The document provides an overview of the decimal number system, basic arithmetic operations, and the classification of numbers including whole numbers, integers, rational numbers, fractions, and decimals. It includes methods for converting between number systems, performing arithmetic operations, understanding percentages, exponents, and the identification of prime and composite numbers. Examples and applications are given to illustrate each concept clearly.

1. Number System & Basic
Arithmetic Operations
Sana Khurshid
Nursing Lecturer

2. The Decimal Number System
 The decimal number system, also known as the base-10 system, is
the most common numeral system used.
 It is based on ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These
symbols are called digits.

3. For example, in the decimal number 456:
 The digit 6 is in the "ones" place, representing 6 units (10^0).
 The digit 5 is in the "tens" place, representing 5 tens (10^1).
 The digit 4 is in the "hundreds" place, representing 4 hundreds
(10^2).
By combining these digits according to their place values, we get the
value of the entire number: 400 + 50 + 6 = 456.

4. Decimal to Binary
To convert a decimal number to binary, repeatedly divide the
decimal number by 2 and note down the remainders.
 25 ÷ 2 = 12 remainder 1
 12 ÷ 2 = 6 remainder 0
 6 ÷ 2 = 3 remainder 0
 3 ÷ 2 = 1 remainder 1
 1 ÷ 2 = 0 remainder 1

5. Decimal to Octal
 To convert a decimal number to octal, repeatedly divide the
decimal number by 8 and note down the remainders. The octal
representation will be the sequence of remainders read from
bottom to top.
 Example: Convert decimal 42 to octal:
 42 ÷ 8 = 5 remainder 2
 5 ÷ 8 = 0 remainder 5

6. Whole Numbers
 Whole numbers are a set of numbers that includes all the non-
negative integers, starting from zero and extending infinitely in
the positive direction.
 Whole numbers are represented by the set {0, 1, 2, 3, ...}.
 They do not include fractions or decimals.

7. Integers
 Integers are a set of numbers that includes all the whole numbers
(positive, negative, and zero) as well as their negative counterparts.
 Integers are represented by the set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
 They include both positive and negative whole numbers, as well as
zero.

8. Rational Numbers
 Rational numbers are numbers that can be expressed as the
quotient or fraction of two integers, where the denominator is not
zero.
 Rational numbers include integers, as any integer can be expressed
as a fraction with a denominator of 1.
 Rational numbers may be terminating (finite) decimals or repeating
(infinite) decimals.
 They are represented as fractions or as decimals that either
terminate or repeat.
 Examples of rational numbers include 1/2, -3, 0, 0.75, -2.5, 1.333...,
etc.

9. Basic Arithmetic Operations
 Addition
 Subtraction
 Multiplication
 Division

10. Addition
 Whole Numbers: Example: 3 + 5 = 8
 Integers: Example: (-3) + 5 = 2
 Rational Numbers: Example: 1/2 + 3/4 = 5/4 (or 1.25 as a
decimal)

11. Subtraction
 Whole Numbers: Example: 8 - 3 = 5
 Integers: Example: 5 - (-3) = 8
 Rational Numbers: Example: 3/4 - 1/2 = 1/4 (or 0.25 as a
decimal)

12. Multiplication
 Whole Numbers: Example: 4 * 7 = 28
 Integers: Example: (-2) * 3 = -6
 Rational Numbers: Example: 1/2 * 3/4 = 3/8 (or 0.375 as a
decimal)

13. Division
 Whole Numbers: Example: 15 ÷ 3 = 5
 Integers: Example: 10 ÷ (-2) = -5
 Rational Numbers: Example: 3/4 ÷ 1/2 = (3/4) * (2/1) = 3/2 (or
1.5 as a decimal)

14. Fractions
 A fraction represents a part of a whole or a ratio of two quantities.
 It consists of two numbers separated by a horizontal or diagonal
line, called the fraction bar or division bar. The number above the
line is called the numerator, and the number below the line is called
the denominator.
 Fractions can be proper (where the numerator is less than the
denominator), improper (where the numerator is greater than or
equal to the denominator), or mixed numbers (a whole number
combined with a proper fraction).
 Example: 3/4 represents three parts out of four equal parts.

15. Decimals
 Decimals are a way to represent parts of a whole number or
fractions using a decimal point.
 They consist of digits (0-9) and a decimal point, which separates the
whole number part from the fractional part.
 The digits to the left of the decimal point represent the whole
number part, and the digits to the right of the decimal point
represent the fractional part.
 Decimals can be finite (terminating) or infinite (repeating).
 Example: 0.75 represents seventy-five hundredths, which is
equivalent to 3/4.

16. Convert between fractions & decimals
Converting Fractions to Decimals:
 To convert a fraction to a decimal, divide the numerator by the
denominator.
 Example: Convert 3/4 to a decimal: 3/4=3÷4=0.7543​=3÷4=0.75

17. Cont.
Converting Decimals to Fractions:
 To convert a decimal to a fraction, write the decimal as a
fraction with the same value and simplify if necessary.
 Example: Convert 0.5 to a fraction: 0.5 can be written as 5/10.
Since both 5 and 10 can be divided by 5, the simplified
fraction is 1/2

18. Arithmetic operations with fractions &
decimals
Addition

3
4
+
1
2
Subtraction

5
6
−
1
3
Multiplication

2
3
×
3
4
Division

5
6
÷
2
3

19. Percentages
Percentages are a way of expressing a proportion or a ratio as a
fraction of 100. The term "percent" means "per hundred," and
percentages are commonly denoted by the symbol "%".

20. Relation to Fractions
 Example: 3/5​ as a percentage is 3/5×100.
Relation to Decimals
 0.75 as a percentage is 0.75×100.

21. Scenarios
 In a class of 30 students, 20% are studying mathematics. How
many students are studying mathematics?
 You have a meal at a restaurant that costs $60, and you want
to leave a 15% tip. How much should you tip?

22. Exponents & Powers
Exponents:
 An exponent is a small number written above and to the right of a
base number. It indicates how many times the base number is
multiplied by itself.
 In the expression 23, the base is 2, and the exponent is 3. It means that
2 is multiplied by itself 3 times, resulting in 2×2×2.
Powers:
 A power is the result of raising a base number to an exponent. It
represents the value obtained by repeated multiplication of the base.
 In the expression 23, the power is 8, because 23=2×2×2=8.

23. Examples
 23×24
 56÷53
 (32)4
 2−3=1/23 ​= 1/ 8

24. Apply the Order of Operations
 5+3×2
 (8−2)2÷2
 (8−2)2
 4×(6−3)2+5
 10−2×3+4
 8÷2(2+2)

25. Prime Numbers
 A prime number is a natural number greater than 1 that has
exactly two distinct positive divisors: 1 and itself.
 The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and
so on.

26. Composite Numbers
 A composite number is a natural number greater than 1 that
has more than two distinct positive divisors.
 The first few composite numbers are 4, 6, 8, 9, 10, 12, 14, 15,
and so on.

27. Prime Factorization of Composite Numbers
Suppose we want to find the prime factors of the composite
number 48.

28. Any question?