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Rounding Percentage Error

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Rounding Percentage Error


1. Let's clarify why rounding to 0 might happen: when a number is very close to zero, rounding to the nearest whole number results in 0 because the decimal part is less than 0.5. 2. To verify calculations with a percentage error, we use the formula: $$\text{Percentage Error} = \left|\frac{\text{Measured Value} - \text{True Value}}{\text{True Value}}\right| \times 100\%$$ 3. Suppose we have a true value $T$ and a measured value $M$ from our calculations. 4. Calculate the percentage error using the formula above. 5. If the percentage error is less than 5%, it means our calculations are acceptably accurate. 6. For example, if $T=10$ and $M=9.7$, then: $$\text{Percentage Error} = \left|\frac{9.7 - 10}{10}\right| \times 100\% = 3\%$$ 7. Since 3% is less than 5%, the calculation is considered correct within the acceptable error margin. This method helps confirm the accuracy of rounding and calculations without fabricating data.