory Trick

Left of the decimal: Ones, Tens, Hundreds... (no "ths") Right of the decimal: Tenths, Hundredths, Thousandths

The "ths" tells you it's a fraction!

Adding & Subtracting Decimals

The Key Rule

Line up the decimal points, then add/subtract as usual

Example: 3.45 + 12.7

   3.45
+ 12.70  ← Add a zero to line up places
-------
  16.15

Answer: 16.15

Multiplying Decimals

Step-by-Step:

1. Ignore the decimals and multiply as whole numbers
2. Count total decimal places in both original numbers
3. Place the decimal in your answer (count from right)

Example: 2.5 × 0.4

1. Multiply: 25 × 4 = 100
2. Count decimal places: 2.5 (1 place) + 0.4 (1 place) = 2 places total
3. Place decimal: 100 → 1.00 = 1.0

Dividing Decimals

When dividing BY a decimal:

Move the decimal in the divisor to make it a whole number. Move the decimal in the dividend the SAME number of places.

Example: 4.5 ÷ 0.5

1. Move decimal in 0.5 one place right → 5
2. Move decimal in 4.5 one place right → 45
3. Now divide: 45 ÷ 5 = 9

✏️ Worked Examples

Example 1: Addition

Problem: 0.75 + 1.8 + 0.025

Step 1 — Line up the decimal points. This is the single most important rule for adding decimals. Write each number so all the decimal points are in the same vertical column.

Step 2 — Add trailing zeros so all numbers have the same length. This doesn't change the values — it just helps you see the columns clearly.

  0.750
  1.800
+ 0.025
-------

Step 3 — Add column by column from right to left, just like whole numbers.

• Thousandths: 0 + 0 + 5 = 5
• Hundredths: 5 + 0 + 2 = 7
• Tenths: 7 + 8 + 0 = 15 → write 5, carry 1
• Ones: 0 + 1 + 0 + 1 (carried) = 2

  0.750
  1.800
+ 0.025
-------
  2.575

Answer: 2.575