`13/48=?`

Options

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B.
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Answer

To solve the question \( \frac{13}{48} = ? \), we will express the fraction in decimal form. Here’s a step-by-step solution:

### Step 1: Set up the division
We need to divide 13 by 48. This can be expressed as:
\[ 13 \div 48 \]

### Step 2: Perform the division
Since 13 is less than 48, we know that the result will be less than 1. We can add a decimal point and zeros to 13 to continue the division:
\[ 13.000 \div 48 \]

### Step 3: Calculate how many times 48 fits into 130
48 goes into 130 two times (since \( 48 \times 2 = 96 \)). We write down 2 after the decimal point:
\[ 0.2 \]
Now, subtract \( 96 \) from \( 130 \):
\[ 130 - 96 = 34 \]

### Step 4: Bring down the next zero
Now, bring down another 0 to make it 340:
\[ 340 \div 48 \]

### Step 5: Calculate how many times 48 fits into 340
48 goes into 340 seven times (since \( 48 \times 7 = 336 \)). We write down 7:
\[ 0.27 \]
Now, subtract \( 336 \) from \( 340 \):
\[ 340 - 336 = 4 \]

### Step 6: Bring down the next zero
Bring down another 0 to make it 40:
\[ 40 \div 48 \]

### Step 7: Calculate how many times 48 fits into 40
48 does not fit into 40, so we write down 0:
\[ 0.270 \]

### Step 8: Bring down the next zero
Bring down another 0 to make it 400:
\[ 400 \div 48 \]

### Step 9: Calculate how many times 48 fits into 400
48 goes into 400 eight times (since \( 48 \times 8 = 384 \)). We write down 8:
\[ 0.2708 \]
Now, subtract \( 384 \) from \( 400 \):
\[ 400 - 384 = 16 \]

### Step 10: Bring down the next zero
Bring down another 0 to make it 160:
\[ 160 \div 48 \]

### Step 11: Calculate how many times 48 fits into 160
48 goes into 160 three times (since \( 48 \times 3 = 144 \)). We write down 3:
\[ 0.27083 \]
Now, subtract \( 144 \) from \( 160 \):
\[ 160 - 144 = 16 \]

### Step 12: Repeat the process
We can see that we will continue this process, and the decimal will keep repeating. Thus, the decimal representation of \( \frac{13}{48} \) is approximately:
\[ \frac{13}{48} \approx 0.270833... \]

### Final Answer:
\[ \frac{13}{48} \approx 0.2708 \text{ (to four decimal places)} \]

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