Which of the following is a rational number? A- 6.678…. B- (-12) C- square root of 19 D- PI
The Correct Answer and Explanation is:
The correct answer is B- (-12).
Explanation:
A rational number is any number that can be expressed as the ratio of two integers (i.e., in the form pq\frac{p}{q}qp, where ppp and qqq are integers and q≠0q \neq 0q=0).
Let’s analyze the options one by one:
A) 6.678….
This number is a decimal that appears to go on infinitely. However, because it is written as a non-terminating, repeating decimal, it would still be considered a rational number if it repeats in a predictable way. If the ellipsis means that the decimal repeats (for example, 6.678678…), then it can be written as a fraction, making it rational. But if the decimal does not repeat and just goes on infinitely in an unpredictable pattern, it would not be rational. So, if this decimal is non-repeating, it is not a rational number.
B) -12
This is a whole number. All integers (whether positive or negative) are rational numbers because they can be expressed as a ratio. For example, -12 can be written as −121\frac{-12}{1}1−12, where both -12 and 1 are integers. Therefore, -12 is a rational number.
C) Square root of 19
The square root of 19 is an irrational number because 19 is not a perfect square. The square root of any number that is not a perfect square is irrational because it cannot be expressed as a simple fraction. In this case, 19\sqrt{19}19 is approximately 4.358898, which continues infinitely without repeating.
D) Pi (π)
Pi is also an irrational number. It cannot be expressed as a simple fraction because it is a non-terminating, non-repeating decimal. The decimal representation of pi goes on forever without any repeating pattern, making it an irrational number.
Conclusion:
The only rational number among the options is B) -12, because it can be expressed as a fraction.
