An IV solution is ordered to run at 3.5 gtts/min. It contains 875 mg in a total of 250 mL. How many milligrams will the patient receive per hour if the set is calibrated to deliver 12 gtts/mL?

Pharmacy technician conversions and calculations involve accurately determining medication dosages, quantities, and concentrations by switching between measurement systems (metric, household, apothecary) and using math to ensure patient safety. Essential skills include calculating ratios/proportions, converting units (e.g., mg to g), and determining IV drip rates or dosages based on weight.  Key Aspects of Pharmacy Conversions and Calculations: Core Systems: Technicians must frequently convert between metric (most common), household (teaspoons, tablespoons), and apothecary units. Common... Show more

Pharmacy technician conversions and calculations involve accurately determining medication dosages, quantities, and concentrations by switching between measurement systems (metric, household, apothecary) and using math to ensure patient safety. Essential skills include calculating ratios/proportions, converting units (e.g., mg to g), and determining IV drip rates or dosages based on weight. 

Key Aspects of Pharmacy Conversions and Calculations:
Core Systems: Technicians must frequently convert between metric (most common), household (teaspoons, tablespoons), and apothecary units.

Common Conversions to Memorize:

Weight:
1 kilogram (kg) = 1000 grams (g)
1 gram (g) = 1000 milligrams (mg)
1 milligram (mg) = 1000 micrograms (mcg)
Weight:
1 grain (gr) = 60 milligrams (mg) (or 64.8 mg for exact, but 60 is pharmacy standard)
1 ounce (oz) = 28.35 grams (g) (often rounded to 28.4 g or 30 g in some settings)
1 pound (lb) = 16 ounces (oz) = 454 grams (g)
Weight:
1 kilogram (kg) = 2.2 pounds (lbs)
Volume:
1 liter (L) = 1000 milliliters (mL)
1 milliliter (mL) = 1 cubic centimeter (cc)
1 teaspoon (tsp) = 5 milliliters (mL)
1 tablespoon (tbsp) = 15 milliliters (mL)
Volume:
1 fluid ounce (fl oz) = 30 milliliters (mL) (often simplified from 29.57)
1 cup = 8 fluid ounces = 240 milliliters (mL)
1 pint (pt) = 16 fluid ounces = 480 milliliters (mL) (often rounded to 500 mL)
1 quart (qt) = 32 fluid ounces = 960 milliliters (mL) (often rounded to 1000 mL / 1 L)
Volume:
1 gallon (gal) = 4 quarts = 8 pints = 128 fluid ounces = 3840 milliliters (mL) (often rounded to 3800 mL)
Weight/Volume:
1 gram per milliliter (g/mL) = 1 gram per cubic centimeter (g/cc) (density of water)
1 milligram per deciliter (mg/dL) = 10 milligrams per liter (mg/L)
Weight/Volume (often rounded to):
1 gram = 1000 milligrams (concentration basis)
1% solution = 1 gram per 100 milliliters (g/100 mL) = 10 milligrams per milliliter (mg/mL)

Bonus: Temperature Conversions
°C to °F: (°C × 9/5) + 32 = °F
°F to °C: (°F − 32) × 5/9 = °C

Essential Calculation Methods:
Dimensional Analysis: A standard method for solving conversion problems by canceling out units.
Ratio and Proportion: Used to determine unknown quantities, such as calculating doses based on body weight (mg/kg) or body surface area.

Applications:
Compounding: Calculating the correct amount of ingredients for creams, ointments, or solutions.
Dosage Calculation: Determining the correct medication amount for pediatric patients or specialized therapies.
IV Flow Rates: Calculating milliliters per hour (mL/hr) or drops per minute. 

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