Which statement(s) is/are true about all irrational numbers? They can be written as a ______________.
Responses
repeating decimal without end
repeating decimal without end
decimal that ends
decimal that ends
non-repeating decimal without end
non-repeating decimal without end
fraction
repeating decimal without end
non-repeating decimal without end
The correct statement is: irrational numbers can be written as a non-repeating decimal without end.
The correct statement 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 first define what an irrational number is. An irrational number is a number that cannot be expressed as a fraction or ratio of two integers. Examples of irrational numbers include the square root of 2 (√2) or the number π (pi).
When we try to express an irrational number as a decimal, we often get a decimal that goes on forever without repeating a pattern. This is because the decimal representation of an irrational number is non-terminating (it does not end) and non-repeating (it does not have a repeating pattern).
On the other hand, a rational number, which can be expressed as a fraction, can always be written as a decimal that either terminates (ends) or repeats a pattern. For example, the fraction 1/4 can be expressed as the decimal 0.25, which terminates. The fraction 1/3 can be expressed as the decimal 0.333..., which repeats the digit 3 indefinitely.
So, to recap, irrational numbers can only be written as non-repeating decimals without end.