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Dimensional Analysis 

To get the full benefit of Dimensional Analysis ( also called The Factor Label Method of Drug Calculation) it is advised that you do the following

1. Print out this page with both explainations of DA
2. Memorize the conversion factors
3. Get all the math for med questions you can and do them step by step, over and over and over and over again. Soon enough you will be able to do them quickly, easily and accurately.

There are 6 steps...using the conversion factors..like.2.2lbs= 1 kg
 or 1000mg = 1gm..you set the problem up with fractions so that the same
 labels will be diagonally  opposite and canceled out , the answer you want is on the right. ( remember cancelling out in fractions ?

Example     10                   3                        1            3              3
                    ------        x       -------   =          ------- x    ------  =   ----- ( the tens were alike
                      30                    10                   30           1             30    and canceled out)

A baby weighs 14 lbs...how much in kg ?

Six steps

1.IDENTIFY THE LABEL YOU WANT IN THE ANSWER.....kg

   write _____________ = kg

2.IDENTIFY THE THE LABEL YOU ARE STARTING WITH, AND FILL IN THE NUMBER
  AND LABEL

   14lbs               =kg

3. DECIDE WHAT CONVERSION FACTORS YOU NEED TO CONVERT FROM THE LABEL YOU
   HAVE TO THE LABEL YOU WANT

    1 kg = 2.2 lbs

4. PUT THE CONVERSION FACTORS INTO YOUR PROBLEM IN FRACTION FORM

    1 kg        or     2.2 lb
   ------                --------
    2.2 lb               1 kg

   here we will put the fraction with kg on top because kg is the answer we
   want,

    14 lbs  x     1 kg
                         ----     = ? kg
                         2.2 lb

5. CHECK TO SEE IF YOU HAVE SET UP THE PROBLEM CORRECTLY BY CANCELING OUT THE LABELS...if the labels don't cancel out and leave the ones you want, you have not set up the problem correctly


   14 lb  x    1 kg       cross out the labels(  diagonally across from one other)
                    -----
                    2.2 lb

    14  x   1 kg                      ( like labels are canceled..in this example it was the lb)                      
               ------
                2.2

6. DO THE MATH

    14        1 KG              14 KG
    ----  x   -----         =    ---------     =  6.36 KG
                    2.2                 2.2


example I want gm's

 2000mg = ? gm        2000mg x  1 gm  ( this is the conversion factor)
                                                           _____
                                                         1000mg

 cross out the mg's  and do the math

                    2000  x   1 kg       2000kg   = 2 kg
                                     -------  = ------
                                    10000      1000

 another example

 Robaxin 0.3 gm, IM is prescribed. Robaxin injectable is available with
 100mg/ml  Give___________ ml ? (1000mg/1gm is the conversion factor)

 0.3 gm x    1000mg x  ml            cross out all factors that are alike and diagonally
                      ------      ----               opposite..here it is gm and mg
                       1 gm   100 mg         what you have left is

 0.3 x 1000 x    1 ml      300 ml
       ----  ----    =  -----    ---------        = 3 ml
        1    100       100       100


Dr orders heparin 900 u per hour, there are 25,000 u / 500cc d5w ..hep. is used with
pumps in cc's/hr

cross out labels that are alike

900 u        500cc       900      500 cc       450,000 cc         18cc
-----    x   -----             ----- x   -----   =        ---------         =     ----
 hr          25,000 u       hr       25,000        25,000 hr               hr

62 ml/hr = how many gtts/min ( drop factor 10gtts/ml)

62 ml      10 gtts       1 hr
-----  x   ------    x  ------       cross out like labels
 1 hr         1 ml         60 min

62         10 gtt      1         620 gtt      10.33 gtt (round down to
---    x   ------  x ----- =    --------  =   --------   10)
 1           1        60 min     6o min         min

One you get the hang of it, it comes really easy..practice practice practice then you
don't need to look at the steps  at all

Here is some homework..use dimensional analysis : )

1. The order reads Ampicillin 750 mg IV...the vial has 250mg/cc
   How many cc's of Ampicillin will you draw up ?

2. Jeff weighs 75lbs. His IV order is for 100cc/kg/day. On a pediatric
   set ( minifrip = 60gtts/ml)   what will his gtts/minute be ?



 DA  by anyother name - Here they call it The Factor Label Method of Drug Calculation


The Factor Label method of drug calculation (sometimes known as dimensional analysis math for nurses) has the following advantages over the methods currently being taught for drug calculation:

1) It is simpler. All calculations are performed in one step rather than in separate stages.

2) It is more accurate. Since there is only one step, there are no intermediate steps at which answers are rounded off before proceeding. When using conversion factors separately with the proportion method, for instance, for ease in calculation, a weight in kilograms will be rounded off to the nearest tenth before proceeding. With the factor label method, all intermediate results are carried in the calculator memory and are accurate to the capacity of the calculator itself. Rounding off is not done until the last step, which is accepted mathematical practice.

3) It is easy to keep track of the units.

a) The unit of measure is included in the answer automatically.

b) All units other than the answer you are looking for will cancel out automatically. If they do not, you know that you have made an error and are alerted to go back and find it..

c) When done, the units on the left of the equation must match the units that remain on the right of the equation, indicating that the answer found is in the form of the units desired.

Procedure:

1. Place a question mark by the units that you need for your answer, followed by an equal sign.

2. Enter the data that is supplied. As a matter of procedure, I find it helpful to make the doctor’s order the first item after the equal sign. However, in a maximum-minimum dose problem, the first item will be the range data from the label. This is followed by a multiplication sign.

3. Enter any further data or conversion factors, each followed by a multiplication sign, in such a manner that the units of each new factor cancel the units of the preceding factor. (See examples below).

4. Cancel all units possible. (I usually cancel my units as I go since I am deliberately choosing the order of my factors so that they will cancel each other sequentially). This will leave only the units of the answer remaining. Put an equal sign at the end of your string of factors.

5. Multiply across the numerator to obtain a figure. Multiply across the denominator to get a figure.

6. Divide the numerator by the denominator. This is your final answer. Place it after the second equal sign. The units of the answer are the units that were left uncanceled in step 4 above. Check to see that the units of the answer match the units that you were looking for when you started the problem. In practice this will usually take the following form:

? answer units = (doctor’s order/1) (conversion factor #1) (conversion factor #2) (etc.) =  answer in remaining (uncanceled) units

7. Troubleshooting: If your units do not work out properly, you know that you have made a mistake and that the answer you have is wrong. Find your mistake. It will usually be that you failed to invert one of your factors so that it would cancel properly and now you have some unit squared instead of having all the units cancel out. Go through the factors and figure out which one has to be flipped to make everything but the answer units you are looking for cancel out. Occasionally, you will find that you have mislabeled a factor (with IV’s, for instance, it is easy to label the drip factor as ggts/min, for instance, instead of gtts/ml).

8. For those who find the idea of conversion factors intimidating, relax. It’s just a phrase which means "how many of one thing are there in some other thing"? For instance, how many milligrams are there in a gram? A thousand, of course. The trick here is that in mathematics we have to express this information in the form of an equality in order to use it in our equation as a conversion factor. The information therefore ends up looking like this when expressed mathematically:

    1 gm/1000 mg = 1

Since every conversion factor that we use is by definition equal to the number one, and since anything multiplied by the number one remains unchanged, the conversion factors have no effect upon the integrity of the doctor’s order–that is to say, they leave it unchanged. They do, however, convert that order into the form that the nurse needs in order to actually administer the med.

9. Relax. I guarantee you that if all of your units cancel and you have entered the numbers correctly on the calculator, you will in fact have the right answer no matter how complicated the problem is or how many conversion factors you have had to string out one after another to get your units to cancel properly. You pay attention to the units. Let the method worry about the answer.



Practice Math Exam Using Factor Label Method

1. How many mg’s are in 2.3 grams?

   (A)                                     (B)                 (C)

? mg =    2.3 g\m            1000 mg   =   2,300 mg

                   1        X        1 g\m

Grams cancel out leaving only mg, which is therefore the unit of the answer. This is the right answer because the unit you are looking for (mg) in part A of the equation (before the first equal sign) is the same as the unit left uncanceled in part B (between the two equal signs) and this in turn is the same as the unit in part C (after the second equal sign). When working the system on an exam, I actually circle the units in each part of the equation to make sure they match before moving on to the next problem. Three matching circles and it’s time for the next one.

2.

Doctor’s Order: Digoxin 0.25 mg p.o. daily in a.m.

Drug Label: Digoxin 0.125 mg tablet

What will you administer to your client (include unit of measure)?

    ?  tablet   =   0.25 m\g            1 tablet            =   2 tablets

                             1           X     0.125 m\g

3.

Doctor’s Order: Gantrisin 500 mg po q6h

Drug Label: Gantrisin 1 Gm/5 ml

What will you administer to your client (include unit of measure)?

? ml   =   500 m\g             1 g\m                     5 m\l      =    2.5 ml

                    1         X      1000 m\g      X      1 g\m

Here you might ask, "why is 5 ml/1gm treated as a conversion factor? I don’t recall seeing that in any book of physical constants". The reason is that any equality can be used as a conversion factor. Here, one of the givens is that 5 ml = 1 gm. That means that if I divide 5 ml by 1 gm I will get the number one. Any proportion (one thing divided by another) which is equal to the number one will preserve the integrity of the doctor’s order.



4.Doctor’s Order: Morphine 10 mg IM stat

Drug Label: Morphine gr 1/4 /ml

What will you administer to your client (include unit of measure)?



    ? ml    =  10 m\g            60 g\r               1 ml           =     2400 ml     

                      1         X      2 m\g      X      1/4 g\r

2.4 liters IM? Not likely. Go back and get the order clarified.



5.

Doctor’s Order: Dramamine 1.25 mg/kg po q6h prn

Drug Label: Dramamine 25 mg in 2 ml

Child’s weight: 58 pounds

What will you administer to your client (include unit of measure)?

? ml = 1.25 m\g               2 ml             1 k\g           58 l\bs    =    2.6 ml

            1 k\g         X     25 m\g    X    2.2 l\bs    X       1

One thing to note here is that it is totally a matter of convenience how we write our conversion factors. For instance, we know that 1 kg = 2.2 lbs and here we have written that as 1 kg/2.2 lbs, with the kg on the top because we needed it to cancel a kg on the bottom in the doctor’s order. However, since the expression 1 kg/2.2 lbs is equal to the number one, it doesn’t actually matter mathematically whether we put kg on the top or on the bottom. It will still be equal to the number one. This is what permits us to keep flipping conversion factors until we get everything but the answer units to cancel out.



6.

Doctor’s Order: Phenobarbital 400 mg po qd

Drug Label: 5-7 mg/kg day

Client’s weight: 138 pounds



Minimum safe dosage?

?  mg  =  5 mg               1 k\g              138 l\bs     =    313.6 mg

               1 k\g     X      2.2 l\bs     X        1

Maximum safe dosage?

? mg  =    7mg             1 k\g            138 l\bs     =   439.1 mg

               1 k\g    X    2.2 l\bs     X        1

Is this a safe dosage? Yes.

In this problem, the doctor’s order is a blind. At no point do you need the information "400 mg". One of the beauties of this way of doing nursing problems is that, in the event that you did not pick up this fact on your own, the method will pick it up for you and tell you something is wrong. If you try to use "400 mg" anywhere in the equation, all of the units will cancel and you will be left with no units for the answer–which is the functional equivalent of having the oil light flashing on the dashboard of your car.

7. IV Therapy

Doctor’s order: 3000 ml/24 hrs

Drip factor: 15 ggts/ml

Determine ggts per minute

? ggts     =    3000 m\l               1 h\r                 15 ggts     =    31 ggts

   min               24 h\r       X       60 min      X        m\l                min



8. IV Therapy

Doctor’s order: 500 ml of D5NSS with 10,000 units of heparin to infuse at 20 ml/hr.

Determine hourly dosage of heparin. Is this within the safe range for heparin?

a) ? U/hr = 10,000 U           20 m\l      =       400 U

                   500 m\l    X      1 hr                    hr

b) yes



9) Pediatric

Doctor’s order: Dolanex elixir

Client: 4 year old child weighing 30 lbs

Normal adult dose: 325 mg every 3 to 6 hours

Drug label: 325 mg/5 ml

What dose should we give?

? ml  =  30 l\bs               325 m\g                   5 ml           =  1.0 ml

            150 l\bs     X          1               X       325 m\g

Here we have to use Clark’s rule, which calculates pediatric dosage based on a child’s weight as a fraction of 150, the nominal value for adult weight. This fraction is then multiplied by the normal adult dosage for a drug to obtain the pediatric dosage. It is also possible to work this problem using Young’s rule, which calculates pediatric dosage on the basis of age, not weight.

? ml    =       4 ye\ars                    325 m\g               5 ml           =   1.25 ml

                4 + 12 ye\ars     X            1             X      325 m\g



10) Critical care

Doctor’s order: 600 mg dopamine HCL in 500 ml D5W at 20 ml/hr

Client weight: 150 lbs

Is this a safe dosage?

For this problem we have to look up the safe dosage range for dopamine, which turns out to be 2-5 mcg/kg/min. This is therefore a range problem and we will have to work it twice to get the answer, once for the top of the range and once for the bottom. We will also have to work it once more to determine what dosage is actually being given.

a) actual dosage being given


    ?  mcg    =   600 m\g             20 m\l             1000 mcg               1 h\r         =      400 mcg

        min           500 m\l      X       1 h\r      X        1 m\g          X      60 min                  min

b) low end of safe range

    ? mcg    =     2 mcg            150 l\bs                1 k\g          =        136 mcg

       min            k\g/min     X       1            X       2.2 l\bs                    min

c) high end of safe range

?  mcg   =   5 mcg               150 l\bs                  1 k\g          =      340 mcg

    min         k\g/min       X       1               X        2.2 l\bs                  min


d) No. This is not a safe dosage.





Memorize the following equivalents:

Household                                                  Apothecary                                         Metric

15 gtt        =                                                  15 minums                               =        1 ml/cc

                                                                    1 dr                                         =         4 ml/cc

1 tsp.      =                                                                                                             5 ml/cc

1 Tbs      =                                                                                                             15 ml/cc

                                                                    1 fl oz                                    =           30 ml

1 cup                                                             8 fl oz                                   =           240 ml

1 qt         =                                                     32 fl oz                                 =          1000 ml/ 1 L

                                                                      1 gr                                      =            60 mg

                                                                      15 gr                                    =         1000 mg/ 1 gm

2.2 lbs       =                                                                                                            1000 gm/ 1 kg

1 inch        =                                                                                                             2.54 cm