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Uncertainties in Measuring Devices All measured quantities have uncertainties associated with them. The purpose of error analysis is to determine how such uncertainties influence the interpretation of the experimental results 1. Systematic Error - Results from consistent bias in observation (ie. Instrument-calibration error, natural errors or personal error). - Can be eliminated by pre-calibrating against a known, trusted standard. - Affects accuracy 2. Random Errors - Results from fluctuations in the readings of a measurement apparatus, experimenter's interpretation of the instrumental reading or randomly changing conditions (weather, humidity, etc.). - Can be reduced by averaging multiple measurements. - Unbiased - Affects precision

Uncertainties in Measuring Devices General rule of thumb used to determine the uncertainty in a single measurement when using a scale or digital measuring device. 1. Uncertainty in a Scale Measuring Device is equal to the smallest increment divided by 2.

2. Uncertainty in a Digital Measuring Device is equal to the smallest increment.

In general, any measurement can be stated in the following preferred form:

The measured value is just an estimate and thus it cannot be more precise than the uncertainty of the device. (i.e. The number of decimal places for the measured value must match the number of decimal places for the uncertainty, and in multiples of the uncertainty)” Example: The smallest increment in a meter rule (scale measuring device) is 0.1 cm. Following the general rule of thumb to determine the uncertainty in a scale measuring device, it would therefore be half of the smallest increment (∆ l = 0.1/2 = 0.05 cm). The uncertainty of a meter rule is ± 0.05 cm, thus for the length measured, l = 31.225 ± 0.05 cm (incorrect) l = 31.23 ± 0.05 cm (incorrect) l = 31.25 ± 0.05 cm (correct)

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