Rational Numbers 068000

1. **State the problem:** We need to identify which numbers from the list are rational numbers. 2. **Recall the definition:** A rational number is any number that can be expressed as a fraction \(\frac{a}{b}\) where \(a\) and \(b\) are integers and \(b \neq 0\). 3. **Analyze each number:** - \(13.070070007...\): This is a non-repeating, non-terminating decimal, so it is **irrational**. - \(\frac{13}{23}\): This is a fraction of two integers, so it is **rational**. - \(95\): An integer is rational because it can be written as \(\frac{95}{1}\). - \(23.713\overline{\!3}\): The bar indicates a repeating decimal, which is rational. - \(0.8125\): This is a terminating decimal, which is rational. - \(3.14159...\): This is a non-repeating, non-terminating decimal (approximation of \(\pi\)), so it is **irrational**. - \(\sqrt{53}\): Since 53 is not a perfect square, this is irrational. - \(\sqrt{1.96}\): \(1.96 = \frac{196}{100} = \left(\frac{14}{10}\right)^2\), so \(\sqrt{1.96} = 1.4\), which is rational. 4. **Summary:** Rational numbers from the list are: - \(\frac{13}{23}\) - \(95\) - \(23.713\overline{\!3}\) - \(0.8125\) - \(\sqrt{1.96} = 1.4\)