Measuring

# 7 Converting Units for Medication Amounts

# Lesson

Learning Outcomes

By the end of this chapter, learners will be able to:

- identify when units require conversion when comparing between the medication order and medication supply, and
- convert between common units of measure.

## Determining When to Convert Units

When an order for medication is supplied in an amount with a different unit of measure than the order, you will need to convert units so they match in order to ensure you are giving the correct dose of medication. Not all orders will require unit conversion.

Sample Exercise 7.1

Which of the following orders require unit conversion before medication administration?

**Order A:**

**Medication Order:**prednisone 25 mg PO once daily**Medication Supply:**prednisone 5 mg tablets

**Order B:**

**Medication Order:**acetaminophen 1 g PO QID prn**Medication Supply:**acetaminophen 500 mg tablets

**Answer:**

Order B requires unit conversion as the order is given in grams and the supply is provided in milligrams. Order A and the supply are both provided in milligrams.

## Converting Units

To convert from one unit of measure to another, you need to know how many of a particular unit is equal to a single unit of the other type of measure. You can refer to the conversion table for quick reference if you are unfamiliar with how many of one unit would be in another for the units commonly used in medication administration. These amounts are called conversion factors. You will then set up an algebraic equation to convert between units, with the conversion factor written as a fraction.

Let’s say we need to give 0.5 grams (g) of a medication and the supply is in milligrams (mg). How many mg are equal to 0.5 g?

[latex]\text{? mg} = 0.5\text{ g}[/latex]

Start the equation with what you need to know, in this case, how many mg. We use **“[latex]x[/latex]“** to represent the unknown amount of mg. Then, we need to use the conversion factor of **1000 mg = 1 g.** When you set up the formula, put the type of units on top which matches the unit you are looking for. In this example, we are trying to find mg, so write in [latex]\dfrac{1000\text{ mg}}{1\text{ g}}[/latex]. Finally, we multiply by the known amount. The formula would look like this:

[latex]x\text{ mg}=\dfrac{1000\text{ mg}}{1\text{ g}}\times0.5\text{ g}[/latex]

To solve this equation, complete the calculation using the standard order of operations. Some people use the acronym **BEDMAS** to help them remember the order of operations: **B**rackets, **E**xponents, **D**ivision or **M**ultiplication, **A**ddition or **S**ubtraction.

You can always check to see if you are ending up with the correct units by cancelling out units which match in the numerator and denominator of the equation. In this case, grams in the numerator and denominator cancel out, leaving us with just an amount of mgs, which is exactly what we want!

[latex]x\text{ mg}=\dfrac{1000 \text{mg}}{1\cancel{\text{g}}}\times0.5\cancel{\text{ g}}[/latex]

[latex]x=500\text{ mg}[/latex]

Sample Exercise 7.2

Sample Medication Order to Convert

**Medication Order:** pulmicort 500 mcg twice a day via nebulizer

**Medication Supply: ** pulmicort 0.25 mg/mL nebule

You can see that the order is written as **mcg** and the supply is measured in **mg/mL. **

First, decide what type of unit you are converting to. This is what you will use to start the set up of your formula. In this example, we need to find out how many milligrams are in 500 micrograms because our supply is available in milligrams.

[latex]x\text{ mg}=[/latex]

Second, start with what you know-the conversion factor:

[latex]x\text{ mg}=\dfrac{\text{1 mg}}{\text {1000 mcg}}[/latex]

Third, multiply by the amount you need to convert:

[latex]x\text{ mg}=\dfrac{\text{1 mg}}{\text {1000 mcg}}\times\text{500 mcg}[/latex]

You can see the units of mcg cancel out as there is one in the numerator and the denominator:

[latex]x\text{ mg}=\dfrac{\text{1 mg}}{1000\cancel{\text { mcg}}}\times500\cancel{\text{ mcg}}[/latex]

Now, complete the calculation:

[latex]\dfrac{\text{500}}{\text{1000}}=\text{0.5 mg}[/latex]

Sample Exercise 7.3

How many milligrams of ciprofloxacin must be administered?

**Medication Order:** Ciprofloxacin 0.75 g PO once daily

**Medication Supply:** Ciprofloxacin 250 mg tablets

**Answer:**

Set up the formula. Start with what you need to know (x mg). Use the conversion factor, with number on top in the same units (mg). Multiply by amount in the order.

[latex]x\text{ mg}=\dfrac{\text{1000 mg}}{\text{1 g}}\times\text{0.75 g}[/latex]

Cancel out units to ensure the formula is set up correctly.

[latex]x\text{ mg}=\dfrac{\text{1000 mg}}{1\cancel{\text{ g}}}\times{0.75\cancel{\text{ g}}}[/latex]

Calculate.

[latex]\text{1000 mg}\times\text{0.75 g}=\text{750 mg}[/latex]

# Practice Set 7.1: When to Convert

Practice Set 7.1: When to Convert

In the following exercises, identify if any units need to be converted (yes/no answer) and what unit to convert to.

- A medication is ordered at a single dose of 500 mg. The capsules provided by the pharmacy are 250 mg each.
- A medication is ordered at a single dose of 1 g. The tablets provided by the pharmacy are 500 mg each.
- A medication is ordered at 0.15 mg BID. The tablets provided by the pharmacy are 0.75 mcg each.
- A medication is ordered at 750 mg TID. The tablets provided by the pharmacy are 250 mg each.
- A medication is ordered at 500 mcg BID. The tablets provided are 1 mg each.
- A medication is ordered for a single dose of 500 mg at 1,000. The tablets provided are 1,000 mg each.
- A medication is ordered at 1 g TID. The capsules provided are 500 mg each.
- A medication is ordered at 500 mcg BID. The capsules provided by pharmacy are 1 g each.
- A medication is ordered at a single dose of 150 mg. The tablets provided are 750 mcg each.
- A medication is ordered at 300 mcg QID. The capsules provided are 200 mcg each.

**Answers:**

- No.
- Yes. Convert 1 g to mg.
- Yes. Convert 0.15 mg to mcg.
- No.
- Yes. Convert 500 mcg to mg.
- No.
- Yes. Convert 1 g to mg.
- Yes. Convert 500 mcg to g.
- Yes. Convert 150 mg to mcg.
- No.

# Practice Set 7.2: Converting Mass

Practice Set 7.2: Converting Mass

In each of the following practice questions you will be given a medication order and a supply provided with an alternate unit of measurement. Convert the order amount so it matches the unit of measurement of the supply.

The answers to this problem set are visible when you click the drop down button below. When you click the word “Answers” you will see the answers for all ten questions with the answer listed first, followed by how to set up the formula. It is worth mentioning this is not the only way to solve this type of problem, and it is acceptable to use another method to convert between units if you are comfortable with a different method.

**Questions:**

- Order: acetaminophen 1 g PO QID

Supply 500 mg tablets - Order: ipratropium 0.5 mg via nebulizer q6h

Supply 250 mcg nebules - Order: lorazepam 500 mcg SL BID prn

Supply 0.5 mg tablets - Order: cloxacillin 0.5 g PO q4h

Supply 250 mg tablets - Order: digoxin 250 mcg PO once daily

Supply 0.125 mg tablets - Order: azithromycin 2 g PO once daily

Supply 500 mg tablets - Order: budesonide 0.4 mg inhaled BID

Supply 200 mcg per metered dose - Order: synthroid 0.15 mg PO once daily

Supply 75 mcg tablets - Order: ciprofloxacin 0.75 g PO q12h

Supply 500 mg tablets - Order: metronidazole 1.5 g PO

Supply 500 mg tablets

**Answers:**

- 1,000 mg [latex]x\text{ mg}=\dfrac{\text{1000 mg}}{\text{1 g}}\times\text{1 g}[/latex]
- 500 mcg [latex]x\text{ mcg}=\dfrac{\text{1000 mcg}}{\text{1 mg}}\times\text{0.5 mg}[/latex]
- 0.5 mg [latex]x\text{ mg}=\dfrac{\text{1 mg}}{\text{1000 mcg}}\times\text{500 mcg}[/latex]
- 500 mg [latex]x\text{ mg}=\dfrac{\text{1000 mg}}{\text{1 g}}\times\text{x0.5 g}[/latex]
- 0.25 mg [latex]x\text{ mg}=\dfrac{\text{1 mg}}{\text{1000 mcg}}\times\text{250 mcg}[/latex]
- 2,000 mg [latex]x\text{ mg}=\dfrac{\text{1000 mg}}{\text{1 g}}\times\text{2 g}[/latex]
- 400 mcg [latex]x\text{ mcg}=\dfrac{\text{1000 mcg}}{\text{1 mg}}\times\text{0.4 mg}[/latex]
- 150 mcg [latex]x\text{ mcg}=\dfrac{\text{1000 mcg}}{\text{1 mg}}\times\text{0.15 mg}[/latex]
- 750 mg [latex]x\text{ mg}=\dfrac{\text{1000 mg}}{\text{1 g}}\times\text{0.75 g}[/latex]
- 1,500 mg [latex]x\text{ mg}=\dfrac{\text{1000 mg}}{\text{1 g}}\times\text{1.5 g}[/latex]

# Practice Set 7.3: Converting Mass

Practice Set 7.3: Converting Mass

In each of the following practice questions you will be given a weight which needs to be converted to an alternate unit of measure, which may be metric or imperial.

- A baby weighs 2,347 grams. A medication is ordered and the amount is based on how heavy a child is in kilograms. How many kilograms is this baby?
- A child weighs 35 kilograms. The parent asks how much the child weighs in pounds. How many pounds is this child?
- A nurse is on light work duty only after returning to work post injury. Worksafe requirements state they can lift a maximum of 10 kilograms. A box of IV bags is labelled 25 lbs. How many kilograms is this?
- A baby weighs 1.27 kilograms. How many grams is this?
- A person weighs 87.5 kilograms. How many pounds is this?
- A child weighs 32 pounds. How many kilograms is this?
- A wheelchair is rated for use for a person up to 400 pounds. The person you would like to transfer using the wheelchair is 167 kilograms. How many pounds is this equivalent to?
- A premature infant weighs 477 grams. How many kilograms is this?
- An infant warmer in the hospital neo-natal intensive care unit has a maximum patient weight of 30 pounds. The baby you are caring for was born weighing 11.8 kilograms. How many pounds is this?
- A newborn weighs 6 pounds and 4 ounces. How many grams is this?

**Answers:**

- 2.35 kg [latex]x\text{ kg}=\dfrac{\text{1 kg}}{\text{1000 g}}\times\text{2347 g}[/latex]
- 77 lb [latex]x\text{ lbs}=\dfrac{\text{2.2 lbs}}{\text{1 kg}}\times\text{35 kg}[/latex]
- 11.36 kg [latex]x\text{ kg}=\dfrac{\text{1 kg}}{\text{2.2 lbs}}\times\text{25 lbs}[/latex]
- 1,270 g [latex]x\text{ g}=\dfrac{\text{1000 g}}{\text{1 kg}}\times\text{1.27 kg}[/latex]
- 192.5 lb [latex]x\text{ lbs}=\dfrac{\text{2.2 lbs}}{\text{1 kg}}\times\text{87.5 kg}[/latex]
- 14.54 kg [latex]x\text{ kg}=\dfrac{\text{1 kg}}{\text{2.2 lbs}}\times\text{32 lbs}[/latex]
- 367.4 lb [latex]x\text{ lbs}=\dfrac{\text{2.2 lbs}}{\text{1 kg}}\times\text{167 kg}[/latex]
- 0.477 kg [latex]x\text{ kg}=\dfrac{\text{1 kg}}{\text{1000 g}}\times\text{477 g}[/latex]
- 25.96 [latex]x\text{ lbs}=\dfrac{\text{2.2 lbs}}{\text{1 kg}}\times\text{11.8 kg}[/latex]
- 2,840.9 grams.

If you use the method demonstrated in this textbook, but you do not have the conversion factor between grams and pounds, you can answer this question using this method:

- Convert ounces to pounds [latex]x\text{ lbs}=\dfrac{\text{1 lb}}{\text{16 oz}}\times\text{4 oz}[/latex] = 0.25
- Add converted ounces (0.25 lbs) to the known amount of pounds (6) from the question. =6.25
- Convert pounds to grams: [latex]x\text{ g}=\dfrac{\text{1000 g}}{\text{1 kg}}\times\dfrac{\text{1 kg}}{\text{2.2 lbs}}\times\text{6.25 lbs}[/latex]

Alternately, you could use the conversion factor for pounds and grams: 1 lb = 454 g, which would give you a slightly different answer due to rounding error as both conversion factors have been rounded from the most precise conversion amount: 2,837.5 g

# Practice Set 7.4: Converting Volume

Practice Set 7.4: Converting Volume

In each of the following practice questions you will be given a measurement which needs to be converted to an alternate unit of measure, which may be metric or imperial.

- Convert 1.15 litres to millilitres.
- Convert 237 millilitres to litres.
- Convert 5,819 millilitres to litres.
- A medication requires you to mix a package of powdered medication into 1.5 cups of water. How many millilitres is this?
- Before an ultrasound, the radiology department calls and asks you to have the patient drink 2 cups of water. How many millilitres is this?
- At the end of your shift, the charge nurse asks you how many litres of intake your patient had today. When you check the fluid balance record you see they have received 1,875 mL of intravenous fluid and 680 mL of fluid from their meal trays.
- You are recording fluid intake for a client. They report in the afternoon they had 2.5 cans of flavoured soda water. Each can holds 355 ml. How many mL is this?
- When caring for a pediatric client, the guardian informs you they gave the child 2.5 teaspoons of children’s Tylenol. You weigh the child and determine the appropriate dose based on their weight is 15 mL. Presuming her teaspoon measurements were precise, was the amount given correct?
- A client has a new prescription for eye drops: One drop in each eye once a day. The client is curious how long the bottle might last and so you help them out with the math. The bottle contains 2.5 mL of fluid. A standard eye drop dispenser releases drops approximately 50 microlitres each. How many days will the bottle likely last for, if the client takes the medication as prescribed and does not waste any drops?
- While discussing effective treatments for constipation on night shift, a senior nurse describes their previous success with milk and molasses enemas to you. While you are researching literature to find out if their anecdotal findings have been experienced by others, you come across a recipe for the treatment: Mix 8-16 oz milk with 8-16 oz molasses and instill slowly. Knowing that a large volume enema can be given safely at a volume of 500-1,000 mL, would this recipe fall in the safe range?

**Answers:**

- 1,150 mL

[latex]x\text{ mL}=\dfrac{\text{1000 mL}}{\text{1 L}}\times\text{1.15 L}[/latex] - 0.237 L

[latex]x\text{ L}=\dfrac{\text{1 L}}{\text{1000 mL}}\times\text{237 mL}[/latex] - 5.819 L

[latex]x\text{ L}=\dfrac{\text{1 L}}{\text{1000 mL}}\times\text{5819 mL}[/latex] - 375 mL

[latex]x\text{ mL}=\dfrac{\text{250 mL}}{\text{1 cup}}\times\text{1.5 cups}[/latex] - 500 mL

[latex]x\text{ mL}=\dfrac{\text{250 mL}}{\text{1 cup}}\times\text{2 cups}[/latex] - 2.555 L

Calculate in two steps:- [latex]\text{1875 mL}+\text{680 mL}=\text{2555 mL}[/latex]
- [latex]x\text{ L}=\dfrac{\text{1 L}}{\text{1000 mL}}\times\text{2555 mL}[/latex]

- 887.5 mL

[latex]x\text{ mL}=\dfrac{\text{355 mL}}{\text{1 can}}\times\text{2.5 cans}[/latex]

- No, not quite enough. She likely gave 12.5 mL.

[latex]x\text{ mL}=\dfrac{\text{5 mL}}{\text{1 tsp}}\times\text{2.5 tsp}[/latex] - 25 days

[latex]x\text{ days}=\dfrac{\text{1 day}}{\text{2 gtts}}\times\dfrac{\text{1 gtt}}{\text{50}\mu\text{L}} \times\dfrac{\text{1000}\mu\text{L}}{\text{1 mL}}\times\text{2.5 mL}[/latex] - Yes, it would be a minimum of 480 mL if 8 oz of milk and 8 oz of molasses was used and a maximum of 960 mL if 16 oz of each were used.

[latex]x\text{ mL}=\dfrac{\text{30 mL}}{\text{1 oz}}\times\text{16 oz}[/latex][latex]x\text{ mL}=\dfrac{\text{30 mL}}{\text{1 oz}}\times\text{32 oz}[/latex]

A conversion factor is a specific number used to change a number with a specific unit to another unit by either multiplying or dividing. The specific number is based on the relationship between the old unit and the new unit.

The order of operations are the rules of which calculation comes first in an expression (when doing expressions with more than one operation).

1. the brackets or parentheses (innermost first)

2. exponent (power)

3. multiplication and division (from left-to-right)

4. addition and subtraction (from left-to-right)

Definition from: Key Concepts of Intermediate Level Math by Meizhong, under a CC BY 4.0 License.