if a number is not rational then it is?
irrational
https://www.factmonster.com/math/numbers/rational-and-irrational-numbers
If a number is not rational, then it is irrational. To understand why, let's quickly review what rational and irrational numbers are:
1. Rational Numbers: These are numbers that can be expressed as a ratio of two integers (numbers without decimal or fractional parts). For example, 2, -4, 1/3, and -5/8 are all rational numbers.
2. Irrational Numbers: These are numbers that cannot be expressed as a ratio of two integers. Instead, they have non-repeating, non-terminating decimal representations. Common examples of irrational numbers include π (pi), √2 (square root of 2), and e (Euler's number).
Now, if a number is not rational, it means it cannot be expressed as a fraction of two integers. Hence, it falls under the category of irrational numbers.
To determine if a number is rational or irrational, you can use two methods:
1. Fraction Test: Express the number as a fraction. If you are successful in finding two integers whose ratio equals the given number, it is rational. If not, it is irrational.
2. Decimal Representation: Convert the number to decimal form. If the decimal representation is non-repeating and non-terminating, it is irrational. If the decimal representation either repeats or terminates, it is rational.
Keep in mind that some numbers can be both rational and irrational, depending on how they are represented. For example, √4 can be expressed as both 2 (rational) and -2 (rational), while √2 can only be expressed as an irrational number.