Math Problem Statement

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

Solution

To solve this problem:

Let the correct operation be multiplying xx by 10. The correct result is:

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

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

Incorrect Result=x10\text{Incorrect Result} = \frac{x}{10}

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

Percentage Error=(Correct ResultIncorrect ResultCorrect Result)×100\text{Percentage Error} = \left( \frac{\text{Correct Result} - \text{Incorrect Result}}{\text{Correct Result}} \right) \times 100

Substituting the values:

Percentage Error=(10xx1010x)×100\text{Percentage Error} = \left( \frac{10x - \frac{x}{10}}{10x} \right) \times 100

First, simplify the numerator:

10xx10=100xx10=99x1010x - \frac{x}{10} = \frac{100x - x}{10} = \frac{99x}{10}

Now, substitute this back into the formula:

Percentage Error=(99x1010x)×100=99100×100=99%\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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Percentage Error
Division
Multiplication

Formulas

Percentage Error = ((Correct Result - Incorrect Result) / Correct Result) × 100

Theorems

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Suitable Grade Level

Grades 9-12