mb101-m8 chapter 01 basic mathematics
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Welcome to
Business Mathematics Course
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elak lIm dWluc
Mathematics for Business
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Lecturer: Lim Delux
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Chapter 01
Basic Mathematics
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Learning Objectives
In this chapter you will learn to :
- Carry out calculations involving wholenumbers
- Carry out calculations involving fractions
- Carry out calculations involving decimals
- Carry out calculations involving exponents
- Use and understand scientific notation
- Use and understand logarithms
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Chapter Outline
Whole numbers
Fractions
Decimals
Exponents
Scientific notation
Logarithms
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Whole Numbers
- Integers: -5,-3,0,2,5 cMnYnKt;
- Whole Numbers: 0,1,2,3 cMnYnKt;viCman
- Natural Numbers: 1,2,3cMnYnKt;;FmCati
Negative integers Positive integers
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Whole Numbers
A digit is defined as one of the numerals
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Example:9- one digit
78- two digits
999- three digits
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Whole Numbers
Write in word of numbers
56 consists of 6 ones and 5 tens
365 consists of 5 ones, 6 tens and 3hundreds
34 998
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Whole Numbers
1 ones or units
10 Tens
100 Hundreds1000 Thousands
10 000 Tens of thousands
100 000 Hundreds of thousands1 000 000 Millions
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Whole Numbers
There are four mathematical operations
1. Multiplication/ Multiply2. Division/ Divide
3. Addition/ Add/Plus
4. Subtraction/ Minus
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Fractions
A fraction is an expression that appears inthe form
a
----
b
a is called numeratorb is called denominator
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Decimals
A decimal consists of three components: aninteger, followed by a decimal point,followed by another integer
Example: 0.3, 0.47
$ 3.030.33
.33
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Decimals
Express as fraction
?
0.3 = ----?
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Exponents
An exponent or power is a number that iswritten as a superscript to another numbercalled the base
an
Where ais called base
nis called exponent or power
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Exponents
- Product
am* an= am + n
- Quotient ( division)am
----- = am - n
an
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Exponents
n mn
m
aa )(
m
m
a
a
1
n
mnnm
i
aa
)1(
1
)(
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Scientific notation
Scientific notation is a shorthand way ofwriting such numbers in a moreconvenient form
Example315.68 = 3.1568* 10 2
0.456 = 4.56 * 10-1
45600 = 4.56 *10 4
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Scientific notation
Scientific notation is a shorthand way ofwriting such numbers in a moreconvenient form
Reference position is immediately to theright of the first non-zero digit
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Logarithms
The logarithm of a number N to a base b is thepower to which b must be raised to obtain N
NblogNx
blog
x
bN
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Logarithms
Characteristic and mantissa
Suppose that the logarithm of a positivenumber is expressed as an integer plus anon-negative decimal fraction
- The integer is called the characteristics
- The decimal fraction is called mantissa
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Logarithms
Example
563.2 = 5.632 *102
Log 563.2 = log (5.632*10 2)
= log 5.632+ log 102
= log 5.632 + 2
Characteristics
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