GEN PHYS 1 | Experimental Errors

True Value

the actual, exact value of the quantity measured (usually unknown)

Measured Value

the value obtained from the experiment or instrument

Absolute Error

the difference between the measured value and true value

Absolute Error Formula

∆x = |x_measured - x_true|

Relative Error

the ratio of the absolute error to the true value, often expressed as a percentage

Relative Error Formula

∆x/x_true

Systematic Errors

• consistent errors caused by faulty equipment or experimental design

• affects accuracy

• instruments must be recalibrated and techniques must be corrected

• has known causes (human error, faulty equipment, problematic design)

Random Errors

• errors caused by unpredictable fluctuations in measurements

• affects precision

• the experiment must be repeated several times and the average results must be used

• accidental

Addition of Errors

1. Add the measured values

2. Add the absolute errors

Multiplying of Measured Quantities

1. Multiply Quantities

2. Add relative errors

3. Multiply relative to product to get absolute error.

Exact Numbers

those values that are known exactly

Inexact Numbers

values with uncertainty

Accuracy

closeness of a measured value to its standard

Precision

closeness of individual measurements with each other