This document is a breakdown of mathematics and scientific calculations specifically for pharmacy students.
The document (notes) was written by me from my understanding but the reference is gotten from University of Portsmouth solely meant for beginners in the first year of pharmacy course.
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1.1 Powers
Consider the symbol x multiplied by itself 4 items. That is x * x * x * x. A simpler way
of writing this is given by the notation of indices such as x 4. In this expression the x
is called the base number and the 4 is the index. We also say that x raised to the
power of 4 or the fourth power of x.
Why do we use powers?
The number characteristics of scientific measurements are often very large or very
small; thus it is convenient to express those using powers of 10 (or base 10).
Example:
103 = 10 x 10 x 10 = 1000
102 = 10 x 10 = 100
Negative powers
If a number is raised to a negative power e.g. 10-5 then it means (1/10)5
1 1 1 1 1
10-5 = 10 x 10 x 10 x 10 x 10 =0.00001
Table 1.1 : Progression of the scale of decimal powers
Number Exponential Notation
1000 103
100 102
10 101
1 100 All numbers raised to the power of zero are equal to 1
0.1 10-1
0.01 10-2
0.001 10-3
Apart from powers of 10, other powers can also be used. However, in all
cases the general rules are the same.
Quite often the following number e, can be used in calculations. It has got a
numerical value of 2.718281828.
,Example :
1 1 1
e-3 is equal to e x e x e
In a similar manner; 3-3 = 3 x 3 x 3 = 27
1 1 1 1
2-3 = 2 x 2 x 2 = 8 =0.125
Questions on Powers
1. Without using calculators find the following values:
i) 53 = 125
ii) 40 = 1
iii)10-2 = 0.01
iv) e1 = e
v) e0 = 1
2. Without using calculators find the following values
2
i) = 18
3−2
1
ii) −1 = 4
4
22
iii) −2 = 16
2
3. Without using calculators find the following values
2 3
i) 2 + −3 = 24.5
2 2
0
e 1
ii) −3 + −2 = 12
2 2
Units of Measurement
Making observations is fundamental to all science. A quantitative observation
or measurement, always consists of two parts: a number and a scale (called
unit). In 1960, an international agreement set up a system of units called the
International System or the SI system.
Table 1.2.1: The Fundamental SI Units
,Physical Quantity Name of Unit Abbreviation
Mass Kilogram Kg
Length Meter m
Time Second s
Temperature Kelvin K
Electric current Ampere A
Amount of substance Mole mol
Luminous intensity Candela cd
Questions on Unit of measurement
1. If we have 0.25mg of a substance, how can this be expressed in grams?
Ans: 1000 mg = 1 g
0.25mg = x
0.25
X = = 2.5 x 10-4g
1000
2. What is 0.0125 g expressed in mg
Ans: 1g = 1000mg
0.0125g = x
X = 0.0125 x 1000 = 12.5 mg
3. What is 0.00000789 moles expressed in millimoles?
Ans: 1 mole = 1000 millimoles
0.00000789 = x
X = 0.00000789 x 1000 = 7.89 x 10-3 = 0.00789 mmol
4. What is 0.23 μg expressed in kg?
Ans: As 1 μg = 1/1000 mg
And 1mg = 1/1000 g
And 1g = 1/1000 kg
Therefore 1 μg = 1/1,000,000,000 kg
, Or, 1 μg = 10-9 kg
0.23 = x
X = 0.23 x 10-9 = 2.3 x 10-10
5. For each pair, underline (& bold) the larger value. If two values are the
same, underline both.
a) 1 µm, 1 nm b) 1 cm, 1 mm c) 10,000 µm, 10 m d) 1000 g, 1 Kg
6. Carry out the following conversions, giving the required symbol:
a) 0.25 grams to milligrams
Ans: 1g = 1000mg
0.25g = x
X = 0.25 x 1000 = 250 mg
b) 0.00000678 moles to millimoles
Ans: 1 mole = 1000 millimoles
0.00000678 = x
X = 0.00000678 x 1000 = 6.78 x10-3 mmol
c) 456 millilitres to litres
Ans: 1000 ml = 1 L
456 ml = x
456
X = = 0.456 L
1000
d) 471 micrograms to milligrams
Ans: 1 μg = 1/1000mg
471μg = x
X = 471 x 1/1000 = 0.471 mg
e) 250 microlitres to millilitres
Ans: 1 μl = 1/1000 ml
250 μl = x
X = 250 x 1/1000 = 0.250 ml
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