Lecture 3: Reading Medication Labels and Basic Dosage Calculations

There are two different ways in which drugs can be administered, often referred to as routes. Drugs may be given orally, by mouth, or injected; medications that are injected are called parenteral medication.

Oral Medications

Many medicines are given by mouth. The abbreviation for medication to be given by mouth is p.o. or PO, which is an abbreviation of the Latin phrase "per os," meaning "by mouth."

Oral medications generally come in 3 forms: tablets, capsules, and liquid. Tablets are pills that are solid; tablets can be split in half if they have a score, or line, in the middle of them. However tablets cannot be cut into smaller pieces such as thirds or fourths. Here is a sample picture of some tablets (notice the score down the middle of the one at the left, where it can be cut in half):


tablets

Capsules are pills that contain liquid or powder, usually in some kind of gelatin cover; capsules can never be broken into smaller pieces because the power or liquid they contain would fall out; therefore doses of capsules must always be in whole numbers. Below are a few pictures of different kinds of capsules:

capsules containing
powder

capsules containing
liquid

When giving a patient an oral medication in pill form, it is never safe to give more than 3 pills. If you have to give more than 3 pills to administer an ordered dosage, you should look for pills with a higher dosage, so that you can give fewer or them, and/or you should check the drug order for safety.

As a general rule, if you have a choice of more than one pill dosage (for example, the pills you want may come in 2 versions: one kind may contain 50 mg and the other kind may contain 100 mg), you should always choose a combination that will result in the smallest number of pills for the patient to swallow. It's also generally better to give whole pills and avoid splitting pills if possible. For example, let us suppose the scored tablets for the drug a patient has been prescribed come in 50 mg or 100 mg dosages. If we have a drug order to give the patient 150 mg of this drug, we have several choices: we can give the patient 3 50-mg tablets, or we can give the patient 1.5 100-mg tablets, or we can give the patient 1 50-mg tablet and 1 100-mg tablet. All three of these choices would be safe. Since the second and third options involve giving fewer pills, we should choose one of those, and since the third option does not require us to split any pills in half, that is the best option.

Not all oral medication comes in pill form, however. Many oral medications are given as liquids. Oral medication for small children or infants will generally be in liquid form, since they cannot swallow pills. Below are photographs of some of the containers often used for dosage of liquid oral drugs:
an oral syringe
another kind of oral syringe
using an oral syringe
to dose an infant
a calibrated oral dropper
a calibrated medicine spoon
a calibrated medicine cup

Adults generally take liquid oral medication by using a calibrated medicine cup of some kind, but droppers, spoons, and oral syringes are often used for dosing small children and infants who may not be able to drink from a cup. It is also important to note that you should never use an oral syringe to give injectable medication, because oral syringes are not sterile.

Parenteral Medications

Routes of Administering Parenteral Medications

Parenteral medications are any medications given by injection. Injection is usually given in one of three different ways:

  • Subcutaneously (subQ): A subcutaneous injection is one that is given in the fatty layer of tissue under the skin. The maximum amount of fluid an adult can safely be given subcutaneously is 1 mL. (Sometimes you may see this abbreviated as s.c., SC, s.q., or SQ, but you should never abbreviate it this way, since these outdated abbreviations have often been misread.)

  • Intramuscularly (IM): An intramuscular injection is one that is given in the muscle. The maximum amount of fluid an adult can safely be given intramuscularly is 3 mL; for a child, the maximum is 1 mL.

  • Intravenously (IV): An intravenous injection is one that is given directly into the vein. Much higher amounts of fluids can be given intravenouly; in fact, the limit on the amount of fluid that can be given intravenously is generally only capped by the limit on the amount of fluid a patient can take in each day (for a healthy patient this range is usually 35-50 mL/kg body weight/day, but this amount can vary greatly depending upon the condition of the patient).

Note the abbreviations for subcutaneously, intramuscularly, and intravenously: subQ, IM, and IV, respectively. We will wait until later lectures to learn in depth about IV medication; for the moment, we will give subQ, IM, and IV medications using syringes only.

Types of Syringes Used for Parenteral Medication

There are several different sizes of syringes that might be used for medication. You should always use the smallest possible syringe in which the dosage will fit, because the smaller the syringe, the more accurately you can measure the dosage:

  • 3 mL syringe (3 cc syringe) : This is the most commonly used syringe. As it's name suggests, it holds a total of 3 mL of fluid. Every tenth of a mL is marked on the syringe, and every half mL is labeled; this means that any dosage we plan to measure using a 3 mL syringe should be rounded to the nearest tenth.

    Dosages between 1-3 mL should always be measured in a 3 mL syringe.

    Some 3 mL syringes have the mL scale to the right and a minim scale to the left; be careful not to measure mL on the minim scale, as this will result in an incorrect dosage!

    3 mL syringe with
    minims marked on the left

    3 mL syringe without
    minims marked

  • Tuberculin syringe: A tuberculin syringe is used to measure small doses, so it is often used to dose small children and infants. There are two different sizes of tuberculin syringes which you might encounter: one kind can hold a total of 1 mL, and another kind can hold a total of 0.5 mL; every hundredth of a mL is marked on a tuberculin syringe, and every fifth of a mL is labeled; this means that any dose we plan to administer with a tuberculin syringe should be rounded to the nearest hundredth.

    Any dose smaller than 0.5 mL should be measured using a tuberculin syringe, and any dose less than 1 mL can be more accurately measured using a tuberculin syringe, if a tuberculin syringe which holds 1 mL is available. Because a tuberculin syringe has every hundredth of a mL marked whereas the 3 mL syringe has only every tenth of a mL marked, it is possible to measure doses with more accuracy in a tuberculin syringe.

    1 mL tuberculin syringe
    0.5 mL tuberculin syringe

  • 5-12 mL syringes: When an IV dose requires a syringe that can hold more than 3 mL, a 5, 6, 10, or 12 mL syringe can be used. On each of these size syringes, every 0.2, or two tenths, is marked, so be very careful not to misread a mark as one tenth of a mL !

    Dosages between 3-12 mL should be measured using one of these syringes; always choose the smallest possible syringe in which the dose will fit to ensure the highest level of accuracy.
    5 mL syringe
    6 mL syringe
    10 mL syringe
    12 mL syringe

  • 20 mL (or more) syringes: Occasionally it is necessary to use even larger syringes to measure IV fluids. In this case there are syringes that can measure a maximum of 20 mL or more; these syringes only have every mL marked.

    Any dosage above 12 mL must be measured using a 20 mL syringe or larger.


    20 mL syringe syringe

  • Tubex and Carpuject cartridges: These are special pre-filled cartridges produced by two specific companies that can be dropped into a plastic injector with a plunger for injection. The ones we will encounter in this class will have markings every tenth of a mL and will contain up to 2.5 mL of fluid.
    Tubex cartridge

    Carpuject cartridge

Measuring Dosages in a Syringe

To measure a dosage in a syringe, we must line up the top of the black rubber plunger exactly with the line that marks the dosage we want to administer.

Example:

If we look closely, we can see that this syringe has the top of the black rubber stopper lined up with the third mark past the 2. Since this is a 3 mL syringe and has every tenth of a mL marked, that means that we are three tenths past 2, which is a total of 2.3 mL.

Example:

If we look closely, we can see that this syringe has the top of the black rubber stopper lined up with the first mark past the 1/2 which follows the 2. Since this is a 3 mL syringe and has every tenth of a mL marked, that means that we are one tenth past 2.5, which is a total of 2.6 mL.

Example:

If we look closely, we can see that this syringe has the top of the black rubber stopper lined up with the third mark past the 4. Since this is a 6 mL syringe and has every 0.2 mL marked, that means that we are three 0.2s past 4, which is a total of 4.6 mL.

Example:

If we look closely, we can see that this syringe has the top of the black rubber stopper lined up with the second mark past the 10. Since this is a 12 mL syringe and has every 0.2 mL marked, that means that we are two 0.2s past 10, which is a total of 10.4 mL.

Example:

If we look closely, we can see that this syringe has the top of the black rubber stopper lined up with the second mark past the 10. Since this is a 20 mL syringe and has every whole mL marked, that means that we are two whole mL past 10, which is a total of 12 mL.

Example:

If we look closely, we can see that this syringe has the top of the black rubber stopper lined up with the third mark past the .60. Since this is a tuerculin syringe and has every hundredth of a mL marked, that means that we are three hundredths of a mL past 0.6, which is a total of 0.63 mL.

Reading Medication Labels and Calculating Dosages

Reading Medication Labels

Before we can even begin to calculate how much medicine to give a patient, we must be able to read a medication label correctly. There are several important pieces of information we should look for whenever we look at a medication label:

  1. Name of the medication
    There are actually at least two names on every medication label:

    • The trade name is the name assigned to the drug by the manufacturer and it varies from one company to another. A single drug may have many different trade names if it is manufactured and sold by many different companies. The trade name of a drug is usually capitalized.
      For example, you may be familiar with the over-the-counter pain relievers Advil and Motrin. These are actually two different brand names for the same drug that is manufactured by two different companies.

    • The generic name is the name assigned to the drug officially in the United States. There is only one generic name for each drug, and all drug labels must list the drug's generic name in addition to any trade names so that the drug can be identified by its offical name. The generic name of a drug is generally written in lower case letters.
      So, Motrin and Advil are trade names that each refer to the same drug, and its offical generic name is ibuprofen. If you look closely at a bottle of Advil or Motrin, you will see that the labels on each bottle state that they contain ibuprofen.

    A drug may be ordered by its brand name or by its generic name, so it is very important to pay attention to both kinds of drug names so that you can identify a drug by either one when it is ordered.

  2. Dosage units
    These are units which are used to measure the drug's weight or action and are the units used whenever an order is written for the drug.
    The most common dosage units are milligrams, grams, micrograms, grains, Units and milliequivalents.

  3. Administration units
    These are units which are used to measure the drug for actual administration to the patient.
    Because it would be very difficult to measure a drug by it's weight or action, we usually measure drugs by their volume or by counting a number of tablets or capsules when we actually want to take out the exact amount we want to give the patient.
    The most common administration units are tablets, capsules, teaspoons, tablespoons, ounces, drops, liters, and milliliters.

  4. Concentration or Dosage strength
    This tells us what the relationship is between the dosage units and the administration units.
    Because almost all drugs are ordered in dosage units but administered in administration units, we must have a way to convert from one set of units to the other; this is what the concentration of a drug allows us to do.

  5. Total amount of the drug contained in the package
    This is exactly what it sounds like: the total number of dosage units or administration units contained in a particular package of the drug.

  6. Expiration date
    All drugs have an expiration date on them, usually prefaced by the abbreviation EXP.; you should always check that the current date is before the drug's expiration date before you give a drug to a patient.

Sample Medication Labels

To better understand the different pieces of information on a drug label, let's look at a few examples:

Example:

  1. Trade name: Verelan
    Generic name: verapamil HCl

  2. Dosage units: mg

  3. Administration units: cap

  4. Concentration: Each capsule is 120 mg.
    Notice that the label just says 120 mg, but does not say whether this is the amount for a single pill or for the whole package; for packages containing pills, a single dosage like this always represents the amount per pill. Be careful though, because if a medicine is measured by volume, a single dosage represents the total amount in the package, NOT the amount per mL.

  5. Total amount in the package: 100 capsules

Example:

  1. Trade name: Thorazine
    Generic name: chlorpromazine HCl

  2. Dosage units: mg

  3. Administration units: mL

  4. Concentration: 25 mg/mL
    This means that there are 25 mg in each 1 mL.

  5. Total amount in the package: 10 mL

Example:

  1. Trade name: Procan SR
    Generic name: procainamide HCl

  2. Dosage units: mg
    This one is a little tricky because the label does not actually state what the units are! However, because mg are the most commonly used units for drug dosages, we are supposed to assume that the 750 on the label means 750 mg. If we are uncertain, we should look inside the package for the package insert, which should state the dosage information in more detail.

  3. Administration units: tab

  4. Concentration: Each tablet is 750 mg.
    Notice that the label just says 750, but does not say whether this is the amount for a single pill or for the whole package; for packages containing pills, a single dosage like this always represents the amount per pill. Be careful though, because if a medicine is measured by volume, a single dosage represents the total amount in the package, NOT the amount per mL.

  5. Total amount in the package: this label does not say - we may need to look at the package insert to find this information if we really want to know

Example:

  1. Trade name: Cleocin Phosphate
    Generic name: clindamycin phosphate

  2. Dosage units: mg

  3. Administration units: mL

  4. Concentration: 900 mg per 6 mL
    The label does not phrase it exactly this way, but if we look closely, we see that the label says that this package contains 900 mg. Because this is a liquid, and not in pill form, we know that this stands for the amount in the whole package. So in order to find out how many mg are in a mL: we already know the number of mg in the whole package, so now we need to see how many mL there are in the whole package - if we look closely at the top we see that this package contains one vial that holds 6 mL total. So there are 900 mg per 6 mL. (If we wanted to, we could simplify this to 150 mg/mL by dividing both numbers by 6, but we don't have to do this unless we want to.)

  5. Total amount in the package: 900 mg, 6 mL
    Notice that this package gives us the total number of dosage units and the total number of administration units. In other words, it gives us two different ways to measure the same total amount of drug in the package. There is a total of 900 mg of the drug in this package; with this particular drug in its given concentration mix, this is the same thing as saying that there are 6 mL of this drug in the package because every 6 mL of this drug contains 900 mg of Cleocin Phospate - one of these measurements measures the mass of the drug itself, and the other one of these measurements measures the volume of the drug in liquid form.

Calculating the Amount of a Drug Needed to Administer a Particular Dosage

When a patient is given an order for a particular drug, that order almost always requests the drug in dosage units such as milligrams, grams, micrograms, grains, Units and milliequivalents. However, to actually measure out the medicine and give it to the patient, we cannot measure milligrams, grams, micrograms, grains, Units and milliequivalents; instead we need to measure the drug by taking out the correct number of pills or the correct volume of the liquid to give to the patient.

So, we need to convert dosage units to administration units before we can give a patient any medication. To see how we might calculate this, we look at several examples:

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: pentozifylline 600 mg

First we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:

_____tab=

Since the ordered dosage is 600 mg, we need to figure out how many tab it takes to make 600 mg:

_____tab=600 mg

So, in order to do this, we must convert 600 mg into tab, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 600 mg

  • and which will also cancel out the mg units we don't want and introduce the tab units we do want.

Where can we find a fraction like this? The concentration given on the label is 400 mg per tab. This tells us that 1 tab is equal to 400 mg, so if we write this as a fraction, it becomes:

1 tab
400 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 tab
    400 mg
    and
    400 mg
    1 tab
    . Why did we choose
    1 tab
    400 mg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has tab on the top, which will introduce the unit tab, which we need!

So, this yields:

_____tab=

600 mg
1
×
1 tab
400 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____tab=

600 mg×1 tab
1×400 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____tab=

600 mg×1 tab
1×400 mg

Now we simplify and multiply out the fraction:

We can divide both 600 and 400 by 200 to get:

_____tab=

6003 mg×1 tab
1×4002 mg

Writing this out more neatly yields:

_____tab=

3×1 tab
1×2

There is nothing now in this fraction that can be simplified, so we multiply 3 by 1 to get 3. Then we divide 3 by 2 to get 1.5.

So, our answer is 1.5 tab.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: Cipro 0.75 g

First we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:

_____tab=

Since the ordered dosage is 0.75 g, we need to figure out how many tab it takes to make 0.75 g:

_____tab=0.75 g

If we look closely, we notice that while the order is written in g, the label actually uses mg. We we need to convert g into mg if we want to be able to do any calculations that use the information given on the label.

So, in order to do this, we must convert 0.75 g into mg, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.75 g

  • and which will also cancel out the g units we don't want and introduce the mg units we do want.

Where can we find a fraction like this?

Well, we know that 1 g=1000 mg. If we write this as a fraction, it becomes:

1000 mg
1 g

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1000 mg
    1 g
    and
    1 g
    1000 mg
    . Why did we choose
    1000 mg
    1 g
    ?

    • It has g on the bottom, which will cancel out the g on the top.

    • And it has mg on the top, which will introduce the unit mg, which we need!

So, this yields:

_____tab=

0.75 g
1
×
1000 mg
1 g

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____tab=

0.75 g×1000 mg
1×1 g

We can then cancel the g which appears in both the top and the bottom of the fraction on the right:

_____tab=

0.75 g×1000 mg
1×1 g

So, now we must find a way to convert mg into tab. In order to do this, we must convert 0.75 g into tab, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.75 g

  • and which will also cancel out the g units we don't want and introduce the tab units we do want.

Where can we find a fraction like this? The concentration given on the label is 250 mg per tab. This tells us that 1 tab is equal to 250 mg, so if we write this as a fraction, it becomes:

1 tab
250 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 tab
    250 mg
    and
    250 mg
    1 tab
    . Why did we choose
    1 tab
    250 mg
    ?

    • It has g on the bottom, which will cancel out the g on the top.

    • And it has tab on the top, which will introduce the unit tab, which we need!

So, this yields:

_____tab=

0.75 g×1000 mg
1×1 g
×
1 tab
250 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____tab=

0.75 g×1000 mg×1 tab
1×1 g×250 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____tab=

0.75 g×1000 mg×1 tab
1×1 g×250 mg

Now we simplify and multiply out the fraction:

We can divide both 250 and 1000 by 250 to get:

_____tab=

0.75 g×10004 mg×1 tab
1×1 g×2501 g

Writing this out more neatly yields:

_____tab=

0.75×4×1 tab
1×1×1

There is nothing now in this fraction that can be simplified, so we multiply 0.75, 4 and 1 to get 3. And we multiply 1 and 1 to get 1. Then we divide 3 by 1 to get 3.

So, our answer is 3 tab.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: Verelan 240 mg

First we look at the label and see that this medication is administered in cap, so we are looking for our answer to be in cap:

_____cap=

Since the ordered dosage is 240 mg, we need to figure out how many cap it takes to make 240 mg:

_____cap=240 mg

So, in order to do this, we must convert 240 mg into cap, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 240 mg

  • and which will also cancel out the mg units we don't want and introduce the cap units we do want.

Where can we find a fraction like this? The concentration given on the label is 120 mg cap. This tells us that 1 cap is equal to 120 mg, so if we write this as a fraction, it becomes:

1 cap
120 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 cap
    120 mg
    and
    120 mg
    1 cap
    . Why did we choose
    1 cap
    120 mg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has cap on the top, which will introduce the unit cap, which we need!

So, this yields:

_____cap=

240 mg
1
×
1 cap
120 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____cap=

240 mg×1 cap
1×120 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____cap=

240 mg×1 cap
1×120 mg

Now we simplify and multiply out the fraction:

We can divide both 240 and 120 by 120 to get:

_____cap=

2402 mg×1 cap
1×1201 mg

Writing this out more neatly yields:

_____cap=

2×1 cap
1×1

There is nothing now in this fraction that can be simplified, so we multiply 2 by 1 to get 2. Then we divide 2 by 1 to get 2.

So, our answer is 2 cap.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: Augmentin 150 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 150 mg, we need to figure out how many mL it takes to make 150 mg:

_____mL=150 mg

So, in order to do this, we must convert 150 mg into mL, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 150 mg

  • and which will also cancel out the mg units we don't want and introduce the mL units we do want.

Where can we find a fraction like this? The concentration given on the label is 125 mg/5 mL. This tells us that 5 mL is equal to 125 mg, so if we write this as a fraction, it becomes:

5 mL
125 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    5 mL
    125 mg
    and
    125 mg
    5 mL
    . Why did we choose
    5 mL
    125 mg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

150 mg
1
×
5 mL
125 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

150 mg×5 mL
1×125 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

150 mg×5 mL
1×125 mg

Now we simplify and multiply out the fraction:

We can divide both 5 and 125 by 5 to get:

_____mL=

150 mg×51 mL
1×12525 mg

We can divide both 150 and 25 by 25 to get:

_____mL=

1506 mg×51 mL
1×125251 mg

Writing this out more neatly yields:

_____mL=

6×1 mL
1×1

There is nothing now in this fraction that can be simplified, so we multiply 6 by 1 to get 6. Then we divide 6 by 1 to get 6.

So, our answer is 6 mL.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: phenobarbital 30 mg

First we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:

_____tab=

Since the ordered dosage is 30 mg, we need to figure out how many tab it takes to make 30 mg:

_____tab=30 mg

So, in order to do this, we must convert 30 mg into tab, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 30 mg

  • and which will also cancel out the mg units we don't want and introduce the tab units we do want.

Where can we find a fraction like this? The concentration given on the label is 15 mg tab. This tells us that 1 tab is equal to 15 mg, so if we write this as a fraction, it becomes:

1 tab
15 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 tab
    15 mg
    and
    15 mg
    1 tab
    . Why did we choose
    1 tab
    15 mg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has tab on the top, which will introduce the unit tab, which we need!

So, this yields:

_____tab=

30 mg
1
×
1 tab
15 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____tab=

30 mg×1 tab
1×15 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____tab=

30 mg×1 tab
1×15 mg

Now we simplify and multiply out the fraction:

We can divide both 30 and 15 by 15 to get:

_____tab=

302 mg×1 tab
1×151 mg

Writing this out more neatly yields:

_____tab=

2×1 tab
1×1

There is nothing now in this fraction that can be simplified, so we multiply 2 by 1 to get 2. Then we divide 2 by 1 to get 2.

So, our answer is 2 tab.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: Synthroid 0.3 mg

First we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:

_____tab=

Since the ordered dosage is 0.3 mg, we need to figure out how many tab it takes to make 0.3 mg:

_____tab=0.3 mg

If we look closely, we notice that while the order is written in mg, the label actually uses mcg. We we need to convert mg into mcg if we want to be able to do any calculations that use the information given on the label.

So, in order to do this, we must convert 0.3 mg into mcg, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.3 mg

  • and which will also cancel out the mg units we don't want and introduce the mcg units we do want.

Where can we find a fraction like this?

Well, we know that 1 mg=1000 mcg. If we write this as a fraction, it becomes:

1000 mcg
1 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1000 mcg
    1 mg
    and
    1 mg
    1000 mcg
    . Why did we choose
    1000 mcg
    1 mg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mcg on the top, which will introduce the unit mcg, which we need!

So, this yields:

_____tab=

0.3 mg
1
×
1000 mcg
1 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____tab=

0.3 mg×1000 mcg
1×1 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____tab=

0.3 mg×1000 mcg
1×1 mg

So, now we must find a way to convert mcg into tab. In order to do this, we must convert 0.3 mg into tab, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.3 mg

  • and which will also cancel out the mg units we don't want and introduce the tab units we do want.

Where can we find a fraction like this? The concentration given on the label is 150 mcg tab. This tells us that 1 tab is equal to 150 mcg, so if we write this as a fraction, it becomes:

1 tab
150 mcg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 tab
    150 mcg
    and
    150 mcg
    1 tab
    . Why did we choose
    1 tab
    150 mcg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has tab on the top, which will introduce the unit tab, which we need!

So, this yields:

_____tab=

0.3 mg×1000 mcg
1×1 mg
×
1 tab
150 mcg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____tab=

0.3 mg×1000 mcg×1 tab
1×1 mg×150 mcg

We can then cancel the mcg which appears in both the top and the bottom of the fraction on the right:

_____tab=

0.3 mg×1000 mcg×1 tab
1×1 mg×150 mcg

Now we simplify and multiply out the fraction:

We can divide both 150 and 1000 by 50 to get:

_____tab=

0.3 mg×100020 mcg×1 tab
1×1 mg×1503 mg

Writing this out more neatly yields:

_____tab=

0.3×20×1 tab
1×1×3

There is nothing now in this fraction that can be simplified, so we multiply 0.3, 20 and 1 to get 6. And we multiply 1 and 3 to get 3. Then we divide 6 by 3 to get 2.

So, our answer is 2 tab.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: Procan 1.5 g

First we look at the label and see that this medication is administered in tab, so we are looking for our answer to be in tab:

_____tab=

Since the ordered dosage is 1.5 g, we need to figure out how many tab it takes to make 1.5 g:

_____tab=1.5 g

If we look closely, we notice that while the order is written in g, the label actually uses mg. We we need to convert g into mg if we want to be able to do any calculations that use the information given on the label.

So, in order to do this, we must convert 1.5 g into mg, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 1.5 g

  • and which will also cancel out the g units we don't want and introduce the mg units we do want.

Where can we find a fraction like this?

Well, we know that 1 g=1000 mg. If we write this as a fraction, it becomes:

1000 mg
1 g

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1000 mg
    1 g
    and
    1 g
    1000 mg
    . Why did we choose
    1000 mg
    1 g
    ?

    • It has g on the bottom, which will cancel out the g on the top.

    • And it has mg on the top, which will introduce the unit mg, which we need!

So, this yields:

_____tab=

1.5 g
1
×
1000 mg
1 g

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____tab=

1.5 g×1000 mg
1×1 g

We can then cancel the g which appears in both the top and the bottom of the fraction on the right:

_____tab=

1.5 g×1000 mg
1×1 g

So, now we must find a way to convert mg into tab. In order to do this, we must convert 1.5 g into tab, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 1.5 g

  • and which will also cancel out the g units we don't want and introduce the tab units we do want.

Where can we find a fraction like this? The concentration given on the label is 750 mg tab. This tells us that 1 tab is equal to 750 mg, so if we write this as a fraction, it becomes:

1 tab
750 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 tab
    750 mg
    and
    750 mg
    1 tab
    . Why did we choose
    1 tab
    750 mg
    ?

    • It has g on the bottom, which will cancel out the g on the top.

    • And it has tab on the top, which will introduce the unit tab, which we need!

So, this yields:

_____tab=

1.5 g×1000 mg
1×1 g
×
1 tab
750 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____tab=

1.5 g×1000 mg×1 tab
1×1 g×750 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____tab=

1.5 g×1000 mg×1 tab
1×1 g×750 mg

Now we simplify and multiply out the fraction:

We can divide both 750 and 1000 by 250 to get:

_____tab=

1.5 g×10004 mg×1 tab
1×1 g×7503 g

Writing this out more neatly yields:

_____tab=

1.5×4×1 tab
1×1×3

There is nothing now in this fraction that can be simplified, so we multiply 1.5, 4 and 1 to get 6. And we multiply 1 and 3 to get 3. Then we divide 6 by 3 to get 2.

So, our answer is 2 tab.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: cefaclor 0.5 g

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 0.5 g, we need to figure out how many mL it takes to make 0.5 g:

_____mL=0.5 g

If we look closely, we notice that while the order is written in g, the label actually uses mg. We we need to convert g into mg if we want to be able to do any calculations that use the information given on the label.

So, in order to do this, we must convert 0.5 g into mg, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.5 g

  • and which will also cancel out the g units we don't want and introduce the mg units we do want.

Where can we find a fraction like this?

Well, we know that 1 g=1000 mg. If we write this as a fraction, it becomes:

1000 mg
1 g

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1000 mg
    1 g
    and
    1 g
    1000 mg
    . Why did we choose
    1000 mg
    1 g
    ?

    • It has g on the bottom, which will cancel out the g on the top.

    • And it has mg on the top, which will introduce the unit mg, which we need!

So, this yields:

_____mL=

0.5 g
1
×
1000 mg
1 g

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

0.5 g×1000 mg
1×1 g

We can then cancel the g which appears in both the top and the bottom of the fraction on the right:

_____mL=

0.5 g×1000 mg
1×1 g

So, now we must find a way to convert mg into mL. In order to do this, we must convert 0.5 g into mL, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.5 g

  • and which will also cancel out the g units we don't want and introduce the mL units we do want.

Where can we find a fraction like this? The concentration given on the label is 250 mg per 5 mL. This tells us that 5 mL is equal to 250 mg, so if we write this as a fraction, it becomes:

5 mL
250 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    5 mL
    250 mg
    and
    250 mg
    5 mL
    . Why did we choose
    5 mL
    250 mg
    ?

    • It has g on the bottom, which will cancel out the g on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

0.5 g×1000 mg
1×1 g
×
5 mL
250 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

0.5 g×1000 mg×5 mL
1×1 g×250 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

0.5 g×1000 mg×5 mL
1×1 g×250 mg

Now we simplify and multiply out the fraction:

We can divide both 5 and 250 by 5 to get:

_____mL=

0.5 g×1000 mg×51 mL
1×1 g×25050 g

We can divide both 50 and 1000 by 50 to get:

_____mL=

0.5 g×100020 mg×51 mL
1×1 g×501 g

Writing this out more neatly yields:

_____mL=

0.5×20×1 mL
1×1×1

There is nothing now in this fraction that can be simplified, so we multiply 0.5, 20 and 1 to get 10. And we multiply 1 and 1 to get 1. Then we divide 10 by 1 to get 10.

So, our answer is 10 mL.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: heparin 3000 U

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 3000 U, we need to figure out how many mL it takes to make 3000 U:

_____mL=3000 U

So, in order to do this, we must convert 3000 U into mL, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 3000 U

  • and which will also cancel out the U units we don't want and introduce the mL units we do want.

Where can we find a fraction like this? The concentration given on the label is 5000 U/mL. This tells us that 1 mL is equal to 5000 U, so if we write this as a fraction, it becomes:

1 mL
5000 U

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 mL
    5000 U
    and
    5000 U
    1 mL
    . Why did we choose
    1 mL
    5000 U
    ?

    • It has U on the bottom, which will cancel out the U on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

3000 U
1
×
1 mL
5000 U

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

3000 U×1 mL
1×5000 U

We can then cancel the U which appears in both the top and the bottom of the fraction on the right:

_____mL=

3000 U×1 mL
1×5000 U

Now we simplify and multiply out the fraction:

We can divide both 3000 and 5000 by 1000 to get:

_____mL=

30003 U×1 mL
1×50005 U

Writing this out more neatly yields:

_____mL=

3×1 mL
1×5

There is nothing now in this fraction that can be simplified, so we multiply 3 by 1 to get 3. Then we divide 3 by 5 to get 0.6.

So, our answer is 0.6 mL.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: furosemide 5 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 5 mg, we need to figure out how many mL it takes to make 5 mg:

_____mL=5 mg

So, in order to do this, we must convert 5 mg into mL, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 5 mg

  • and which will also cancel out the mg units we don't want and introduce the mL units we do want.

Where can we find a fraction like this? The concentration given on the label is 20 mg/2 mL. This tells us that 2 mL is equal to 20 mg, so if we write this as a fraction, it becomes:

2 mL
20 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    2 mL
    20 mg
    and
    20 mg
    2 mL
    . Why did we choose
    2 mL
    20 mg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

5 mg
1
×
2 mL
20 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

5 mg×2 mL
1×20 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

5 mg×2 mL
1×20 mg

Now we simplify and multiply out the fraction:

We can divide both 2 and 20 by 2 to get:

_____mL=

5 mg×21 mL
1×2010 mg

We can divide both 5 and 10 by 5 to get:

_____mL=

51 mg×21 mL
1×20102 mg

Writing this out more neatly yields:

_____mL=

1×1 mL
1×2

There is nothing now in this fraction that can be simplified, so we multiply 1 by 1 to get 1. Then we divide 1 by 2 to get 0.5.

So, our answer is 0.5 mL.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: Cleocin Phosphate 450 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 450 mg, we need to figure out how many mL it takes to make 450 mg:

_____mL=450 mg

So, in order to do this, we must convert 450 mg into mL, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 450 mg

  • and which will also cancel out the mg units we don't want and introduce the mL units we do want.

Where can we find a fraction like this? The concentration given on the label is 900 mg in 6 mL. This tells us that 6 mL is equal to 900 mg, so if we write this as a fraction, it becomes:

6 mL
900 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    6 mL
    900 mg
    and
    900 mg
    6 mL
    . Why did we choose
    6 mL
    900 mg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

450 mg
1
×
6 mL
900 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

450 mg×6 mL
1×900 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

450 mg×6 mL
1×900 mg

Now we simplify and multiply out the fraction:

We can divide both 6 and 900 by 6 to get:

_____mL=

450 mg×61 mL
1×900150 mg

We can divide both 450 and 150 by 150 to get:

_____mL=

4503 mg×61 mL
1×9001501 mg

Writing this out more neatly yields:

_____mL=

3×1 mL
1×1

There is nothing now in this fraction that can be simplified, so we multiply 3 by 1 to get 3. Then we divide 3 by 1 to get 3.

So, our answer is 3 mL.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: Atropine 0.5 mg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 0.5 mg, we need to figure out how many mL it takes to make 0.5 mg:

_____mL=0.5 mg

If we look closely, we notice that while the order is written in mg, the label actually uses mcg. We we need to convert mg into mcg if we want to be able to do any calculations that use the information given on the label.

So, in order to do this, we must convert 0.5 mg into mcg, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.5 mg

  • and which will also cancel out the mg units we don't want and introduce the mcg units we do want.

Where can we find a fraction like this?

Well, we know that 1 mg=1000 mcg. If we write this as a fraction, it becomes:

1000 mcg
1 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1000 mcg
    1 mg
    and
    1 mg
    1000 mcg
    . Why did we choose
    1000 mcg
    1 mg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mcg on the top, which will introduce the unit mcg, which we need!

So, this yields:

_____mL=

0.5 mg
1
×
1000 mcg
1 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

0.5 mg×1000 mcg
1×1 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

0.5 mg×1000 mcg
1×1 mg

So, now we must find a way to convert mcg into mL. In order to do this, we must convert 0.5 mg into mL, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.5 mg

  • and which will also cancel out the mg units we don't want and introduce the mL units we do want.

Where can we find a fraction like this? The concentration given on the label is 400 mcg/mL. This tells us that 1 mL is equal to 400 mcg, so if we write this as a fraction, it becomes:

1 mL
400 mcg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 mL
    400 mcg
    and
    400 mcg
    1 mL
    . Why did we choose
    1 mL
    400 mcg
    ?

    • It has mg on the bottom, which will cancel out the mg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

0.5 mg×1000 mcg
1×1 mg
×
1 mL
400 mcg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

0.5 mg×1000 mcg×1 mL
1×1 mg×400 mcg

We can then cancel the mcg which appears in both the top and the bottom of the fraction on the right:

_____mL=

0.5 mg×1000 mcg×1 mL
1×1 mg×400 mcg

Now we simplify and multiply out the fraction:

We can divide both 400 and 1000 by 200 to get:

_____mL=

0.5 mg×10005 mcg×1 mL
1×1 mg×4002 mg

Writing this out more neatly yields:

_____mL=

0.5×5×1 mL
1×1×2

There is nothing now in this fraction that can be simplified, so we multiply 0.5, 5 and 1 to get 2.5. And we multiply 1 and 2 to get 2. Then we divide 2.5 by 2 to get 1.25.

So, our answer is 1.25 mL.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: cyanocobalamin 600 mcgmcgis mcg

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 600 mcg, we need to figure out how many mL it takes to make 600 mcg:

_____mL=600 mcg

If we look closely, we notice that while the order is written in mcg, the label actually uses mg. We we need to convert mcg into mg if we want to be able to do any calculations that use the information given on the label.

So, in order to do this, we must convert 600 mcg into mg, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 600 mcg

  • and which will also cancel out the mcg units we don't want and introduce the mg units we do want.

Where can we find a fraction like this?

Well, we know that 1000 mcg=1 mg. If we write this as a fraction, it becomes:

1 mg
1000 mcg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 mg
    1000 mcg
    and
    1000 mcg
    1 mg
    . Why did we choose
    1 mg
    1000 mcg
    ?

    • It has mcg on the bottom, which will cancel out the mcg on the top.

    • And it has mg on the top, which will introduce the unit mg, which we need!

So, this yields:

_____mL=

600 mcg
1
×
1 mg
1000 mcg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

600 mcg×1 mg
1×1000 mcg

We can then cancel the mcg which appears in both the top and the bottom of the fraction on the right:

_____mL=

600 mcg×1 mg
1×1000 mcg

So, now we must find a way to convert mg into mL. In order to do this, we must convert 600 mcg into mL, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 600 mcg

  • and which will also cancel out the mcg units we don't want and introduce the mL units we do want.

Where can we find a fraction like this? The concentration given on the label is 1 mg/mL. This tells us that 1 mL is equal to 1 mg, so if we write this as a fraction, it becomes:

1 mL
1 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 mL
    1 mg
    and
    1 mg
    1 mL
    . Why did we choose
    1 mL
    1 mg
    ?

    • It has mcg on the bottom, which will cancel out the mcg on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

600 mcg×1 mg
1×1000 mcg
×
1 mL
1 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

600 mcg×1 mg×1 mL
1×1000 mcg×1 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

600 mcg×1 mg×1 mL
1×1000 mcg×1 mg

Now we simplify and multiply out the fraction:

We can divide both 600 and 1000 by 200 to get:

_____mL=

6003 mcg×1 mg×1 mL
1×10005 mcg×1 mcg

Writing this out more neatly yields:

_____mL=

3×1×1 mL
1×5×1

There is nothing now in this fraction that can be simplified, so we multiply 3, 1 and 1 to get 3. And we multiply 5 and 1 to get 5. Then we divide 3 by 5 to get 0.6.

So, our answer is 0.6 mL.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: calcium gluconate 1.86 mEq

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 1.86 mEq, we need to figure out how many mL it takes to make 1.86 mEq:

_____mL=1.86 mEq

So, in order to do this, we must convert 1.86 mEq into mL, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 1.86 mEq

  • and which will also cancel out the mEq units we don't want and introduce the mL units we do want.

Where can we find a fraction like this? The concentration given on the label is 0.465 mEq/mL. This tells us that 1 mL is equal to 0.465 mEq, so if we write this as a fraction, it becomes:

1 mL
0.465 mEq

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 mL
    0.465 mEq
    and
    0.465 mEq
    1 mL
    . Why did we choose
    1 mL
    0.465 mEq
    ?

    • It has mEq on the bottom, which will cancel out the mEq on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

1.86 mEq
1
×
1 mL
0.465 mEq

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

1.86 mEq×1 mL
1×0.465 mEq

We can then cancel the mEq which appears in both the top and the bottom of the fraction on the right:

_____mL=

1.86 mEq×1 mL
1×0.465 mEq

Now we simplify and multiply out the fraction:

Writing this out more neatly yields:

_____mL=

1.86×1 mL
1×0.465

There is nothing now in this fraction that can be simplified, so we multiply 1.86 by 1 to get 1.86. Then we divide 1.86 by 0.465 to get 4.

So, our answer is 4 mL.

Example:

Calculate the number of tab, cap, or mL needed to administer the dosage below:
Order: medroxyprogesterone 0.1 g

First we look at the label and see that this medication is administered in mL, so we are looking for our answer to be in mL:

_____mL=

Since the ordered dosage is 0.1 g, we need to figure out how many mL it takes to make 0.1 g:

_____mL=0.1 g

If we look closely, we notice that while the order is written in g, the label actually uses mg. We we need to convert g into mg if we want to be able to do any calculations that use the information given on the label.

So, in order to do this, we must convert 0.1 g into mg, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.1 g

  • and which will also cancel out the g units we don't want and introduce the mg units we do want.

Where can we find a fraction like this?

Well, we know that 1 g=1000 mg. If we write this as a fraction, it becomes:

1000 mg
1 g

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1000 mg
    1 g
    and
    1 g
    1000 mg
    . Why did we choose
    1000 mg
    1 g
    ?

    • It has g on the bottom, which will cancel out the g on the top.

    • And it has mg on the top, which will introduce the unit mg, which we need!

So, this yields:

_____mL=

0.1 g
1
×
1000 mg
1 g

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

0.1 g×1000 mg
1×1 g

We can then cancel the g which appears in both the top and the bottom of the fraction on the right:

_____mL=

0.1 g×1000 mg
1×1 g

So, now we must find a way to convert mg into mL. In order to do this, we must convert 0.1 g into mL, and the only way to do this is to multiply by a fraction that

  • is actually equal to one, so it does not change the value of 0.1 g

  • and which will also cancel out the g units we don't want and introduce the mL units we do want.

Where can we find a fraction like this? The concentration given on the label is 400 mg per mL. This tells us that 1 mL is equal to 400 mg, so if we write this as a fraction, it becomes:

1 mL
400 mg

 

  • This fraction is equal to one because the top is equal to the bottom.

  • There were actually 2 possibilities:

    1 mL
    400 mg
    and
    400 mg
    1 mL
    . Why did we choose
    1 mL
    400 mg
    ?

    • It has g on the bottom, which will cancel out the g on the top.

    • And it has mL on the top, which will introduce the unit mL, which we need!

So, this yields:

_____mL=

0.1 g×1000 mg
1×1 g
×
1 mL
400 mg

We recall that to multiply fractions, we just multiply across the top and then multiply across the bottom, so this equals:

_____mL=

0.1 g×1000 mg×1 mL
1×1 g×400 mg

We can then cancel the mg which appears in both the top and the bottom of the fraction on the right:

_____mL=

0.1 g×1000 mg×1 mL
1×1 g×400 mg

Now we simplify and multiply out the fraction:

We can divide both 400 and 1000 by 200 to get:

_____mL=

0.1 g×10005 mg×1 mL
1×1 g×4002 g

Writing this out more neatly yields:

_____mL=

0.1×5×1 mL
1×1×2

There is nothing now in this fraction that can be simplified, so we multiply 0.1, 5 and 1 to get 0.5. And we multiply 1 and 2 to get 2. Then we divide 0.5 by 2 to get 0.25.

So, our answer is 0.25 mL.

Other Methods for Doing Dosage Calculations

Throughout this course, we will show you how to do dosage calculations using a method called dimensional analysis. All the examples you have seen above use this method. However, if you would prefer to try some other methods for solving these kinds of problems, read chapters 14-16 in your book. First you should work to master one method; once you understand how to solve problems correctly using one method, it can be good to use an alternate method to check your work.