07/01/2024
When you have two measurements with tolerances, you can add, subtract, multiply, or divide them by considering the tolerance in each operation. Here's how you can do it:
1. Addition and Subtraction:
When adding or subtracting measurements with tolerances, you should add or subtract the measured values and then add the tolerances separately. For example:
- If you have a measurement of 10.0 cm ± 0.1 cm and another measurement of 5.0 cm ± 0.2 cm, the sum would be 15.0 cm ± (0.1 cm + 0.2 cm) = 15.0 cm ± 0.3 cm.
2. Multiplication and Division:
When multiplying or dividing measurements with tolerances, you should first perform the multiplication or division using the measured values and then calculate the tolerance for the result. For example:
- If you have a measurement of 10.0 cm ± 0.1 cm and another measurement of 5.0 cm ± 0.2 cm, the product would be 50.0 cm² ± (10.0 cm * 0.1 cm + 5.0 cm * 0.2 cm) = 50.0 cm² ± (1.0 cm² + 1.0 cm²) = 50.0 cm² ± 2.0 cm².
It's important to consider the tolerances in each operation to ensure that the resulting measurement reflects the combined uncertainty from the original measurements.
