| Uncertainty | Systematic Errors | Random Errors |
Many unit factors are based on definitions. There are exactly 5280 feet in a mile and2.54 centimeters in an inch, for example. Unit factors based on definitions are known withcomplete certainty. There is no error or uncertainty associated with these numbers.Measurements, however, are always accompanied by a finite amount of error or uncertainty,which reflects limitations in the techniques used to make them.
There are two sources of error in a measurement: (1) limitations in the sensitivity ofthe instruments used and (2) imperfections in the techniques used to make the measurement.These errors can be divided into two classes: systematic and random.
Systematic error can be caused by an imperfection in the equipment being used or frommistakes the individual makes while taking the measurement. A balance incorrectlycalibrated would result in a systematic error. Consistently reading the buret wrong wouldresult in a systematic error.
Random errors most often result from limitations in the equipment or techniques used tomake a measurement. Suppose, for example, that you wanted to collect 25 mL of a solution.You could use a beaker, a graduated cylinder, or a buret. Volume measurements made with a50-mL beaker are accurate to within ±5 mL. In other words, you would be as likely toobtain 20 mL of solution (5 mL too little) as 30 mL (5 mL too much). You could decreasethe amount of error by using a graduated cylinder, which is capable of measurements towithin ±1 mL. The error could be decreased even further by using a buret, which iscapable of delivering a volume to within 1 drop, or ±0.05 mL.
Which of the following procedures would lead to systematic errors, and which would produce random errors?
(a) Using a 1-quart milk carton to measure 1-liter samples of milk.
(b) Using a balance that is sensitive to ±0.1 gram to obtain 250 milligrams of vitamin C.
(c) Using a 100-milliliter graduated cylinder to measure 2.5 milliliters of solution.
Units | Errors | Significant Figures | Scientific Notation
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