A number was divided by 8 instead of being multiplied by 8. As a result of this, there was an error in the answer. What is the percentage difference (correct to two places of decimal) in the answer due to this miscalculation?

Options

A. `48.67%`
B. `67.33%`
C. `98.44%`
D. `72.00%`

Answer

To solve the problem, we need to determine the percentage difference in the answer when a number is divided by 8 instead of being multiplied by 8. Let's break down the steps:

### Step 1: Define the variable
Let the number be represented as \( x \).

### Step 2: Calculate the correct answer
If the number is multiplied by 8, the correct answer would be:
\[ \text{Correct Answer} = 8x \]

### Step 3: Calculate the erroneous answer
If the number is divided by 8, the erroneous answer would be:
\[ \text{Erroneous Answer} = \frac{x}{8} \]

### Step 4: Find the difference between the correct and erroneous answers
To find the difference between the correct answer and the erroneous answer:
\[ \text{Difference} = \text{Correct Answer} - \text{Erroneous Answer} = 8x - \frac{x}{8} \]

### Step 5: Simplify the difference
To simplify \( 8x - \frac{x}{8} \), we need a common denominator:
\[ 8x = \frac{64x}{8} \]
Thus, the difference becomes:
\[ \text{Difference} = \frac{64x}{8} - \frac{x}{8} = \frac{64x - x}{8} = \frac{63x}{8} \]

### Step 6: Calculate the percentage difference
The percentage difference can be calculated using the formula:
\[ \text{Percentage Difference} = \left( \frac{\text{Difference}}{\text{Correct Answer}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Difference} = \left( \frac{\frac{63x}{8}}{8x} \right) \times 100 \]

### Step 7: Simplify the percentage difference
This simplifies to:
\[ \text{Percentage Difference} = \left( \frac{63}{8 \times 8} \right) \times 100 = \left( \frac{63}{64} \right) \times 100 \]

### Step 8: Calculate the final value
Calculating \( \frac{63 \times 100}{64} \):
\[ \text{Percentage Difference} = \frac{6300}{64} \approx 98.4375 \]
Rounding this to two decimal places gives:
\[ \text{Percentage Difference} \approx 98.44\% \]

### Final Answer
The percentage difference in the answer due to the miscalculation is approximately **98.44%**.

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