John multiplied a number by 3232 instead of 2323. Find percentage error in calculation.

1. Break Down the Problem

To find the percentage error in John's calculation, we need to calculate the difference between the incorrect result and the correct result, then express that difference as a percentage of the correct result.

1. Let the original number be $x$.
2. The incorrect multiplication is $3232x$.
3. The correct multiplication is $2323x$.
4. The error in calculation is $3232x - 2323x$.

2. Relevant Concepts

The percentage error can be calculated using the formula: $\text{Percentage Error} = \left( \frac{\text{Error}}{\text{Correct Value}} \right) \times 100$

3. Analysis and Detail

1. Calculate the error: $\text{Error} = 3232x - 2323x = (3232 - 2323)x = 909x$
2. The correct value is: $\text{Correct Value} = 2323x$
3. Substitute the error and correct value into the percentage error formula: $\text{Percentage Error} = \left( \frac{909x}{2323x} \right) \times 100$
4. Simplifying yields: $\text{Percentage Error} = \left( \frac{909}{2323} \right) \times 100$

4. Verify and Summarize

Calculate $\frac{909}{2323}$: $\frac{909}{2323} \approx 0.3911$ Multiplying this by 100 gives approximately $39.11\%$.

Final Answer

The percentage error in John's calculation is approximately 39.11%.