Convert each of the following fractions into a decimal :
`37/40`

Answer

To convert the fraction \( \frac{37}{40} \) into a decimal, we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Division**: We need to divide 37 by 40. Since 37 is less than 40, we will need to add a decimal point and zeros to 37. We can write it as \( 37.00 \).

2. **Perform the Division**:
- Start by determining how many times 40 can fit into 37. It cannot fit, so we put a 0 before the decimal point.
- Now, we add a decimal point and a zero, making it 370.
- Now, we check how many times 40 fits into 370.

3. **Calculate**:
- 40 fits into 370 a total of 9 times because \( 40 \times 9 = 360 \).
- Write down 9 after the decimal point: \( 0.9 \).
- Subtract \( 360 \) from \( 370 \):
\[ 370 - 360 = 10 \]

4. **Continue the Division**:
- Bring down another 0, making it 100.
- Now, determine how many times 40 fits into 100.
- 40 fits into 100 a total of 2 times because \( 40 \times 2 = 80 \).
- Write down 2: \( 0.92 \).
- Subtract \( 80 \) from \( 100 \):
\[ 100 - 80 = 20 \]

5. **Final Step**:
- Bring down another 0, making it 200.
- Now, determine how many times 40 fits into 200.
- 40 fits into 200 a total of 5 times because \( 40 \times 5 = 200 \).
- Write down 5: \( 0.925 \).
- Subtract \( 200 \) from \( 200 \):
\[ 200 - 200 = 0 \]
- Since there is no remainder left, we have completed the division.

### Final Answer:
The decimal representation of \( \frac{37}{40} \) is \( 0.925 \).

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