what is the difference between an irrational number and integer
An irrational number is a number that cannot be expressed as a ratio of two integers and has a non-repeating, non-terminating decimal expansion. Examples of irrational numbers include √2, π, and e.
An integer, on the other hand, is a whole number that can be positive, negative, or zero. Examples of integers include -3, 0, and 7.
Therefore, the main difference between irrational numbers and integers is that irrational numbers cannot be expressed as fractions with integer denominators, while integers can.
An irrational number and an integer are both types of numbers, but they are different in terms of their properties and representation.
1. Integer:
- An integer is a whole number that can be positive, negative, or zero.
- Integers include numbers like -3, -2, -1, 0, 1, 2, 3, etc.
- They can be written without fractional or decimal parts and can be represented on a number line.
- Integers can be operated upon using addition, subtraction, multiplication, and division operations.
2. Irrational number:
- An irrational number is a real number that cannot be expressed as a simple fraction or ratio of two integers.
- Irrational numbers include numbers like √2, √3, π (pi), e (Euler's number), etc.
- They cannot be written as a finite or repeating decimal.
- Irrational numbers have an infinite number of decimal places that do not repeat or terminate.
- They are represented using radical symbols (√), decimal approximations, or by using mathematical expressions.
- Irrational numbers are not closed under operations like addition, subtraction, and division. For example, adding or subtracting irrational numbers may result in another irrational number or a rational number.
In summary, an integer is a whole number, whereas an irrational number is a real number that cannot be expressed as a simple fraction or ratio of two integers.