Number System and Basic Arithmetic Operations
Introduction:
• The number system forms the foundation of quantitative reasoning,
encompassing various types of numbers and their operations.
• Understanding the number system is crucial for performing basic arithmetic
operations and solving quantitative problems.
Types of Numbers:
1. Natural Numbers (N): Integers greater than zero, used for counting.
Example: 1, 2, 3, ...
2. Whole Numbers (W): Natural numbers along with zero. Example: 0, 1, 2, 3, ...
3. Integers (Z): Positive and negative whole numbers including zero. Example: -
3, -2, -1, 0, 1, 2, 3, ...
4. Rational Numbers (Q): Numbers expressible as a quotient or fraction of
integers, including terminating and repeating decimals. Example: 1/2, 0.75, -
3.25, 2.333...
5. Irrational Numbers: Numbers that cannot be expressed as fractions, such as
π (pi) and √2. Example: π (approximately 3.14159), √2 (approximately 1.41421)
6. Real Numbers (R): Combination of rational and irrational numbers,
representing all points on the number line.
7. Complex Numbers (C): Numbers in the form of a + bi, where 'a' and 'b' are
real numbers, and 'i' represents the imaginary unit (√-1).
Basic Arithmetic Operations:
1. Addition (+): Combining two or more numbers to find their sum. Example: 3
+5=8
2. Subtraction (-): Finding the difference between two numbers. Example: 10 - 4
=6
3. Multiplication (×): Repeated addition or grouping of numbers. Example: 4 ×
3 = 12
4. Division (÷): Distributing a quantity into equal parts or finding how many
times one number is contained within another. Example: 20 ÷ 5 = 4
5. Exponentiation (^): Raising a number to a power, indicating repeated
multiplication. Example: 2^3 = 2 × 2 × 2 = 8
6. Root Extraction (√): Finding a number that, when multiplied by itself a
certain number of times, equals a given value. Example: √9 = 3, since 3 × 3 =
9
7. Order of Operations (PEMDAS/BODMAS): Following a specific sequence in
solving expressions involving multiple operations (Parentheses, Exponents,
Introduction:
• The number system forms the foundation of quantitative reasoning,
encompassing various types of numbers and their operations.
• Understanding the number system is crucial for performing basic arithmetic
operations and solving quantitative problems.
Types of Numbers:
1. Natural Numbers (N): Integers greater than zero, used for counting.
Example: 1, 2, 3, ...
2. Whole Numbers (W): Natural numbers along with zero. Example: 0, 1, 2, 3, ...
3. Integers (Z): Positive and negative whole numbers including zero. Example: -
3, -2, -1, 0, 1, 2, 3, ...
4. Rational Numbers (Q): Numbers expressible as a quotient or fraction of
integers, including terminating and repeating decimals. Example: 1/2, 0.75, -
3.25, 2.333...
5. Irrational Numbers: Numbers that cannot be expressed as fractions, such as
π (pi) and √2. Example: π (approximately 3.14159), √2 (approximately 1.41421)
6. Real Numbers (R): Combination of rational and irrational numbers,
representing all points on the number line.
7. Complex Numbers (C): Numbers in the form of a + bi, where 'a' and 'b' are
real numbers, and 'i' represents the imaginary unit (√-1).
Basic Arithmetic Operations:
1. Addition (+): Combining two or more numbers to find their sum. Example: 3
+5=8
2. Subtraction (-): Finding the difference between two numbers. Example: 10 - 4
=6
3. Multiplication (×): Repeated addition or grouping of numbers. Example: 4 ×
3 = 12
4. Division (÷): Distributing a quantity into equal parts or finding how many
times one number is contained within another. Example: 20 ÷ 5 = 4
5. Exponentiation (^): Raising a number to a power, indicating repeated
multiplication. Example: 2^3 = 2 × 2 × 2 = 8
6. Root Extraction (√): Finding a number that, when multiplied by itself a
certain number of times, equals a given value. Example: √9 = 3, since 3 × 3 =
9
7. Order of Operations (PEMDAS/BODMAS): Following a specific sequence in
solving expressions involving multiple operations (Parentheses, Exponents,
