Determine whether each statement is true or false.

Question

2/3 is a rational number.
√64 is a rational number.
0 is a natural number.
-9 is a whole number.
π is a irrational number.

Answer 1

Let's evaluate each statement:

1. 2/3 is a rational number.

   • True. A rational number is any number that can be expressed as the quotient of two integers (where the denominator is not zero). Since 2 and 3 are integers and 3 is not zero, 2/3 is a rational number.

2. √64 is a rational number.

   • True. The square root of 64 is 8, and since 8 can be expressed as the ratio of integers (8/1), it is a rational number.

3. 0 is a natural number.

   • False. Natural numbers are typically defined as the set of positive integers (1, 2, 3, ...). In some definitions, 0 is included in the set of whole numbers but is not considered a natural number.

4. -9 is a whole number.

   • False. Whole numbers are non-negative integers (0, 1, 2, 3, ...). Since -9 is a negative number, it is not a whole number.

5. π is an irrational number.

   • True. π (pi) cannot be expressed as a ratio of two integers, making it an irrational number.

In summary:

1. True
2. True
3. False
4. False
5. True