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Percentages

A percentage represents a part of 100. The word "percent" literally means "per hundred." In nursing, percentages appear most often as solution concentrations on IV bags and medication labels.

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

Converting Between Forms

Percentage to decimal

Divide by 100 — move the decimal point two places left:

\[45\% = 0.45 \qquad 0.9\% = 0.009 \qquad 0.45\% = 0.0045\]

Decimal to percentage

Multiply by 100 — move the decimal point two places right:

\[0.25 = 25\% \qquad 0.009 = 0.9\%\]

Solution Concentrations

The clinical convention

IV solution concentrations are labeled as grams of solute per 100 mL of solution. A 5% solution contains 5 g per 100 mL. A 0.9% solution contains 0.9 g per 100 mL.

This means every percent concentration is a conversion factor you can use directly in a dimensional analysis chain:

\[\text{0.9\% NaCl} \rightarrow \frac{0.9\text{ g}}{100\text{ mL}} \quad \text{or} \quad \frac{100\text{ mL}}{0.9\text{ g}}\]

Example — D5W: A 500 mL bag of D5W (dextrose 5% in water). How many grams of dextrose does it contain?

\[500 \cancel{\text{ mL}} \times \frac{5\text{ g}}{100 \cancel{\text{ mL}}} = \frac{2500}{100} = 25\text{ g}\]

Example — D10W: A 500 mL bag of D10W. How many grams of dextrose?

\[500 \cancel{\text{ mL}} \times \frac{10\text{ g}}{100 \cancel{\text{ mL}}} = 50\text{ g}\]

Concentration verification

A 10% solution is ten times more concentrated than a 1% solution. Always verify the label concentration against the medication order before hanging a bag. Hanging the wrong concentration of a high-alert solution is a serious medication error.

Practice Problems

Problem 1

Convert 0.45% to a decimal.

Answer
\[0.45\% = 0.45 \div 100 = 0.0045\]

Note: 0.45% and 0.45 are not the same. 0.45% divided by 100 gives 0.0045 — two places further left than it appears.

Problem 2

Normal saline is labeled 0.9% NaCl. How many grams of NaCl are in a 1000 mL bag?

Answer
\[1000 \cancel{\text{ mL}} \times \frac{0.9\text{ g}}{100 \cancel{\text{ mL}}} = \frac{900}{100} = 9\text{ g NaCl}\]

Problem 3

Half-normal saline is 0.45% NaCl. How many grams of NaCl are in a 500 mL bag?

Answer
\[500 \cancel{\text{ mL}} \times \frac{0.45\text{ g}}{100 \cancel{\text{ mL}}} = \frac{225}{100} = 2.25\text{ g NaCl}\]

Problem 4

A patient's oxygen saturation reads 96%. Express as a decimal.

Answer
\[96\% = 0.96\]

Oxygen saturation is reported as a percentage and read directly — no further calculation required.

Self-Check