Every Rational number is a Natural number. T or F?

Question

Every natural number is also an integer. T or F?

Every Irrational number is also an Integer. T or F?

0.128128128… is an Irrational number. T or F?

Answer 1

Let's analyze each statement one by one.

1. Every Rational number is a Natural number.
   False. A rational number can be expressed as the ratio of two integers (e.g., \( \frac{1}{2} \)), but not all rational numbers are natural numbers (which are positive integers like 1, 2, 3, ...).

2. Every natural number is also an integer.
   True. Natural numbers (0 or the set of positive integers) are a subset of integers. Therefore, every natural number is indeed an integer.

3. Every Irrational number is also an Integer.
   False. Irrational numbers cannot be expressed as a fraction of two integers, such as \( \sqrt{2} \) or \( \pi \). Since integers are whole numbers (positive, negative, or zero) and rational numbers, irrational numbers cannot be integers.

4. 0.128128128… is an Irrational number.
   False. The number 0.128128128… is a repeating decimal, which means it can be expressed as a fraction (in this case, \( \frac{128}{990} \)). Therefore, it is a rational number, not an irrational number.

So the final answers are:

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