A comprehensive review from basic
math review to critical care
intravenous calculations
• Always check your answer against common
sense.
• Have an idea if your answer will be big or
small.
• Calculators calculate EXACTLY as you put it in.
YOU need to remember order of operations.
• When in doubt, put it into the calculator again
to confirm your answer.
Hundreds
Tens
Ones
. (and)
Tenths
Hundredths
Thousandths
Thousandths
Hundredths
Tenths
. (and)
Ones
Tens
Hundreds
Place value
5
3
1
.
0
6
7
What place value is the 6 in?
Hundreds
Tens
Ones
. (and)
Tenths
Hundredths
Thousandths
To round a number:
1. Look at the number after the
requested place value
2. If that number is 5 or above
(5, 6, 7, 8, 9) round the
requested place value
number up to the next
numeric value
3. If that number is below 5 (1,
2, 3, 4) leave the requested
place value alone.
4. The numbers after the
requested place value either
become zeroes (if before the
decimal) or are left off
entirely (if after the decimal)
5
3
1
.
0
6
7
Round 531.067 to the nearest hundredth:
1. Number after: 7
2. It is 5+ so round up: 6 becomes 7
3. New number is 531.07 (leave off thousandths)
Round 531.067 to the nearest tens place:
1. Number after: 1
2. It is below 5 so leave alone: 3 remains 3
3. New number is 530 (zero for the ones place
and everything else after is left off)
• Addition and Subtraction
– Line up decimals
– Add trailing zeroes as necessary
– Perform the necessary function
53.45 + 21.3 + 7.0006 =
53.45
21.3
+7.0006
81.7506
53.4500
21.3000
+7.0006
81.7506
• Value
– Line up decimals
– Compare numbers from left to right
Compare 3.1 & 3.2
3.1
3.2
3.1 < 3.2
Compare 3.1 & 3.01
3.1
3.01
3.1 > 3.01
Put 4.1, 4.4, 3.1 and 3.06 in
order from least to greatest
4.1
4.4
3.1
3.06
3.06, 3.1, 4.1, 4.4
• Parts of a fraction
Numerator
1
Fraction
bar
4
Denominator
• Add and subtract with like denominators
– Simply add (or subtract) the numerators
– Keep the denominator the same
2
5

1
5

3
5
• Equivalent fractions
3
?
=
5
10
3
x2
6
x?...2
10
Start here!
5
• Add and subtract with unlike denominators
1
2

4

5
1
LCD is
10 (2x5)
Find equivalent
fractions with
LCD then add
2
4
5
x5
x5
5
10
x2
8
x2
10
5
10

8
10

13
10
or 1 103
• Value
– Find equivalent fractions with the same
denominator
– Compare the numerators
2 1 3
Write
, , in order from least to greatest
3 2 5
Common
denominator
is 30 (3*2*5)
New
fractions
:
20
30
15  1  18
In order :
 ,
30  2  30
,
15
,
18
30 30
 3  20  2 
 ,
 
 5  30  3 
• I=1
• V=5
• X = 10
• Add if numbers to right are smaller than those
immediately preceding them (ex: VI = 6)
• Subtract if numbers to right are larger than
those immediately preceding them (ex: IV = 4)
BID
TID
• Twice a day
• Bis in die
PRN
• Three times a
day
• Ter in die
NPO
• As needed
• Pro re nata
IV
SubQ
PR
• Nothing by
mouth
• Nil per os
PO
• intravenous
• Subcutaneous
• Intramuscular
q__h (q2h)
• By rectum
• Per rectum
ac
• By mouth
• Per os
IM
• Every __ hours
• Quaque __
hora
pc
• Before meals
• Ante cibum
• After meals
• Post cibum
Abbreviation
Potential Problem
Preferred Term
U (for unit)
Mistaken as zero, four or cc
Write “unit”
IU (for international unit)
Mistaken as IV or 10
Write “international unit”
QD, QOD (daily and every other day)
Mistaken for each other
Write “daily” and “every other day”
Trailing zero (X.0 mg), No leading zero
(.X mg)
Decimal point is missed
Do NOT use trailing zero (use X mg),
USE leading zero (0.X mg)
MS, MSO4, MgSO4
Confused for one another, can mean
morphine sulfate or magnesium sulfate
Write “morphine sulfate” or
“magnesium sulfate”
g (for microgram)
Mistaken for mg
Write “mcg”
HS (for half-strength or at bedtime)
Mistaken for each other, qHS mistaken
for every hour
Write “half-strength” or “at bedtime”
TIW (for three times a week)
Mistaken for 3 times a day or twice
weekly
Write “3 times weekly” or “three times
weekly”
SC, SQ (for subcutaneous)
Mistaken for SL (sublingual) or “5
every”
Write “Sub-Q”, “subQ” or
“subcutaneous”
D/C (for discharge)
Mistaken for discontinue whatever
medications follow (discharge meds)
Write “discharge”
cc (for cubic centimeter
Mistaken for U (units)
Write “ml” for milliliters
as, ad, au, os, od, ou (for left, right and
both ears and eyes respectively)
Mistaken for each other
Write out “left ear”, etc.
Volume
Length
Weight
Cup [c]
Meter [m]
Pound [lb/#]
Gram [g]
(pt, qt, gal)
(cm, km)
(oz)
(mg, mcg)
Liter [L]
Foot [ft]
(ml)
(inch, yard)
Kilogram [kg]
Grain [gr]
Fluid ounce
[fl. oz]
Tablespoon
[tbs/tbsp]
(tsp)
Mass
Measurements - Systems
• Military time
– Enables quick look at AM/PM distinction
• (eliminates confusion)
– No colon (:)
– AM is always the normal time
• Single digit numbers have a leading 0 (ex – 0800)
– PM is the normal time plus 12
• 3:3O PM would be (3 +12 = 15) 1530
• Adding and subtracting time
– 42 minutes, 1 hour 12 minutes and 38 minutes
(what is the total time this IV bag has infused?)
– Convert all to minutes by multiplying the number
of hours by 60 minutes and add the minutes.
– 42 min + 72 min + 38 min = 152 minutes
– Now convert back to hours by dividing by 60
minutes (152/60 = 2 hours 32 minutes)
– The remainder is the minutes
• Syringe
– Needle syringe – withdraw and measure in upright
position with syringe below medication vial.
– Oral syringe – withdraw and measure vertically
with syringe above medication vial.
• Dose cup
– ALWAYS measure with the cup flat on a counter or
other flat surface.
– Eyes should be level with the dose cup
– Be sure to note the dosage increments
• Distracters – extra information that is NOT needed to solve
the problem.
An adult patient comes into the hospital with an acute infection. The
doctor orders Ampicillin 500 mg IM q4h. The hospital stores Ampicillin
500mg in powdered form. The directions for reconstitution state to add 1.8
ml of diluent to yield a concentration of 250 mg/ml. How much Ampicillin
will the nurse give the patient?
• What information is unnecessary for the solving this problem?
• After getting rid of the distracters, re-read the problem.
The doctor orders Ampicillin 500 mg IM q4h. After reconstituting,
Ampicillin yields a concentration of 250 mg/ml. How much Ampicillin will
the nurse give the patient?
Skim the problem.
Note the requested information
What
answer is
the problem
looking for?
Underline IMPORTANT information
If distracters are distracting, cross them out.
When you get an answer ALWAYS go back and look to see if it makes sense.
Rework problem if necessary
You wouldn’t
give 20 pills,
would you?
•
•
•
•
•
1 cc = 1 ml
1000mg = 1 g
1000 mcg (µg) = 1 mg
1 tbsp = 3 tsp
1 tsp = 5 ml
•
•
•
•
1 oz = 30 ml
1 gr = 60 – 65 mg
1 cup = 8 fl. oz
1 kg = 2.2 lb
• Use units to help determine how to set up the problem…
– if the units are right, you KNOW you’re right.
• Process of cancelling units
• No memorized formulas
• Works with ANY kind of problem!
• Go back to the question
and determine the unit
requested
What unit is
wanted
Wanted unit
on TOP
• Always start with the
unit that is specified in
problem on top
• Fill in the other units
such that they cancel out
• If an undesired unit is on
top, put it on bottom in
the next part
Fill in units
The doctor orders spironolactone 25mg for a
patient experiencing mild heart failure. The nurse
has 50 mg tablets of spironolactone on hand. How
many tablets will the nurse administer?
x tab 
x tab 
1 tab
x tab 
1 tab
50 mg
The doctor orders Diabinese 0.1 g po daily for a
patient with type 2 diabetes. The nurse has
Diabinese 100 mg tablets in the Pyxis. How many
tablets will the nurse administer?
x tab 
x tab 
1 tab
x tab 
1 tab
100 mg
x tab 
1 tab
100 mg
x
1000 mg
1g
A client is ordered 50 milligrams of Amoxicillin
trihydrate orally. 125 milligrams in 5 milliliters of
Syrup is available. How many milliliters will you
administer?
x ml 
x ml 
5 ml
x ml 
5 ml
125 mg
The doctor has ordered promethazine with codeine
gr 1/6 po q6h prn for cough. On hand is
promethazine with codeine solution 10mg per 5 ml.
How much syrup should the nurse administer?
x ml 
x ml 
5 ml
x ml 
5 ml
10 mg
x ml 
5 ml
10 mg
x
60 mg
1 gr
The medication order states that 12,000 units of
heparin are to be added to 250 milliliters of D5W. The
patient is to receive 1200 units per hour IV. How many
milliliters per hour will your patient receive?
x
ml
hr

250 ml
12000 units
x
1200 units
1hr
 25
ml
hr
The doctor orders D5LR 1500 ml IV to run for 12
hours on a postoperative patient. The tubing has a
drop factor of 20 gtt/ml. How many gtt/min will the
nurse count out in order to comply with this order?
x
gtt
min

x
gtt
min

20 gtt
1ml
x
gtt
min

20 gtt
1ml
x
1500 ml
12 hrs
Your shift is 0700 to 1500. You make rounds at 0730 and find an IV of D5 ½ NS
is regulated on an electronic infusion pump at the ordered rate of 75 ml/hr
with 400 ml remaining. The order specifies a continuous infusion. At what
time should you anticipate hanging the next IV bag?
How long until
the bag is
empty
Convert it to
hours
0730  5 hr 20 min  1250
Check and
change IV bag
on or before
1250 or 12:50
PM
Order: dicloxacillin sodium 125 mg po q6h for a child who weighs 55 lb. The
recommended dosage of dicloxacillin sodium for children weighing less than 40
kg is 12.5 to 25 mg/kg/day po in equally divided doses q6h for moderate to severe
infections. Is this dosage safe?
Safe
Dose!
The recommended dosage of tobramycin for adults with
serious infections that are not life-threatening is 3
mg/kg/day in 3 equally divided doses q8h. What should
you expect the total daily dosage of tobramycin to be for
an adult with a serious infection who weighs 80kg?
x
mg
day

3 mg
kg  day
x
80 kg
 240
mg
day
The doctor orders Procainamide 1 g IV in 500 ml
D5W to infuse at 2 mg/min for a patient you are
caring for in the ICU. You should program the IV
pump at what rate?
x
ml
hr

500 ml
1g
x
1g
1000 mg
x
2 mg
1 min
x
60 min
1hr
 60
ml
hr
The doctor orders dobutamine IV to increase the
patient’s cardiac output. The dobutamine is
supplied at a concentration of 250 mg in 250 ml
D5W. The doctor orders the dobutamine to infuse
at 5 mcg/kg/min. The patient weighs 176 lbs. At
what rate should the nurse program the IV pump?
x
ml
hr

250 ml
250 mg
x
1mg
1000 mcg
x
5 mcg
1kg  min
x
60 min
1hr
x
1kg
2 . 2 lb
x
176 lb
 24
ml
hr