1.1 Rational and Irrational Numbers Write each fraction as a decimal or each decimal as a fraction. \( \begin{array}{lll}\text { 1. } \frac{7}{20} & \text { 2. } 1 . \overline{27} & \text { 3. } 1 \frac{7}{8} \\ \text { Solve each equation for } x . & \text { 5. } x^{3}=343 & \text { 6. } x^{2}=\frac{1}{100}\end{array} \) \( \begin{array}{lll}\text { 4. } x^{2}=81 & \text { (0) } & \text { ( }\end{array} \)

To convert the fraction \(\frac{7}{20}\) to a decimal, divide 7 by 20, which gives you 0.35. For the repeating decimal \(1.\overline{27}\), you can express it as a fraction using some algebra: let \(x = 1.272727...\). Then, \(100x = 127.2727...\), subtracting gives \(99x = 126\), leading to \(x = \frac{126}{99}\), which simplifies to \(\frac{14}{11}\). For \(1 \frac{7}{8}\), convert the mixed number to an improper fraction: \(1 \frac{7}{8} = \frac{8}{8} + \frac{7}{8} = \frac{15}{8}\) and if you want it as a decimal, divide 15 by 8 to get 1.875. Now, solving the equations: 5. To solve \(x^{3} = 343\), take the cube root: \(x = \sqrt[3]{343} = 7\). 6. For \(x^{2} = \frac{1}{100}\), take the square root: \(x = \pm \sqrt{\frac{1}{100}} = \pm \frac{1}{10}\). 7. Solving \(x^{2} = 81\) gives \(x = \pm \sqrt{81} = \pm 9\).