Write \( \frac{14}{11} \) as a decimal.

1. We begin by writing the fraction as a division: \[ \frac{14}{11} = 14 \div 11 \] 2. Since \(11\) goes into \(14\) one time, we have: \[ 1 \times 11 = 11 \] \[ 14 - 11 = 3 \quad \text{(remainder)} \] Thus, \( \frac{14}{11} = 1 + \frac{3}{11} \). 3. To convert the fractional part \(\frac{3}{11}\) into a decimal, we perform the division: - Write \(3\) as \(3.000\ldots\) and divide by \(11\). 4. Dividing step-by-step: - **Step 1:** \(11\) goes into \(30\) (after bringing down a \(0\)) \(2\) times because: \[ 2 \times 11 = 22 \] Subtracting: \[ 30 - 22 = 8 \] So far, the decimal is \(1.2\ldots\). - **Step 2:** Bring down another \(0\) to the remainder \(8\) to get \(80\). \(11\) goes into \(80\) \(7\) times because: \[ 7 \times 11 = 77 \] Subtracting: \[ 80 - 77 = 3 \] Now, the decimal is \(1.27\ldots\). - **Step 3:** The remainder is again \(3\). Repeating the process will yield the same sequence of digits (\(2\) then \(7\)). 5. We see the digits \(2\) and \(7\) repeat indefinitely. Therefore, the decimal representation is: \[ 1.\overline{27} \] Thus, \( \frac{14}{11} \) written as a decimal is \( 1.\overline{27} \).