Which statement(s) is/are true about all irrational numbers? They can be written as a ______________.
Responses
fraction
fraction
non-repeating decimal without end
non-repeating decimal without end
repeating decimal without end
repeating decimal without end
decimal that ends
non-repeating decimal without end
The statement that is true about all irrational numbers is that they can be written as a non-repeating decimal without end.
The statement(s) that is/are true about all irrational numbers is that they can be written as a non-repeating decimal without end.
To understand why this is true, we need to know the definition of an irrational number. An irrational number is a number that cannot be expressed as a simple fraction or ratio of two integers. It cannot be written as a terminating or repeating decimal either.
Since irrational numbers cannot be expressed as fractions, they can only be represented as decimals. However, not all decimals are considered irrational numbers. Rational numbers can be expressed as either terminating decimals (decimals that end) or repeating decimals (decimals that have a repeating pattern).
On the other hand, irrational numbers cannot be written as a repeating or terminating decimal. They have an infinite and non-repeating decimal representation. This means that the decimal representation of an irrational number will continue without an end and without repeating any pattern.
Therefore, the accurate statement(s) about all irrational numbers is that they can be written as a non-repeating decimal without end.