Write the decimal representations of the following rational numbers:
`(4)/(9)`

Answer

To find the decimal representation of the rational number \( \frac{4}{9} \), we can follow these steps:

### Step 1: Set up the division
We need to divide 4 by 9. Since 4 is smaller than 9, we will add a decimal point and zeros to the dividend (4). This means we will be dividing 4.000... by 9.

### Step 2: Perform the division
1. **Divide 40 by 9**:
- 9 goes into 40 four times (since \( 9 \times 4 = 36 \)).
- Write down 4 after the decimal point.
- Subtract \( 36 \) from \( 40 \) which gives us a remainder of \( 4 \).

2. **Bring down the next 0**:
- Now we have 40 again (since the remainder is 4, we bring down another 0).
- Repeat the division: 9 goes into 40 four times again.
- Subtract \( 36 \) from \( 40 \) to get a remainder of \( 4 \) again.

### Step 3: Identify the pattern
Since we keep getting a remainder of 4 every time we bring down a 0, this means the decimal will keep repeating. Therefore, we can denote this repeating decimal as \( 0.4444...\).

### Step 4: Write the final answer
The decimal representation of \( \frac{4}{9} \) is \( 0.\overline{4} \), where the bar indicates that the digit 4 repeats indefinitely.

### Summary
The decimal representation of \( \frac{4}{9} \) is \( 0.4444...\) or \( 0.\overline{4} \).

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