Question

are the numbers -0.07, sqrt99, 4/9, -0.03521, sqrt121 rational or irrational numbers and would they be non-terminating/ non-repeating decimals, terminating decimals, or a repeating decimals?

Answer 1

Let's analyze each number one by one to determine whether they are rational or irrational, and whether they are terminating, non-terminating, or repeating decimals.

1. **-0.07**:
- This is a rational number because it can be expressed as a fraction: \(-0.07 = -\frac{7}{100}\).
- It is also a terminating decimal.

2. **\(\sqrt{99}\)**:
- This is an irrational number because it cannot be expressed as a ratio of two integers (99 is not a perfect square).
- The decimal representation of \(\sqrt{99}\) is non-terminating and non-repeating.

3. **\(\frac{4}{9}\)**:
- This is a rational number as it is a fraction of two integers (4 and 9).
- The decimal representation is \(0.4444...\), which is a repeating decimal.

4. **-0.03521**:
- This is a rational number because it can be expressed as a fraction: \(-0.03521 = -\frac{3521}{100000}\).
- It is also a terminating decimal.

5. **\(\sqrt{121}\)**:
- This is a rational number because \(\sqrt{121} = 11\), which can be expressed as a ratio of integers (11/1).
- It is a terminating decimal.

### Summary:
- -0.07: Rational, terminating decimal
- \(\sqrt{99}\): Irrational, non-terminating, non-repeating decimal
- \(\frac{4}{9}\): Rational, repeating decimal
- -0.03521: Rational, terminating decimal
- \(\sqrt{121}\): Rational, terminating decimal