Question

Determine whether each number is rational or irrational and then drag the check mark to the appropriate box. Options:

A. Rational
B. Irrational

Answer 1

To determine whether a number is rational or irrational, look at its representation: whether it can be expressed as a fraction (rational) or if it has a non-repeating, non-terminating decimal form (irrational). It is also essential to check if the answer is reasonable in context.

Step-by-step explanation:

The question asked requires determining whether a number is rational or irrational. A rational number is any number that can be expressed as a fraction or quotient of two integers where the denominator is not zero. Examples of rational numbers include integers, fractions, and finite or repeating decimals. An irrational number, on the other hand, cannot be written as a simple fraction; it is a non-repeating, non-terminating decimal. Examples include numbers like π (pi) and √2 (the square root of 2).

To determine if a number is rational or irrational, follow these steps:

1. Check if the number can be expressed as a fraction with integer values in both the numerator and the denominator.
2. If it is a decimal, observe whether it terminates or repeats. If it does, it is rational. If it does not, it is likely irrational.
3. For square roots or other roots, determine whether the radicand (the number under the root) is a perfect square (or perfect cube, etc.). If it is not, the root is typically irrational.

Additionally, it is important to check if the answer is reasonable. This involves ensuring the values and units make sense within the context of the problem. Numbers should have the correct sign, and the magnitude should be plausible.