Which statement is true about all irrational numbers? They can be written as a ______________.(1 point) Responses fraction fraction non-repeating decimal without end non-repeating decimal without end decimal that ends decimal that ends repeating decimal without end

Answer 1

The true statement about all irrational numbers is that they can be written as a non-repeating decimal without end.

Answer 2

explain are you sure

Answer 3

Yes, I’m sure. Here’s a detailed explanation:

Irrational numbers are numbers that cannot be expressed as a fraction of two integers (i.e., they cannot be written in the form \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \) is not zero). Because of this property, irrational numbers cannot be written as a terminating decimal (a decimal that ends) or a repeating decimal (a decimal that has a sequence of digits that repeats indefinitely).

Instead, irrational numbers can be expressed as non-repeating, non-terminating decimals. This means that their decimal representation goes on forever without repeating any sequence of digits. Examples of irrational numbers include:

• \( \sqrt{2} \) (approximately 1.414213562...)
• \( \pi \) (approximately 3.14159265...)
• \( e \) (approximately 2.71828182...)

In summary, the correct characteristic of irrational numbers is that they can be represented as non-repeating decimals without end. This distinguishes them from rational numbers, which can either terminate or repeat in their decimal form.