1. **Problem Statement:** Convert the recurring decimals to fractions. 2. **Part (a):** Convert $0.\overline{4}$ to a fraction. Let $x=0.4444\ldots$ Multiply by 10: $10x=4.4444\ldots$ Subtract original: $10x - x = 4.4444\ldots - 0.4444\ldots$ This gives: $9x=4$ Solve for $x$: $x=\frac{4}{9}$ 3. **Part (b):** Convert $3.\overline{7}$ to a fraction. Let $y=3.7777\ldots$ Multiply by 10: $10y=37.7777\ldots$ Subtract original: $10y - y = 37.7777\ldots - 3.7777\ldots$ This gives: $9y=34$ Solve for $y$: $y=\frac{34}{9}$ 4. **Part (c):** Convert $0.\overline{56}$ to a fraction. Let $z=0.565656\ldots$ Multiply by 100 (since the repeat has 2 digits): $100z=56.565656\ldots$ Subtract original: $100z - z = 56.565656\ldots - 0.565656\ldots$ This gives: $99z=56$ Solve for $z$: $z=\frac{56}{99}$ **Final answers:** - $0.\overline{4} = \frac{4}{9}$ - $3.\overline{7} = \frac{34}{9}$ - $0.\overline{56} = \frac{56}{99}$