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Which one of the following statements is not always true?

A) Every number that can be expressed as a tion is a real number.
B) Every whole number that is also a perfect square is an integer.
C) Every decimal number is a rational number.
D) Every counting number is a rational number.

1 Answer

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Final answer:

The statement 'Every decimal number is a rational number' is not always true, as decimal numbers can be irrational if they have a non-repeating and non-terminating sequence.

Step-by-step explanation:

The statement that is not always true among the options provided is: C) Every decimal number is a rational number. This is because a decimal number can be either rational or irrational. Rational numbers are those that can be expressed as a fraction with integer values in the numerator and a non-zero integer in the denominator. However, decimal numbers that have a non-repeating and non-terminating sequence cannot be represented as a fraction, and are therefore irrational. An example of an irrational number is pi (π), which is approximately 3.14159...

On the other hand:

  • A) Every number that can be expressed as a fraction is a real number, which is accurate since all rational numbers are real numbers.
  • B) Every whole number that is also a perfect square is an integer. By definition, a perfect square is a number that is the square of an integer, and whole numbers are already integers.
  • D) Every counting number is a rational number. This is true because counting numbers (also known as natural numbers) can be written as fractions with 1 as the denominator (for example, 2 can be written as 2/1).
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