3.6 Measurement and Unit Conversions

Why Conversions Matter

Measurement and unit conversion belong to the TEAS Measurement and Data reporting area, and they are arguably the most clinically important math you will study. A misplaced decimal in a unit conversion is exactly how medication errors happen, so the exam stresses accuracy. You convert within the metric system, between metric and US customary units, and into household units patients actually use at home (teaspoons, tablespoons, cups). Master a small set of equivalencies and one technique — dimensional analysis — and every conversion question becomes mechanical.

The Metric System Runs on Powers of 10

Metric units share base units (the gram for mass, liter for volume, meter for length) and add prefixes that multiply or divide by powers of 10. Because each step is ×10, converting means only moving the decimal point.

A memory device for the order kilo → hecto → deka → base → deci → centi → milli is "King Henry Died By Drinking Chocolate Milk." Each step left divides by 10; each step right multiplies by 10.

Converting Within Metric

• Moving to a smaller unit (e.g., g → mg) → multiply (decimal moves right).
• Moving to a larger unit (e.g., mg → g) → divide (decimal moves left).

Example: Convert 2.5 kg to grams. kg is larger than g, so multiply: 2.5 × 1,000 = 2,500 g.

Example: Convert 4,500 mg to grams. g is larger than mg, so divide: 4,500 ÷ 1,000 = 4.5 g.

US Customary and Cross-System Conversions

The US customary system does NOT run on powers of 10, so each equivalency must be memorized.

To cross between systems, memorize these bridge conversions: 1 kg = 2.2 lb, 1 inch = 2.54 cm, 1 L ≈ 1.06 qt. Temperature is converted with formulas rather than a factor: °F = (°C × 9/5) + 32 and °C = (°F - 32) × 5/9.

Household-to-Metric for Dosing

Patients measure liquids at home in spoons and cups, so nurses translate to metric. These approximate equivalencies appear directly on the TEAS:

• 1 teaspoon (tsp) = 5 mL
• 1 tablespoon (tbsp) = 15 mL (so 3 tsp = 1 tbsp)
• 1 fluid ounce (fl oz) = 30 mL (so 2 tbsp = 1 fl oz)
• 1 cup = 240 mL; 1 L = 1,000 mL

Dimensional Analysis (Factor-Label Method)

Dimensional analysis treats conversion factors as fractions equal to 1 and arranges them so the unwanted units cancel diagonally, leaving only the target unit. Set up the chain, cancel, then multiply across the top and divide across the bottom.

Worked Conversion: A patient weighs 176 lb. Convert to kilograms using 1 kg = 2.2 lb. 176 lb × (1 kg / 2.2 lb) = 176 / 2.2 = 80 kg. The "lb" cancels, leaving kg.

Worked Conversion: An order says give 10 mL of a syrup; how many teaspoons should the caregiver give at home? Use 1 tsp = 5 mL: 10 mL × (1 tsp / 5 mL) = 10 / 5 = 2 tsp.

Perimeter, Area, and Volume Units

Measurement questions also test geometric size. Perimeter (distance around) uses the same units as length (cm, in). Area (space inside a flat shape) uses square units (cm²); rectangle area = length × width. Volume (space inside a solid) uses cubic units (cm³); a box's volume = length × width × height. One handy clinical link: 1 mL = 1 cm³, which is why a 10-mL syringe and a 10-cm³ volume describe the same amount.

Recap

Within metric, just slide the decimal — multiply going smaller, divide going larger. Across systems and to household units, anchor on the memorized bridges (2.2 lb/kg, 2.54 cm/inch, 5 mL/tsp, 15 mL/tbsp, 30 mL/oz) and run them through dimensional analysis so the units cancel. Track whether the answer should be square (area) or cubic (volume) units, and remember 1 mL equals 1 cm³.