Find the decimal expansion of `31/16`.

Answer

To find the decimal expansion of \( \frac{31}{16} \), we can follow these steps:

### Step 1: Convert the fraction to a decimal
To convert \( \frac{31}{16} \) to a decimal, we can perform long division of 31 by 16.

1. **Divide 31 by 16**:
- 16 goes into 31 once (1).
- \( 1 \times 16 = 16 \)
- Subtract \( 16 \) from \( 31 \):
\[ 31 - 16 = 15 \]

### Step 2: Add a decimal point and continue division
2. **Add a decimal point and a zero**:
- Bring down a zero to make it 150.
- 16 goes into 150 nine times (9).
- \( 9 \times 16 = 144 \)
- Subtract \( 144 \) from \( 150 \):
\[ 150 - 144 = 6 \]

### Step 3: Continue the division
3. **Bring down another zero**:
- Now we have 60.
- 16 goes into 60 three times (3).
- \( 3 \times 16 = 48 \)
- Subtract \( 48 \) from \( 60 \):
\[ 60 - 48 = 12 \]

### Step 4: Continue the division
4. **Bring down another zero**:
- Now we have 120.
- 16 goes into 120 seven times (7).
- \( 7 \times 16 = 112 \)
- Subtract \( 112 \) from \( 120 \):
\[ 120 - 112 = 8 \]

### Step 5: Continue the division
5. **Bring down another zero**:
- Now we have 80.
- 16 goes into 80 five times (5).
- \( 5 \times 16 = 80 \)
- Subtract \( 80 \) from \( 80 \):
\[ 80 - 80 = 0 \]

### Conclusion
The division ends here since we have reached 0. Therefore, the decimal expansion of \( \frac{31}{16} \) is:
\[ 1.9375 \]

### Final Answer
Thus, the decimal expansion of \( \frac{31}{16} \) is \( 1.9375 \).

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