Which of the following are rational numbers? Select all correct answers. Select all that apply:
0.1212212221…
1.5
11/7
0.8080080008
-2
The correct answer and explanation is :
Correct Answers:
The rational numbers from the given list are:
✅ 1.5
✅ 11/7
✅ -2
Explanation:
A rational number is any number that can be expressed as a fraction p/q, where p and q are integers, and q ≠ 0. This includes:
- Integers (like -2, 0, 3, etc.) because they can be written as fractions (e.g., -2 = -2/1).
- Finite decimals (like 1.5) since they can be converted to fractions (1.5 = 3/2).
- Repeating decimals with a clear repeating pattern, as they can be represented as fractions.
Now, let’s analyze each number:
- 0.1212212221… ❌
- This number does not have a repeating pattern, making it an irrational number.
- 1.5 ✅
- This can be written as 3/2, which is a rational number.
- 11/7 ✅
- This is already in fraction form, so it’s clearly a rational number.
- 0.8080080008… ❌
- This does not have a repeating pattern, so it is irrational.
- -2 ✅
- Any integer is rational because it can be written as a fraction, -2/1.
Thus, the rational numbers from the given options are 1.5, 11/7, and -2.
