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.