# How do you find the uncertainty of a weighing balance?

## How do you find the uncertainty of a weighing balance?

The quarter weighs about 6.72 grams, with a nominal uncertainty in the measurement of ± 0.01 gram. If we weigh the quarter on a more sensitive balance, we may find that its mass is 6.723 g. This means its mass lies between 6.722 and 6.724 grams, an uncertainty of 0.001 gram.

In principle, the uncertainty quantifies any possible difference between the calibrated value and its reference base (which normally depends on reference standards).

The smallest division of a 30-cm ruler is one millimeter, thus the uncertainty of the ruler is dx = 0.5mm = 0.05cm. For example, an object is measured to be x ± δx = (23.25 ± 0.05) cm.

If you’re adding or subtracting quantities with uncertainties, you add the absolute uncertainties. If you’re multiplying or dividing, you add the relative uncertainties. If you’re multiplying by a constant factor, you multiply absolute uncertainties by the same factor, or do nothing to relative uncertainties.

For a mass balance that can give readings to 2 decimal places, the uncertainty is assumed to be ±0.01.

In the absence of some disturbance factor like water adsorption phenomena, evaporation, magnetic and electrostatic effects, the measurement uncertainty for an electronic balance in our laboratory is in the 10-4 to 10-3 range (100 to 1000 ppm). analysis.

In the absence of some disturbance factor like water adsorption phenomena, evaporation, magnetic and electrostatic effects, the measurement uncertainty for an electronic balance in our laboratory is in the 10-4 to 10-3 range (100 to 1000 ppm).

We know that, 1 Gram = 1000 Milligram. Uncertainty in measurement of the analytical balance = plus or minus 1.

The uncertainty of a measuring instrument is estimated as plus or minus (±) half the smallest scale division. For a thermometer with a mark at every 1.0°C, the uncertainty is ± 0.5°C. This means that if a student reads a value from this thermometer as 24.0°C, they could give the result as 24.0°C ± 0.5°C.

Rule 1. If you are adding or subtracting two uncertain numbers, then the numerical uncertainty of the sum or difference is the sum of the numerical uncertainties of the two numbers. For example, if A = 3.4± . 5 m and B = 6.3± . 2 m, then A+B = 9.7± .

This is a measure of how well a scale can be read. For an analogue scale, the uncertainty is ± half of the smallest scale division. For a digital scale, the uncertainty is ± 1 in the least significant digit.

Therefore, the balance linearity contribution is 0.15mg/(3)^1/2 = 0.09 mg. This contribution may have to be counted twice if the sample is weighed by difference — once for the tare and once for the gross weight, giving a standard uncertainty that equals (2 x (0.09)2)^1/2 = 0.13 mg.

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