Ch 1 Arithmetic Needed for Dosage
Fractions
Decimals
Percents
Ratios
Proportions
Ch 2 Interpreting the Language of Prescriptions
Abbreviations
English
SI – Metric System
Apothecary
Routes of Administration
Ch 3 Drug Labels and Packaging
How to read drug labels
Ch 4 Metric, Apothecary, Household Systems of
Measurement
Ch 5 Drug Preparations and Equipment to
Measure Doses
Ch 6 Calculations of Oral Medication – Solid and
Liquid forms
1
Ch 7 Liquids for Injection
Ch 8 Calculation of Basic IV Drip Rates
Microdrips
Macrodrips
PUMPs
Ch 9 Special Types of Calculations
Ch 10 Dosage Problems for Infants and Children
Is it Safe???
Low range --- High range
Ch 11 Dimensional Analysis
__10mg__ x __1g___ =
1000mg
1/100 g = 0.01 g
Ch 12 Information Basic to Administering Drugs
Ch 13 Administration Procedures
2
Ch 1 Arithmetic Needed for Dosage
Multiply Divide Add Subtract
Order of Operations
PEMDAS
Parentheses
Exponentiations
Multiplication
Division
Addition
Subtraction
(5+6)^7/8*4
Rule for Rounding (p.11)
When the number to be dropped is 5 or more,
drop the number and add 1 to the previous
number. When the last number is 4 or less, drop
the number. Round the following to the nearest
hundredth
.450
.451
.452
.453
.454
.455
.456
3
.457
.458
.459
Convert Fraction to Decimal: divide the
numerator by the denominator
Convert any number to Percent: multiply the
number by 100 (moving decimal point two
places to the right)
0.0045 x 100 = 0.45%
0.045 x 100 = 4.5%
0.45 x 100 = 45%
4.50 x 100 = 450 %
45 x 100 = 4500 %
Convert percent to decimal: divide the number
(5) by 100 (moving decimal point two places to
the left)
650 % /100 = 6.50
65 % /100 = 0.65
6.5 % /100 = 0.065
0.65 % /100 = 0.0065
0.065 % /100 = 0.00065
4
Significant Figures
Taken from:
http://en.wikipedia.org/wiki/Significant_figures
Identifying significant digits
1. All non-zero digits are significant. Example: '123.45' has five
significant figures: 1,2,3,4 and 5.
45.6666655555666 15 significant digits
2. Zeros appearing in between two non-zero digits are
significant. Example: '101.12' has five significant figures: 1,0,1,1,2.
0.34450078
8 significant
3. All zeros appearing to the right of an understood decimal
point and non-zero digits are significant. Example: '12.2300'
has six significant figures: 1,2,2,3,0 and 0. The number '0.00122300'
still only has six significant figures (the zeros before the '1' are not
significant).
15.65000
7 significant
0.000122400 6 significant figures
0.010 2 significant figures
4. All zeros appearing in a number without a decimal point
and to the right of the last non-zero digit are not significant
unless indicated by a bar. Example: '1300' has two significant
figures: 1 and 3. The zeros are not considered significant because
they don't have a bar. However, 1300.0 has five significant figures.
2600 2 significant figures (zeros are after non-zero digits AND
there is NO decimal point)
5
2600.0 five significant figures
600 1 sf
601 3 sf
600.0 4 sf
0.600 3 sf
0.00600 3 sf
0.000600 3 sf
0.00060 2 sf
0.0006 1 sf
Round that number to nearest thousandth = 0.001
Round 0.0004 to nearest thousandth = 0.000
However, this last convention is not universally used; it is often necessary to
determine from context whether trailing zeros in a number without a decimal
point are intended to be significant.
Digits may be important without being 'significant' in this usage. For
instance, the zeros in '1300' or '0.005' are not considered significant digits, but
are still important as placeholders that establish the number's magnitude.
A number with all zero digits (e.g. '0.000') has no significant digits, because the
uncertainty is larger than the actual measurement.
1
3
0
0
Thousand hundred ten one
0.1 3 1 3 0 0
Tenth hundredth thousandth ten-thousandth
6
Rounding conventions
When rounding to n significant digits, there are a few general rules that are followed:[1]




If the digit immediately to the right of the nth significant digit is greater than 5, the
number is rounded up.
If the digit immediately to the right of the nth significant digit is less than 5, the
number is rounded down.
If the digit immediately to the right of the nth significant digit is 5 and there are
non-zero digits after the 5, the number is rounded up.
If the digit immediately to the right of the nth significant digit is 5 and there are no
subsequent non-zero digits, there are two commonly-used conventions (see
rounding for longer discussion). In 'common rounding', such a digit is always
rounded up; in 'unbiased rounding' (also known as 'round-to-even'), it is rounded
in whichever direction leaves the nth digit even. For instance, under unbiased
rounding, 51.5 would be rounded up to 52, but 54.5 would be rounded down to
54.
Ratio and Proportion
1:10 (1/10) one to ten
3:5 :: 4:7 3 is to 5 AS 4 is to 7
3:5 :: X:7 Solve for x!!!!
Product of the Outer digits = product of inner
digits
3x7=5xX
21=5x
X=21/5 (fraction form)
X = 4.2 (decimal form)
Order: 0.5mg of drug A
7
Supply: A liquid labeled 0.125 mg per 4 mL
.5mg
= x mL
0.125 mg
4 mL
0.5 mg x 4mL = 16 mL
0.125 mg
10:x :: 12 : 35 Solve for x!
10 x 35 = 12 x X
X = 350/12 = 29.16666666 (repeating
decimal)=> 29.17 => 29.2 => 29 (rounded to
the nearest number)
1a-16 Property tax : value of the house
3000: 250000
1a-23
4
0.16 = 16/100 = 4/25
25
8
1a-20
3 x 12 = 36
4 x 12
48
3+4 = 7
84/7 = 12
Num + dem = 84
3/5
SUM of num and denom = 64
3+5 = 8
64/8 = 8 (multiple needed for num and denom)
3 x8 = 24
5 x8
40
1a-12 lcd for 8, 12, 21
8x1=8
8 x 2 = 16
8 x 3 = 24
12 x 1 = 12
12 x 2 = 24
21 x 1
21 X 2
…
21 X 8 = 168
9
WHEN IN A HURRY: multiply each denominator
value with each other to get a common
denominator
1a-25
4 (1/5) – 2(2/3)
=21/5 - 8/3 = (21x3)/15 - (8x5)/15
= 63/15 – 40/15 = 23/15 = 1 8/15
9dimes:6 quarters -> 90cents/125cents
9d x 2n/d: 6q x 5/q
18 n/30n = 3/5
21/51 = used
(51-21) = 30/51 = 10/17
24 hours in a day
16hr/24 = 2/3
1 inch = 24 miles
6 inches = 24 x 6 = 144 mi
1:6 :: 24:x
10
4 + 10 + 6 = 20 m
14/20
500-50=450x(3/5) =270
84/(3/4) = 84/.75 = 112
PRIME NUMBER = any number that can be
divisible by 1 and divisible by itself
1, 3, 5 , 7, 11, 13, 17, 19, 23, 29, 31
Area = length x width
3/7 x 2/3 = 2/7 sq ft
.375
375/1000 = 15/40 = 3/8
0.000453 = 3 sf
0.000
19 +21 + 20 + 22 + 1 + 10 + 0
.1x + .25(25-x) = 3.55
.1x + 6.25 - .25x = 3.55
-.15x = -2.70
11
X=18
A = LxW
P = 2L + 2W = 2(17.8 ft) + 2(12.2 ft)
= 35.6 ft + 24.4 ft = 60.0 ft
31 = 361.15
33 = x
X= 384.45
Total hours = 45.25
40 hr regular
5.25 hr
Pay = 40x15 + 5.25 x 15 x 1.5 = 718.13
.16 -> 16/100 = 4/25
.086 2 sf
86/1000 = 43/500
0.000250 3 sf
0.012560 -> 0.01 nearest hundredth
0.013 nearest thousandth
12
18/119 = .1513
15/98 = .1531
16 oz/1.65 = 26.4
14/1.44 = 9.722
C = 9.60x + 1250.00
X =5050
Cost = 9.6(5050) + 1250
0.3322
- 0.1224
.3322 x .1224
13
http://en.wikipedia.org/wiki/Significant_figures
1. All non-zero digits are significant. Example: '123.45' has five significant figures:
1,2,3,4 and 5.
2. Zeros appearing in between two non-zero digits are significant. Example: '101.12' has
five significant figures: 1,0,1,1,2.
3. All zeros appearing to the right of an understood decimal point and non-zero digits are
significant. Example: '12.2300' has six significant figures: 1,2,2,3,0 and 0. The number
'0.00122300' still only has six significant figures (the zeros before the '1' are not
significant).
4. All zeros appearing in a number without a decimal point and to the right of the last
non-zero digit are not significant unless indicated by a bar. Example: '1300' has two
significant figures: 1 and 3. The zeros are not considered significant because they don't
have a bar. However, 1300.0 has five significant figures.
However, this last convention is not universally used; it is often necessary to determine
from context whether trailing zeros in a number without a decimal point are intended to
be significant.
Digits may be important without being 'significant' in this usage. For instance, the zeros
in '1300' or '0.005' are not considered significant digits, but are still important as
placeholders that establish the number's magnitude. A number with all zero digits (e.g.
'0.000') has no significant digits, because the uncertainty is larger than the actual
measurement.
14