Question

Identify which condition is necessary for a number to be rational. It must be able to be expressed as an integer divided by a nonzero integer.
It must be able to be expressed as an integer divided by a nonzero integer.

It must be written as a fraction.
It must be written as a fraction.

It must not be an endless decimal.
It must not be an endless decimal.

It must not be negative.

Answer 1

The necessary condition for a number to be rational is that **it must be able to be expressed as an integer divided by a nonzero integer**. This means that a rational number can always be written in the form \( \frac{a}{b} \), where \( a \) is an integer and \( b \) is a nonzero integer.

The other statements are not correct conditions for a number to be rational:
- A rational number can indeed be written as a fraction, but it's the form of \( \frac{a}{b} \) that defines it more precisely.
- A rational number can be an endless decimal if it is a repeating decimal (like 0.333...).
- A rational number can be negative (for example, -3 is rational because it can be expressed as \( \frac{-3}{1} \)).

Thus, the correct and necessary condition is indeed that it must be able to be expressed as an integer divided by a nonzero integer.