2UncertaintyThe pin is ½ way between the smallest lines on the ruler – what do we do?We can estimate visually that it is probably around 2.85 cmWe have to IMAGINE that there are 10 more spaces between those smallest lines and ESTIMATEWe can see it is between the 2.8 and 2.9 mark, but…
3UncertaintyWe can estimate visually that it is probably around 2.85 cmThis is just a visual estimation though – that last number is uncertain – it could just as easily be 2.84 or 2.86 cm!!Note that the first two numbers in that measurement are always the same – just the last number, the estimated number, is uncertain
4Rules for uncertaintyWhen making a measurement, record all numbers that are known, plus ONE uncertain digit.These numbers (all certain numbers + 1 uncertain number) are called significant figures
5****Nonzero integers are always significant Sig Fig Rules****Nonzero integers are always significantExample: 1457 has four nonzero integers and four significant figuresWhen 0’s are between sig. figs., 0’s are always significantExample: 101 has 3 sig. fig. and has 5 sig. figWhen the measurement is a whole number ending with 0’s, the 0’s are never significantExample: 210 has 2 sig. figs. and 71,000,000 also has 2 sig. figs
6When the measurement is less than a whole number, the 0’s between the decimal and other significant numbers are never significant (they are place holders). Example: has 2 sig. fig. and has 3 sig. fig.When the measurement is less than a whole number and the 0’s fall after the other significant numbers, the 0’s are always significantExample: has 3 sig. fig. and has 4 sig. fig
7When the measurement is less than a whole and there is a 0 to the left of the decimal, the 0 is not significant.Example: has only 1 sig. fig. and has 3 sig. fig.When the measurement is a whole number but ends with 0’s to the right of the decimal, the 0’s are significant.Example: has 3 sig. fig., has 8 sig. fig.
8Example ProblemsGive the # of significant figures in each measurement:A sample of orange juice contains g of vitamin CA forensic chemist in a crime lab weighs a single hair and records its mass as gThe distance between two points is found to be 5.030x103 ft.
9Rounding RulesIf the number you want to “round off” is less than 5, then the preceding digit stays the sameIf that number is more than 5, round the preceding number UP.ALWAYS wait till the end to round off numbers – don’t round as you go or your # might be off!
10Rounding Examples Round 4 321 211 to 4 sig figs Round 2.35x10 to 2 sig figsRound to 2 sig figs
11Sig Figs in Calculations For addition or subtraction: the limiting number is the one with the smallest number of decimal places.Example: = ?Example: – 0.1 = ?
12Sig Figs in Calculations For multiplication and division:the number of sig figs in your answer is the same as the SMALLEST number of sig figs (total) in the problem (this is the limiting measurement).Example: 4.56 x 1.4 = how do we do sig figs?Example: x 1.0 x 100 = ?
13Note: for multiplication & division, sig figs are counted. For addition & subtraction, the numbers to the right of the decimal place are counted.
14Precision vs. Accuracy Accuracy is telling the truth . . . Precision is telling the same story over and over again.
15Accuracy: the degree of conformity with “the truth”
16Precision & accuracy, cont’d. Precision: the quality, uniformity, or reproducibility of a measurement.Note that this has nothing to do with how “true” the result is, just whether or not you can repeat it exactly.
17Precision vs. Accuracy, cont’d. Accuracy with precision: the person shooting these arrows has performed both accurately (on the bull’s eye) and precisely (over and over)
18Precision vs. Accuracy, cont’d. Precision with blunder – because all of your other results are accurate and precise, it is easy to see the “bad” data and toss it out.Accuracy with blunder – although this is accurate, it is not as precise – it may be easier to overlook the error
19Percent Error Accepted Value – Experimental Value x 100 = %