5.1 US Customary & Metric Systems

5.1 US Customary & Metric Systems

Accurate measurement is one of the most critical quantitative skills in nursing and healthcare. Whether you are calculating drug dosages, measuring patient height and weight, tracking intake and output (I&O), or determining wound dimensions, you must be completely fluent in the Metric system, the US Customary system, and Household measurement systems. On the ATI TEAS 7 Mathematics section, measurement questions test both your conceptual understanding of these units and your ability to convert efficiently between them using basic arithmetic.

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The Metric System (SI)

The Metric System—officially known as the Système International d'Unités (SI)—is the standard system of measurement used worldwide in science, medicine, and clinical nursing. The primary advantage of the metric system is that it is a base-10 decimal system. Moving between larger and smaller units simply involves multiplying or dividing by powers of 10 (which corresponds to shifting the decimal point to the right or left).

Metric Base Units

The metric system is anchored by three fundamental base units:

1. Length: Meter (m) — used for measuring distance, patient height, and anatomical dimensions.
2. Mass / Weight: Gram (g) — used for measuring body weight, organ mass, and solid medication dosages.
3. Volume: Liter (L) — used for measuring liquid volume, blood volume, IV fluids, and urinary output.

Metric Prefixes and Decimal Multipliers

Prefixes are attached to the base units to indicate fractional parts or multiples of ten. The table below lists the essential metric prefixes required for the TEAS 7 exam, ordered from largest to smallest:

Memory Mnemonic: To remember the order of the primary prefixes from largest to smallest, use the classic phrase: "King Henry Died By Drinking Chocolate Milk" (Kilo-, Hecto-, Deka-, Base, Deci-, Centi-, Milli-).

Core Clinical Metric Equivalences

In healthcare, you will frequently work with kilograms (kg), grams (g), milligrams (mg), micrograms (mcg), liters (L), and milliliters (mL). Memorize these exact clinical relationships:

• Mass / Weight:
  • 1 kilogram (kg) = 1,000 grams (g)
  • 1 gram (g) = 1,000 milligrams (mg)
  • 1 milligram (mg) = 1,000 micrograms (mcg)
• Fluid Volume:
  • 1 liter (L) = 1,000 milliliters (mL)
  • 1 milliliter (mL) = 1 cubic centimeter (cm³ or cc)
• Length:
  • 1 meter (m) = 100 centimeters (cm) = 1,000 millimeters (mm)
  • 1 centimeter (cm) = 10 millimeters (mm)

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The US Customary System

The US Customary System is derived from historical British imperial units. Unlike the metric system, US Customary units do not use a base-10 decimal structure. Instead, conversions rely on specific historical conversion factors that must be memorized.

Length, Weight, and Volume Equivalences

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Household Measurement System in Nursing

When nurses give discharge instructions to patients at home, liquid medications are often measured using Household units such as teaspoons, tablespoons, cups, and drops (gtt). Standard clinical practice equates these household units to precise metric volumes.

Standard Household-to-Metric Equivalences

Clinical Nursing Note: While 1 fluid ounce technically equals 29.5735 mL, ATI TEAS 7 math problems and nursing pharmacology standardized tests use the rounded clinical equivalence of 1 fl oz = 30 mL unless explicitly instructed otherwise.

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Step-by-Step Worked Math Examples

Worked Example 1: Multi-Step Metric Mass Conversion

Problem: A physician orders 0.045 grams of a cardiac medication. Convert this dose into milligrams (mg) and micrograms (mcg).

• Step 1: Convert grams (g) to milligrams (mg). Since 1 g = 1,000 mg, multiply by 1,000 (shift decimal point 3 places right): 0.045 g × 1,000 = 45 mg
• Step 2: Convert milligrams (mg) to micrograms (mcg). Since 1 mg = 1,000 mcg, multiply by 1,000 (shift decimal point 3 places right): 45 mg × 1,000 = 45,000 mcg
• Conclusion: 0.045 g = 45 mg = 45,000 mcg.

Worked Example 2: US Customary Volume Conversion

Problem: A clinic orders 3 gallons 2 quarts of liquid antiseptic solution. How many fluid ounces (fl oz) of solution were ordered in total?

• Step 1: Convert gallons to quarts. 3 gallons × 4 qts/gal = 12 quarts.
• Step 2: Add the additional 2 quarts: 12 qts + 2 qts = 14 quarts.
• Step 3: Convert quarts to fluid ounces. Since 1 quart = 32 fluid ounces: 14 quarts × 32 fl oz/qt = 448 fl oz
• Conclusion: Total volume ordered is 448 fl oz.

Worked Example 3: Household-to-Metric Liquid Dosage

Problem: A patient is instructed to take 1.5 tablespoons of cough syrup every 6 hours. The syringe provided by the pharmacy is marked in milliliters (mL). How many milliliters should the nurse instruct the patient to draw up for each dose?

• Step 1: Recall the household-to-metric equivalence: 1 tablespoon (tbsp) = 15 mL.
• Step 2: Multiply the ordered tablespoons by 15 mL/tbsp: 1.5 tbsp × 15 mL/tbsp = 22.5 mL
• Conclusion: The patient should draw up 22.5 mL per dose.

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TEAS 7 Calculator Tips & Common Traps

Calculator Tips for the 4-Function Calculator

• Decimal Point Movement: For metric conversions, you can quickly check your calculator results by manually counting decimal places. Moving from smaller to larger units (e.g., mg → g) means dividing by 1,000 (move decimal 3 places left). Moving from larger to smaller units (e.g., g → mg) means multiplying by 1,000 (move decimal 3 places right).
• Chained Conversions: When converting 3 gal 2 qts on your calculator, perform the operations sequentially without clearing: key in 3 * 4 = (12), + 2 = (14), * 32 = (448).

Common Student Traps

1. Confusing Mass (mg, mcg) with Volume (mL): mg measures weight/mass, while mL measures liquid volume. You cannot convert mg directly to mL without knowing the liquid medication's concentration (mg/mL).
2. Mixing Up Fluid Ounces (fl oz) and Weight Ounces (oz): Fluid ounces measure volume (liquid space); standard ounces measure mass/weight. 16 oz = 1 lb, whereas 8 fl oz = 1 cup.
3. Misplacing Microgram (mcg) Conversions: Remember that 1 mg = 1,000 mcg (a factor of 1,000). Misplacing a decimal point by one digit can lead to a tenfold dosage error!