State in each case whether true or false:
`(2)/(7)` is an irrational number .

Answer

To determine whether the statement "2/7 is an irrational number" is true or false, we can follow these steps:

### Step 1: Understand the definition of rational and irrational numbers.
- **Rational numbers** are numbers that can be expressed in the form of \( \frac{p}{q} \), where \( p \) and \( q \) are integers, and \( q \neq 0 \).
- **Irrational numbers** are numbers that cannot be expressed in the form of \( \frac{p}{q} \).

### Step 2: Analyze the given number \( \frac{2}{7} \).
- Here, \( 2 \) and \( 7 \) are both integers.
- The denominator \( 7 \) is not equal to zero.

### Step 3: Determine if \( \frac{2}{7} \) fits the definition of a rational number.
- Since \( \frac{2}{7} \) can be expressed in the form \( \frac{p}{q} \) (where \( p = 2 \) and \( q = 7 \)), it is a rational number.

### Step 4: Conclude whether the statement is true or false.
- Since \( \frac{2}{7} \) is a rational number, the statement "2/7 is an irrational number" is **false**.

### Final Answer:
The statement "2/7 is an irrational number" is **false**.

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