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See the mistake a student made by multiplying with 3/5 instead of 5/3. Figure out how much the calculation is wrong in percentage terms.
A Student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?
The percentage error in the calculation is 64%
Explanation
Let’s call the number the student multiplied by “x”.
- The correct calculation would be: x * (5/3)
- The student’s calculation was: x * (3/5)
The difference between these two calculations is:
(x * 5/3) – (x * 3/5) = (25x – 9x) / 15 = 16x / 15
To find the percentage error, we divide this difference by the correct calculation and multiply by 100%:
(16x / 15) / (x * 5/3) * 100% = (16x * 3 * 100%) / (15 * 5x) = 64%
Therefore, the percentage error in the calculation is 64%.
What is Percentage Error in Mathematics?
In mathematics, percentage error tells you how big the difference is between an estimated value and the actual value, expressed as a percentage of the actual value. It helps you understand how precise or accurate your estimation or measurement is.
Here’s how it works:
Formula:
Percent Error = |(Estimated Value – Actual Value)| / Actual Value * 100
Where:
- | | – represents absolute value (ignoring any negative sign)
- Estimated Value – the value you obtained through estimation or measurement
- Actual Value – the true or accepted value
Steps to calculate:
- Find the absolute difference between the estimated and actual values.
- Divide that difference by the actual value.
- Multiply the result by 100 to express it as a percentage.
Interpretation:
- A smaller percentage error indicates that your estimated value is closer to the actual value, meaning your estimation or measurement is more accurate.
- A larger percentage error indicates a bigger difference between the estimated and actual values, meaning your estimation or measurement is less accurate.
Example:
You estimate the length of a table to be 1.5 meters, but when you measure it, you find it’s actually 1.6 meters.
- Percent Error = |(1.5m – 1.6m)| / 1.6m * 100
- Percent Error = 0.1m / 1.6m * 100
- Percent Error ≈ 6.25%
This means your estimate was off by about 6.25% from the actual length.
Applications:
- Science experiments: When measuring different quantities, understanding the percentage error helps assess the reliability of your data.
- Engineering: Estimating material properties or dimensions often involves some error, and percentage error helps quantify how precise the estimate is.
- Everyday life: Comparing prices of similar products, estimating distances or quantities, etc., can all involve some level of error, and percentage error helps analyze that difference.
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Source: Math Hello Kitty
Categories: Math
