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.
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-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.
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\(\sqrt{99}\):
- 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.
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\(\frac{4}{9}\):
- 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.
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-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.
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\(\sqrt{121}\):
- 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