Rational and Irrational Numbers Question 6 of 10 2 Points Which number is rational? A. ? B. ?5 C. 0.36458121… D. 0.777..
The Correct Answer and Explanation is:
The correct answer is:
D. 0.777…
Explanation:
To determine which number is rational, we must understand the definition of rational numbers.
A rational number is any number that can be expressed as a ratio of two integers (a fraction), where the denominator is not zero. Rational numbers either:
- Terminate (e.g., 0.5 = 1/2), or
- Repeat in a predictable pattern (e.g., 0.333… = 1/3, 0.777… = 7/9)
Let’s analyze the choices:
- A. π (pi): This is an irrational number. It never terminates or repeats and cannot be written as a fraction.
- B. √5: This is also irrational. The square root of any number that is not a perfect square is irrational.
- C. 0.36458121…: This decimal neither terminates nor repeats in a pattern, so it is irrational.
- D. 0.777…: This is a repeating decimal. It can be written as the fraction 7/9, so it is rational.
Therefore, the only rational number among the options is 0.777…, which repeats and can be expressed as a ratio of two integers.
Additional Insight:
Many students confuse long decimals with irrational numbers. But length doesn’t determine irrationality—pattern does. If a decimal repeats or ends, it’s rational. Only decimals that go on forever without any pattern are irrational.
So, even though 0.777… looks infinite, it’s predictably repeating, which fits the definition of a rational number. Always look for repetition or clear fractions when identifying rational numbers
.