3.3 Decimals and Percentages

Decimals and Percentages on the TEAS

Healthcare runs on decimals and percentages: a glucose reading of 95.5 mg/dL, a 0.9% saline solution, a 0.25 mg tablet. The ATI TEAS 7 reflects this by testing decimal operations and the ability to move fluidly among fractions, decimals, and percentages. Because a misplaced decimal in nursing can be a tenfold dosing error, the exam rewards careful place-value alignment over speed.

Decimal Place Value

Reading place value also drives rounding: to round 3.7846 to the nearest hundredth, look at the thousandths digit (4, less than 5) and round down to 3.78.

Decimal Operations

Adding/Subtracting: line up the decimal points (add placeholder zeros so the columns match), then add or subtract as with whole numbers and bring the point straight down.

Worked Example: 3.45 + 2.6 → align as 3.45 + 2.60 = 6.05.

Multiplying: ignore the points and multiply, then count the total number of decimal places in both factors and place that many in the product.

Worked Example: 1.5 × 2.4. Compute 15 × 24 = 360. The factors have 1 + 1 = 2 decimal places, so the product is 3.60 = 3.6.

Dividing: move the divisor's decimal point to make it a whole number, move the dividend's point the same number of places, then divide.

Worked Example: 4.5 ÷ 0.5 → shift one place each to 45 ÷ 5 = 9.

Converting Among Fractions, Decimals, and Percentages

High-Yield Equivalents to Memorize

Knowing these by sight lets you skip conversion steps — if a question asks for 75% of a quantity, you can immediately think "three-quarters."

Percentage Calculations

Percent OF a number: convert the percent to a decimal and multiply.

Worked Example: What is 15% of 80? 0.15 × 80 = 12.

What percent one number is of another: divide the part by the whole, then multiply by 100.

Worked Example: 15 is what percent of 60? 15 ÷ 60 = 0.25 → 25%.

Find the whole from a part and a percent: divide the part by the decimal form of the percent.

Worked Example: 12 is 20% of what number? 12 ÷ 0.20 = 60.

Percent Change (Increase and Decrease)

Percent change = (new − original) ÷ original × 100. A positive result is an increase; a negative result is a decrease.

Worked Example (decrease): A patient's weight drops from 200 lb to 180 lb. Change = 180 − 200 = −20; −20 ÷ 200 × 100 = −10%, i.e., a 10% decrease.

Worked Example (increase): A heart rate rises from 60 to 75 bpm. Change = 75 − 60 = 15; 15 ÷ 60 × 100 = 25% increase. Note that you always divide by the original value, not the new one.

Dosage-Relevant Decimal Reasoning

Decimals are the backbone of dosage math. A common safety rule is to write a leading zero (0.5 mg, never .5 mg) and to avoid trailing zeros (5 mg, not 5.0 mg) so a misread point cannot create a tenfold error.

Worked Example (concentration): A 0.9% sodium chloride solution means 0.9 g of NaCl per 100 mL. How many grams are in 250 mL? Set up 0.9 g / 100 mL = x / 250 mL, or simply 0.009 × 250 = 2.25 g. Percent-as-decimal reasoning turns a wordy clinical statement into one multiplication.

Healthcare Applications