How would you classify the number 0.666...?

How would you classify the number 0.666...?

• A. Rational number
• B. Irrational number
• C. Whole number
• D. Integer

Answer: (A)

The number 0.666... is classified as a rational number because it can be expressed as a fraction. Specifically, it is equivalent to the fraction 2/3. Rational numbers are those that can be written in the form of a fraction where both the numerator and the denominator are integers, and the denominator is not zero. Since 0.666... continues indefinitely but consistently represents a specific value, it fits the definition of a rational number. Whole numbers and integers are subsets of rational numbers, but they do not include fractions or decimal representations like 0.666.... Whole numbers are non-negative integers (0, 1, 2, 3, ...) and integers include both positive and negative whole numbers and zero. Since 0.666... is not a whole number or an integer, it cannot be classified as either of those. An irrational number, on the other hand, cannot be expressed as a fraction of two integers and its decimal representation is non-repeating and non-terminating. Since 0.666... has a repeating decimal, it is not classified as irrational. Thus, the correct classification is as a rational number.

The number 0.666... is classified as a rational number because it can be expressed as a fraction. Specifically, it is equivalent to the fraction 2/3. Rational numbers are those that can be written in the form of a fraction where both the numerator and the denominator are integers, and the denominator is not zero. Since 0.666... continues indefinitely but consistently represents a specific value, it fits the definition of a rational number.

Whole numbers and integers are subsets of rational numbers, but they do not include fractions or decimal representations like 0.666.... Whole numbers are non-negative integers (0, 1, 2, 3, ...) and integers include both positive and negative whole numbers and zero. Since 0.666... is not a whole number or an integer, it cannot be classified as either of those.

An irrational number, on the other hand, cannot be expressed as a fraction of two integers and its decimal representation is non-repeating and non-terminating. Since 0.666... has a repeating decimal, it is not classified as irrational. Thus, the correct classification is as a rational number.