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To add uncertain measurements, simply add the measurements and add their uncertainties: (5 cm .2 cm) + (3 cm .1 cm) = (5 cm + 3 cm) (.2 cm +. 1 cm) = 8 cm .3 cm To subtract uncertain measurements, simply subtract the measurements while still adding their uncertainties: (10 cm .4 cm) - (3 cm .2 cm) = (10 cm - 3 cm) (.4 cm +. 2 cm) = 7 cm .6 cm To multiply uncertain measurements, simply multiply the measurements while adding their RELATIVE uncertainties (as a percentage): Calculating uncertainties with multiplication does not work with absolute values (like we had in addition and subtraction), but with relative ones. You get the relative uncertainty by dividing the absolute uncertainty with a measured value and multiplying by 100 to get percentage. For example: (6 cm .2 cm) = (.2 / 6) x 100 and add a% sign. That is 3.3% Therefore: (6 cm .2 cm) x (4 cm .3 cm) = (6 cm 3.3% ) x (4 cm 7.5%) (6 cm x 4 cm) (3.3 + 7.5) = 24 cm 10.8% = 24 cm 2.6 cm To divide uncertain measurements, simply divide the measurements while adding their RELATIVE uncertainties:The process is the same as in multiplication! (10 cm .6 cm) (5 cm .2 cm) = (10 cm 6%) (5 cm 4%) (10 cm 5 cm) (6% + 4%) = 2 cm 10% = 2 cm 0.2 cm To increase an uncertain measurement exponentially, simply raise the measurement to the designated power, and then multiply the relative uncertainty by that power: (2.0 cm 1.0 cm)3 = (2.0 cm)3 (50%) x 3 = 8.0 cm3 150% or 8.0 cm3 12 cm3
Add uncertain measurements. Subtract uncertain measurements. Multiply uncertain measurements. Divide uncertain measurements. Increase an uncertain measurement exponentially.