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To solve this problem:

Let the correct operation be multiplying \( x \) by 10. The correct result is:

\[
\text{Correct Result} = 10x
\]

However, the number is mistakenly divided by 10. So the incorrect result is:

\[
\text{Incorrect Result} = \frac{x}{10}
\]

Now, we need to find the percentage error. The percentage error is given by the formula:

\[
\text{Percentage Error} = \left( \frac{\text{Correct Result} - \text{Incorrect Result}}{\text{Correct Result}} \right) \times 100
\]

Substituting the values:

\[
\text{Percentage Error} = \left( \frac{10x - \frac{x}{10}}{10x} \right) \times 100
\]

First, simplify the numerator:

\[
10x - \frac{x}{10} = \frac{100x - x}{10} = \frac{99x}{10}
\]

Now, substitute this back into the formula:

\[
\text{Percentage Error} = \left( \frac{\frac{99x}{10}}{10x} \right) \times 100 = \frac{99}{100} \times 100 = 99\%
\]

Thus, the percentage error is **99%**.

Would you like further clarification or details on this calculation?

Here are some related questions you might explore:
1. How is percentage error calculated in other contexts?
2. What if the error was multiplying by 10 instead of dividing by 10?
3. How would the error change if the number were divided by another factor, like 5 instead of 10?
4. Can this type of error analysis apply to scientific measurements?
5. How can this concept of error be applied in real-world scenarios involving miscalculations?

**Tip:** Always check the operation performed against what was intended to avoid calculation errors like this one.

A number x is mistakenly divided by 10 instead of being multiplied by 10. What is the percentage error in the result?

Learn how to calculate the percentage error when a number x is mistakenly divided by 10 instead of being multiplied by 10. This detailed step-by-step solution explains the use of the percentage error formula, division, and multiplication concepts. Suitable for students in Grades 9-12.

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