irrational numbers
Irrational numbers are numbers that cannot be expressed as a ratio (fraction) of two integers
Irrational numbers are numbers that cannot be expressed as a ratio (fraction) of two integers. These numbers cannot be represented by terminating or repeating decimals. The decimal form of an irrational number goes on indefinitely without repeating.
Examples of irrational numbers include:
1. √2 (the square root of 2): The decimal representation of √2 is approximately 1.41421356…, and the digits continue without repeating.
2. π (pi): This irrational number represents the ratio of a circle’s circumference to its diameter. The decimal representation of pi is approximately 3.14159265…, and it goes on indefinitely.
3. e (Euler’s number): It is the base of the natural logarithm and is approximately equal to 2.71828182…. The decimal representation of e is another example of an irrational number.
Irrational numbers can also be expressed as infinite continued fractions or continued square roots.
It is important to note that irrational numbers, although they cannot be represented exactly as fractions, still exist on the number line and have important applications in mathematics, physics, and other fields.
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