10 What is \( 1 \frac{50}{99} \) expressed as a decimal? Show your work.

To express the mixed number \(1 \frac{50}{99}\) as a decimal, follow these steps: ### Step 1: Understand the Mixed Number A mixed number consists of an integer and a proper fraction. In this case: - **Integer part:** 1 - **Fractional part:** \(\frac{50}{99}\) ### Step 2: Convert the Fraction to Decimal To convert \(\frac{50}{99}\) to a decimal, perform the division \(50 \div 99\). \[ \frac{50}{99} = 50 \div 99 \] Let's carry out the division: 1. **Set Up the Division:** \[ 99 \overline{)50.000000} \] 2. **Divide 50 by 99:** - 99 doesn't go into 50, so we add a decimal point and a zero to make it 500. 3. **First Division:** - \(99 \times 5 = 495\) - Subtract: \(500 - 495 = 5\) - Bring down a zero to make it 50 again. 4. **Second Division:** - \(99 \times 0 = 0\) - Subtract: \(50 - 0 = 50\) - Bring down another zero to make it 500. 5. **Repeat the Process:** - You can see this will repeat the pattern \(50 \div 99 = 0.\overline{50}\), where "50" repeats indefinitely. So, \[ \frac{50}{99} = 0.\overline{50} = 0.505050\ldots \] ### Step 3: Combine the Integer and Decimal Parts Now, add the integer part to the decimal: \[ 1 \frac{50}{99} = 1 + 0.\overline{50} = 1.505050\ldots \] ### Final Answer \[ 1 \frac{50}{99} = 1.\overline{50} = 1.505050\ldots \] This means that \(1 \frac{50}{99}\) expressed as a decimal is a repeating decimal **1.505050…**, where "50" repeats indefinitely.