Dimensional Analysis Practice Problems

A pharmacist needs to prepare a prescription for a patient who requires a daily dose of 1.5 g of cefuroxime to be taken every eight hours. The medication is available in 750 mg vials. How many vials will the pharmacist need to dispense for a day of treatment?

A 70-year-old patient weighing 166 pounds has 24% body fat. Determine how many kilograms (in 2 s.f.) of body fat the patient has.

To alleviate acute pain from dental surgery, a dental surgeon prescribes 1 tablet of etoricoxib per day for 3 days. Determine how many ounces of the medication should be taken within 3 days if each tablet is 90 mg. 

Solve the following problem using the appropriate conversion factors: A patient is required to take 0.060 g of medication. If the medication is available in 15 mg capsules, how many capsules should the patient take?

A certain brand of natural lawn fertilizer highlighted the following details: "Net wt. 20 lb" and "9-0-2". The label "9-0-2" indicates the percentage of N-P-K (nitrogen, phosphorus, and potassium) and implies that the fertilizer has 9% N, 0% P, and 2% K by mass. How many grams (in 1 s.f.) of nitrogen are in 20 lb of lawn fertilizer? 

A fitness coach who weighs around 75 kg has 17% body fat by weight. Using one or more conversion factors, calculate the weight of the person's fat in pounds.

A professional boxer weighs around 151 lb. Using one or more conversion factors, calculate the boxer's mass in kilograms.

Solve the following problem using the appropriate conversion factors: You need a total of 56.7 L of distilled water for a trip. What is the volume of the water in gallons?

A technical-grade muriatic acid used in households is 28% HCl by volume. Calculate the volume (in mL) of HCl present in a 3.78 L bottle of muriatic acid.

An equipment room for housing a spectrometer was set to have the following dimensions: length = 4.0 m, width = 4.0 m, and height = 5.0 m.

Determine the width of the room in yards.

A cup contains 0.760 qt of soda. Using the appropriate conversion factors, calculate the volume of the soda in milliliters.

A square container for fragile equipment has a length of 24.0 inches. 

Convert the length of the box to centimeters. 

A pound of kiwis costs 1.24 euros in Germany. Determine the price of a kilogram of kiwis in dollars if the exchange rate is 1.07 dollars/euro.

A kilogram of apples costs 710.88 yen in Japan. Calculate the price of a pound of apples in dollars if the exchange rate is 131.40 yen/dollar.

A rectangular floor mat has a width of 105 in and a length of 215 in. What is its area in cm²? Express the answer to the correct number of significant figures. (The area of a rectangle is the product of its width and length.)

Calculate the number of platelets in a human adult with 5.0 L of blood. The normal platelet concentration is 450,000 cells/µL of blood. Express the answer using scientific notation.

Iron is a common dietary supplement that keeps the blood healthy. The daily dietary intake of iron for adult men is 8.7 mg. Calculate the mass of steak an adult man should eat to meet the recommended daily dietary intake. Assume that 100 g of steak contains 2.4 mg of iron.

The weight of a gemstone is usually denoted in carats, where 1 carat = 200 mg. Calculate the mass (in grams) of a 20-carat diamond.

A teen eats two medium bananas. The teen looks up the caloric value of a medium banana and finds that one medium banana contains 105 Calories. Suppose that jogging burns 7 Calories per minute. How long should the teen engage in jogging to burn the calories contained in the bananas?

The nitrogen level in an urban apartment is 521 µg/m³. Calculate the mass of nitrogen gas in grams if the urban apartment is 10.2 ft x 9.8 ft x 21.5 ft in dimension.

Calculate the amount of wine in liters that can be held in a wine barrel with a capacity of 28.7 gals. (1 gal = 4 qt = 3.7854 L)

The recommended acetaminophen suspension dosage for infants is 14 mg/kg body weight. If an acetaminophen suspension contains 70 mg/0.67 mL, how much should be given to a 12 lb infant? (Assume two significant figures)

A student grabbed a handful of paper clips. It weighed 32.4 grams. Determine the number of paper clips he grabbed if one paper clip weighs 1.2 grams.

Determine the measurement with the SMALLEST mass

What is 132 cm in inches?

A row of helium atoms has 5.04x10²³ atoms. What is its length in km if the diameter of one helium atom is 64 pm (1 pm = 10 ^-12 m)?

Calculate the gas mileage of an automobile, which is 15 km/L, in miles per gallon (mi/gal).

Calculate the density of copper, which is 8.96 g/cm³, in pounds per cubic inch (lb/in³).

What is the growth rate in inches per hour of a plant growing at 10.0 cm/day?

How long does it take for a light signal to make a round trip from the earth to the satellite and back to the earth if the satellite is 25 miles above earth? Express your answer in milliseconds (speed of light = 3.0x10⁸ m/s)

Determine the measurement in square miles of a real estate that is 345 acres.

(1 acre = 43,560 ft², 1 mile = 5280 ft)