Convert the following rational numbers into decimals:
`(9)/(16)`

Answer

To convert the rational number \( \frac{9}{16} \) into a decimal, we can follow these steps:

### Step 1: Set up the division
We need to divide 9 by 16. Since 9 is smaller than 16, we will add a decimal point and a zero to 9, making it 9.0.

### Step 2: Perform the division
Now, we perform the division \( 9.0 \div 16 \).

1. **First Division**:
- 16 goes into 90 (the first two digits after the decimal) how many times?
- 16 fits into 90 five times (since \( 16 \times 5 = 80 \)).
- Write down 5 after the decimal point.

2. **Subtract**:
- Subtract \( 80 \) from \( 90 \):
\[ 90 - 80 = 10 \]

### Step 3: Bring down the next zero
Now, bring down another zero making it 100.

### Step 4: Continue the division
Now, divide 100 by 16.

1. **Second Division**:
- 16 goes into 100 six times (since \( 16 \times 6 = 96 \)).
- Write down 6 after the 5.

2. **Subtract**:
- Subtract \( 96 \) from \( 100 \):
\[ 100 - 96 = 4 \]

### Step 5: Bring down another zero
Bring down another zero to make it 40.

### Step 6: Continue the division
Now, divide 40 by 16.

1. **Third Division**:
- 16 goes into 40 two times (since \( 16 \times 2 = 32 \)).
- Write down 2 after the 6.

2. **Subtract**:
- Subtract \( 32 \) from \( 40 \):
\[ 40 - 32 = 8 \]

### Step 7: Bring down another zero
Bring down another zero to make it 80.

### Step 8: Continue the division
Now, divide 80 by 16.

1. **Fourth Division**:
- 16 goes into 80 five times (since \( 16 \times 5 = 80 \)).
- Write down 5 after the 2.

2. **Subtract**:
- Subtract \( 80 \) from \( 80 \):
\[ 80 - 80 = 0 \]

### Final Result
Since there is no remainder, we can conclude that:
\[ \frac{9}{16} = 0.5625 \]

### Summary
The decimal form of \( \frac{9}{16} \) is \( 0.5625 \).

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