Percentages

What Is a Percentage?

A percentage represents a part of 100. The word "percent" literally means "per hundred."

\[25\% = \frac{25}{100} = 0.25\]

In nursing, percentages appear in IV solution concentrations, oxygen saturation, body surface area calculations, and more.

Converting Between Forms

Percentage to Decimal

Divide by 100 (or move decimal point two places left):

[45\% = 45 \div 100 = 0.45] [0.9\% = 0.9 \div 100 = 0.009]

Decimal to Percentage

Multiply by 100 (or move decimal point two places right):

[0.25 \times 100 = 25\%] [0.009 \times 100 = 0.9\%]

Percentage to Fraction

Place the percentage over 100 and simplify:

\[25\% = \frac{25}{100} = \frac{1}{4}\]

Fraction to Percentage

Divide numerator by denominator then multiply by 100:

\[\frac{1}{4} = 0.25 \times 100 = 25\%\]

Finding a Percentage of a Number

Multiply the number by the decimal form of the percentage:

\[20\% \text{ of } 500 = 0.20 \times 500 = 100\]

Clinical Application

IV Solution Concentrations

IV solutions are labeled by percentage concentration, meaning grams of solute per 100 mL of solution.

Example: Normal saline is labeled 0.9% NaCl. This means:

\[0.9 \text{ g of NaCl per } 100 \text{ mL of solution}\]

Example: Dextrose 5% in water (D5W) means:

\[5 \text{ g of dextrose per } 100 \text{ mL of solution}\]

Example: A patient's oxygen saturation is 98%. Express this as a decimal:

\[98\% = 0.98\]

Practice Problems

Problem 1

Convert 35% to a decimal.

Answer

\[35\% = 35 \div 100 = 0.35\]

Problem 2

Convert 0.45 to a percentage.

Answer

\[0.45 \times 100 = 45\%\]

Problem 3

What is 15% of 200?

Answer

\[0.15 \times 200 = 30\]

Problem 4

A 500 mL bag of D10W contains 10% dextrose. How many grams of dextrose are in the bag?

Answer

10% means 10 g per 100 mL. [\frac{10 \text{ g}}{100 \text{ mL}} \times 500 \text{ mL} = 50 \text{ g of dextrose}]

Problem 5

A patient scored 18 out of 20 on a pain assessment tool. What is their score as a percentage?

Answer

\[\frac{18}{20} \times 100 = 90\%\]

Clinical Tip

When reading IV solution labels, pay close attention to the percentage concentration. A 10% solution is 10 times more concentrated than a 1% solution. Always verify the label against the medication order before hanging a bag.