Lesson
Volumes and the Stated Conversion Factor
Convert the unit while preserving the amount, and keep the same conversion convention throughout a problem.
- Liters, deciliters, and milliliters
- Household volume relationships
- Stated versus approximate factors
- Fluid ounces versus mass ounces
Starting volume
Liters cancel
The amount is preserved
Keep the amount and the unit together
One liter is 1,000 mL and 10 dL. A change from liters to milliliters makes the number larger because the unit becomes smaller; the amount of liquid stays the same. For example, 0.75 L x 1,000 mL/L = 750 mL. Reversing the factor gives 750 mL x 1 L/1,000 mL = 0.75 L. A concentration such as mg/dL has a volume denominator; it is not a volume by itself.
Read household quantities as volume
The book uses 5 mL per teaspoon and 15 mL per tablespoon. Its household relationships are 8 fluid ounces per cup, 16 fluid ounces per pint, 2 pints per quart, and 4 quarts per gallon. In this context an ounce is a fluid-volume unit. A mass ounce belongs to a different conversion and must not be inserted into a liquid-volume calculation. For an original example, 1.5 tablespoons x 15 mL/tablespoon = 22.5 mL.
Keep one conversion convention
The book gives both rounded and more precise volume factors: 30 or 29.57 mL per fluid ounce; 240 or 236.56 mL per cup; 480 or 473 mL per pint; 960 or 946 mL per quart; and 3,840 or 3,785 mL per gallon. These are the book's reference values, not a claim that the more precise decimals are exact. Use a factor supplied in the question. If none is supplied, the book permits its approximate or more precise convention and explains that the requested rounding accounts for the difference. Do not mix conventions in the middle of a calculation.
Apply the given factor before subtracting
Suppose an arithmetic problem defines 1 fluid ounce as 30 mL and starts with 12 fluid ounces of liquid. The starting amount is 12 x 30 = 360 mL. After 45 mL is removed, 315 mL remains. Using 29.57 mL per fluid ounce would answer a different version of the problem because its explicit conversion instruction was 30 mL.
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Lesson
Mass, Body Weight, and Height
Follow each metric step and convert feet and inches into a single height quantity before applying the centimeter factor.
- kg, g, mg, mcg, and ng
- Pounds and kilograms
- Grains and mass ounces
- Feet, inches, centimeters, and meters
Convert feet to inches
Add the remaining inches
Apply the centimeter factor
Walk through the metric scale
Each step from kg to g to mg to mcg to ng multiplies the numerical quantity by 1,000. Each step in the opposite direction divides by 1,000. Thus 0.004 g x 1,000 mg/g x 1,000 mcg/mg = 4,000 mcg. Similarly, 2,500,000 ng divided by 1,000 three times is 0.0025 g. Count the unit changes; converting g to mcg takes two steps, while converting ng to g takes three.
Distinguish similar abbreviations
The metric gram is g; the grain is gr. They are different units. The book lists 65 mg per grain as an approximate factor and 64.8 mg as its more precise factor. It also lists 28.4 g per mass ounce, 454 g per pound, and the commonly used 2.2 pounds per kilogram. These rounded reference factors need not be perfectly reciprocal. Choose the factor required by the question and retain it throughout that calculation.
Convert body weight with units
Using 2.2 lb/kg, an original example of 198 lb converts to 198 lb x 1 kg/2.2 lb = 90 kg. In a proportion, write 198 lb/X kg = 2.2 lb/1 kg and solve for X. Both setups give the same result. Multiplying 198 by 2.2 produces a larger number and leaves the wrong unit relationship for a pounds-to-kilograms conversion.
Combine feet and inches first
One foot is 12 inches, one inch is 2.54 cm, and one meter is 100 cm. A height of 5 feet 7 inches is (5 x 12) + 7 = 67 inches. Then 67 x 2.54 = 170.18 cm, or 1.7018 m. Five feet seven inches is not 5.7 feet: the extra 7 is an inch count and must be combined with the 60 inches from the feet.
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Lesson
Milliequivalents and Millimoles
The mEq-to-mmol relationship depends on the ion's valence; it is not one universal numerical conversion.
- Monovalent ions
- Divalent ions
- Conversion direction
- Quantity versus concentration
18 mEq = 18 mmol
18 mEq = 9 mmol
9 mmol x 2 = 18 mEq
Read the ion as well as the number
The book's conversion guide pairs 1 mEq with 1 mmol for monovalent ions such as sodium and potassium. For divalent ions such as calcium, it pairs 1 mEq with 0.5 mmol. The relationship depends on valence, so a number labeled mEq cannot be converted correctly unless the relevant ion is identified.
Convert in both directions
For an original potassium example, 18 mEq corresponds to 18 mmol because potassium is monovalent. For an original calcium example, 18 mEq corresponds to 9 mmol because calcium is divalent. Reversing that calcium conversion gives 9 mmol x 2 mEq/mmol = 18 mEq. State the ion and unit at each step; halving every electrolyte quantity would be incorrect.
Retain the concentration denominator
A potassium concentration of 6 mEq/L corresponds to 6 mmol/L. A calcium concentration of 6 mEq/L corresponds to 3 mmol/L. The per-liter denominator stays with the result. These conversions establish equivalent ways to express the stated quantity; they do not determine how much electrolyte a patient needs or how quickly it should be administered.
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Lesson
Unit Cancellation, Proportions, and Final Rounding
A traceable setup identifies the answer unit, preserves intermediate precision, and follows the particular rounding instruction.
- Dimensional analysis
- Matched proportions
- Decimal places versus multiples of ten
- Whole-container quantities
Do not round this first
Complete the multiplication
Apply the stated rounding
Let units determine the factor's direction
For 1.25 L to mL, write 1.25 L x 1,000 mL/1 L. The L units cancel and 1,250 mL remains. A proportion can express the same relationship as 1.25 L/X mL = 1 L/1,000 mL. Match the units in corresponding positions before cross-multiplying. Correct proportions and dimensional analysis agree; the choice of method does not change the answer.
Round once at the end
Retain intermediate precision. For an original exercise of 2.75 mL per administration and 6 administrations, the total is 16.5 mL. If the instruction is the nearest whole milliliter, the answer is 17 mL. Rounding each administration to 3 mL first would give 18 mL and answer the wrong calculation. For positive values, inspect the next digit: 5 through 9 round the retained place upward; 0 through 4 leave it unchanged.
Distinguish the requested place
An original result of 73.46 mg becomes 73 mg to the nearest whole milligram, 73.5 mg to the nearest tenth of a milligram, and 70 mg to the nearest 10 mg. The nearest tenth means one decimal place; the nearest 10 means a multiple of ten. If a problem supplies a rounding policy, apply that stated policy rather than turning it into a universal drug-dosing rule.
Whole containers answer a different question
An exercise requires 1,250 mL and specifies that only intact 500 mL containers may be supplied. The ratio is 1,250/500 = 2.5 containers. Supplying the whole quantity requires 3 containers because 2 would contain only 1,000 mL. The supplied container volume becomes 1,500 mL; that does not mean the required or administered amount changes to 1,500 mL. Whole-container reasoning is distinct from rounding a measured dose to a decimal place.
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Module practice
Check the connections.
Each attempt draws 10 questions from the complete 25 question bank.
Each attempt draws a fresh set and rearranges the answer choices.
References
Book source and calculation scope.
The cited pages support the conversion methods and rounding rules in this module. Examples and questions are original; they do not reproduce the book's practice items or establish current prescribing recommendations.
- RxPrep 2023 Course Book
Chapter 1, required-formulas checklist, printed page 7 (PDF page 19); Chapter 9, equivalent measurements, conversions, rounding, proportions, and dimensional analysis, printed pages 116-119 (PDF pages 124-127).