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Chapter Contents
INTRODUCTION
What are real numbers?
• Real numbers are the set of numbers that include all rational and irrational numbers.
Real numbers are denoted by the symbol R.
Rational numbers are
•
Those numbers that can be written in the form
p q , where p and q are integers and q ≠ 0.
• They consist of both fractions (such as 1 2 , −3 4 , 5 6 ), as well as integers (such as −3, −2, −1, 0, 1, 2, and 3), as every integer can be represented as fractions with denominator 1.
For example:
– The integer 5 can be expressed as the fraction 5 1 .
– The integer −3 can be expressed as the fraction −3 1 .
• Rational numbers can be written in decimal forms also which can be both
terminating ( 1 5 = 0.2) or non-terminating ( 1 3 = 0.3̅)
p q , where p and q are integers and q ≠ 0.
• They consist of both fractions (such as 1 2 , −3 4 , 5 6 ), as well as integers (such as −3, −2, −1, 0, 1, 2, and 3), as every integer can be represented as fractions with denominator 1.
For example:
– The integer 5 can be expressed as the fraction 5 1 .
– The integer −3 can be expressed as the fraction −3 1 .
• Rational numbers can be written in decimal forms also which can be both
terminating ( 1 5 = 0.2) or non-terminating ( 1 3 = 0.3̅)
INTRODUCTION
•Irrational numbers, on the other hand, cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. They include numbers like π (pi), √2 (the square root of 2). Irrational numbers are infinite in nature and have an infinite number of non-repeating decimal places.
CHART FOR REAL NUMBERS
