Select whether the number is rational, irrational, or imaginary. 3/11 rational irrational imaginary
The Correct Answer and Explanation is:
✅ Correct Answer: Rational
📘 Explanation
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, if a number can be written in the form a/b, where a and b are both integers and b ≠ 0, then it is considered rational.
Let’s look at the number in question:
3/11
This is a fraction, and:
- The numerator (top number) is 3, which is an integer.
- The denominator (bottom number) is 11, which is also an integer and not equal to zero.
Since 3/11 fits the definition of a rational number (an integer divided by a nonzero integer), it is rational.
🔍 Why It’s Not Irrational:
An irrational number cannot be written as a fraction of two integers. Examples of irrational numbers include:
- √2 (square root of 2)
- π (pi)
- e (Euler’s number)
These numbers go on forever without repeating and cannot be expressed exactly as fractions. But 3/11 is a repeating decimal (approximately 0.272727…), which means it can be written as a fraction, so it’s not irrational.
🔍 Why It’s Not Imaginary:
An imaginary number is a number that involves the square root of a negative number. The basic imaginary unit is i, where i = √(-1). Examples of imaginary numbers include:
- i
- 2i
- -5i
Since 3/11 is a real number and does not involve i or the square root of a negative number, it is not imaginary.
✅ Conclusion:
3/11 is a rational number because it is a fraction made of two integers and has a nonzero denominator.
