Question

Error Analysis Richie says that 2.141441444... is a rational number. Elsa disagrees and says the number is irrational. Decide who is correct and what might likely cause one of them to make the error. Who is correct? What might likely cause one of them to make the error?

A. Richie is correct. Elsa may see 2.141441444... as not showing a repeating pattern.
B. Both Elsa and Richie are correct. Numbers like 2.141441444... are both rational and irrational.
C. Elsa is correct. Richie may see 2.141441444... as showing a repeating pattern.
D. Both Elsa and Richie are incorrect. The number cannot be classified as rational or irrational.

Answer 1

In this case, Elsa is correct. The number 2.141441444... is actually an irrational number. The likely cause of Richie's error is that he may see a repeating pattern in the number.

Step-by-step explanation:

In this case, Elsa is correct. The number 2.141441444... is actually an irrational number. To be classified as a rational number, a number must be expressed as a quotient of two integers. However, the number 2.141441444... cannot be expressed as a fraction, as it goes on forever without repeating. This is a characteristic of irrational numbers.

The likely cause of Richie's error is that he may see the number 2.141441444... and mistakenly see a repeating pattern. It's important to understand that not all decimal expansions have repeating patterns, and decimals that go on indefinitely without repeating are called irrational numbers.