# cal-1

```Scope of pharmaceutical calculations
Units of Measurement
Two systems are widely used:
1) CGS system or Metric system
2) MKS system or SI (System International)
Fractions and Multiples
Pico- (p)
10-12
0.000000000001
Nano- (n)
10-9
0.000000001
Micro- (µ)
10-6
0.000001
Milli- (m)
10-3
0.001
Centi- (c)
10-2
0.01
Deci- (d)
10-1
0.1
Main unit
1
1
Deka-
101
10
Hecto-
102
100
Kilo- (k)
103
1000
Myria-
104
10,000
Mega- (M)
106
1000,000
Giga- (G)
109
1000,000,000
Tera- (T)
1012
1000,000,000,000
Fundamental Dimensions:
Length, Mass, Time, electric charge, temperature
Derived Dimensions:
Area, Volume, Force, Density, Work etc.
Dimensions
Metric/ CGS
SI/ MKS
Length (L)
Centimeter (cm) Meter (m)
Mass (M)
Gram (g)
Kilogram (kg)
Time (T)
Second (sec)
Second (s)
Some important derived units
Dimensions19
Dimensional
symbol
Metric/ CGS
SI/ MKS
Area (A)
L2
cm2
M2
Volume (V)
L3
cm3 (cc)
m3, dm3
Density (d,  )
ML-3
g/cm3
kg m-3
Velocity (v, u)
LT-1
cm/sec
m s-1
Acceleration (a)
LT-2
cm/sec2
m s-2
Force (F, f)
MLT-2
g cm/sec2 or
dyne
kg m s-2 or N
Pressure (P, p)
ML-1T-2
dyne/cm2
N m-2 or Pa
ML2T-2
dyne cm or
g cm2/sec2 or
erg
kg m2 s-2 or
N m or J
Energy (E)
N = Newton, Pa = Pascal, J = Joule
Volume:
1 liter (L) = 1000 ml = 1000 cm3 (cc)
1ml = 1 cm3 (CC)
Energy:
1 J = 107 ergs
Rules of Exponents
1.
2.
3.
4.
5.
6.
7.
8.
a x a x a = a3
am x an = am+n
(am)n = am x n
am / an = am-n
a-m = 1/am
a° = 1
a0.5 = a1/2 = √a
(a / b)m = am / bm
Logarithm

Common Logarithm: base 10
102 = 100
Therefore, log10 100 = log100 = 2
And antilog 2= 100
10 x = y Therefore log10 y = log y = x
 Natural logarithm: base e
(e=2.71828……..)
If, ex = y then, x = loge y = ln y
ln x = 2.303 log x
Rules of Logarithm
1)
2)
3)
4)
5)
6)
7)
8)
Log ab = log a + log b
Log a/b = log a - log b
Log 1 = 0 since 10° =1
Log 1/a = log 1 - log a = -log a
Log a2 = 2 log a
Log an = n log a
Log √a = log a1/2 = 0.5log a = ½ log a
Log a-2 = -2 log a = 2 log 1/a
Proportional set of numbers and
Proportionality constant
x
5
10
15
20
25
30
y
10
20
30
40
50
60
y / x = 10 / 5 = 20 / 10 = 30 / 15 = 40 / 20 = 50 / 25 =
60 / 30 = 2
Therefore y / x = constant.
These are proportional set of numbers.
y = 2 x x or y ∞ x ( y is directly proportional to x)
2 is known as the proportionality constant.
y = k x x , k is the proportionality constant.
y = f (x) , y is a function of x
If y ∞ 1 / x then y is said to be inversely proportional to x
x
5
10
15
20
25
30
y
0.2
0.1
0.06
0.05
0.04
0.03
```