Which statement(s) is/are true about all irrational numbers? They can be written as a ______________.
Responses
non-repeating decimal without end
non-repeating decimal without end
fraction
fraction
decimal that ends
decimal that ends
repeating decimal without end
The statement "They can be written as a fraction" is true about all irrational numbers.
The correct statement about all irrational numbers is that they can be written as a non-repeating decimal without end. Irrational numbers cannot be expressed as fractions or decimals that end or repeat.
The statement that is true about all irrational numbers is that they can be written as a non-repeating decimal without an end.
To understand this concept, it is important to know what irrational numbers are. Irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers. They are numbers that cannot be written as a terminating decimal or as a repeating decimal.
To explain why the statement "non-repeating decimal without an end" is true, let's consider some examples of irrational numbers:
1. √2 = 1.41421356...
The square root of 2 is an irrational number. It cannot be expressed as a fraction and its decimal representation neither terminates nor repeats. It goes on indefinitely without any pattern.
2. π (pi) = 3.14159265...
Pi is another example of an irrational number. It is the ratio of a circle's circumference to its diameter and cannot be expressed accurately as a fraction. Its decimal representation is also non-terminating and non-repeating.
3. e ≈ 2.718281828...
The Euler's number (e) is another irrational number. It is a mathematical constant that has various applications in mathematics. Its decimal representation is non-terminating and non-repeating as well.
From these examples and many others, you can observe that irrational numbers have decimal representations that continue indefinitely without any repeating pattern.
In summary, the true statement about all irrational numbers is that they can be written as a non-repeating decimal without an end.