To find two rational numbers between -3 and -2, let's follow these detailed steps:
1. Understand the problem: We need to identify two rational numbers that lie in the interval between -3 and -2. Rational numbers are numbers that can be expressed as a fraction [tex]\(\frac{p}{q}\)[/tex] where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers and [tex]\(q \neq 0\)[/tex].
2. Consider the interval: The interval given is [tex]\(-3 < x < -2\)[/tex]. We need to pick two numbers that fit within this range.
3. Choose the first rational number: A rational number that lies between -3 and -2 could be -2.5. This is because -2.5 is greater than -3 and less than -2, satisfying the condition of lying in the interval [tex]\(-3 < x < -2\)[/tex].
4. Choose the second rational number: Another rational number within the same interval is -2.75. Similar to -2.5, -2.75 is greater than -3 and less than -2, fulfilling the requirement of lying between the boundaries.
5. Verify the choices:
- For -2.5: [tex]\(-3 < -2.5 < -2\)[/tex], which is true.
- For -2.75: [tex]\(-3 < -2.75 < -2\)[/tex], which is also true.
Thus, the two rational numbers between -3 and -2 are:
- [tex]\(-2.5\)[/tex]
- [tex]\(-2.75\)[/tex]
Therefore, we have identified that -2.5 and -2.75 are the two rational numbers that lie between -3 and -2.
