Uncertainty & significant figures Feb 7, 2013

Accuracy & precision All measurements have some amount of uncertainties, also called “errors”. The uncertainty is generally one half of the smallest scale division. The uncertainty is the measure of the precision of an instrument. A precise measurement has more significant figures than less precise measurements.

Which measurement is precise? 5.3, 5.34, 6.001 3.12, 4.190, 0.00001

Significant figures: Why need to learn? Significant figures reflect how accurate and precise a measurement is. Eg. 11s - The time is accurate to the nearest second. What about 11.0s & 10.97s?

Uncertainties of some instruments

Adding/subtracting measurements: correct to the least accuracy Add the measurements: 3.2 m and 5.16 m 100 m and 2.14 m Subtract the 1st measurement from the 2nd one 12.5 kg and 25.47 kg 36.52 m and 4.35 m Multiplying & dividing …..

Multiplying/dividing Keep the least significant figures! 32.5 x 1.2 =

What about multiplying a whole number? It depends! Eg1. The thickness of a book is 2.1 cm. The total thickness of 3 books is: 3 x 2.1=6.3 cm Eg2. A student measured a basketball court of WSC. Its length is 28.65 m and width is 23 m Its area is: 28.65 x 23 = 658.95 sq. m its area is 660 sq. m (least s. f.)

Adding /subtracting measurements with uncertainties Add/subtract the measurements Add the absolute uncertainties. Q1. Given that a = 20.23 0.05 m, b = 12.02 0.05 m a. find a+b b. complete the sentence: The sum of a and b is between _________ and __________.

Multiplying/dividing measurements? Add relative uncertainties. Find axb. Convert the absolute uncertainties to relative uncertainties. Add the relative uncertainties. State your result with uncertainties.

0.05/20.23=0.002472 =0.002 (1 s.f.) =0.2% 0.05/12.02=0.00416 =0.004 (1 s.f.) =0.4% axb=243.2 0.6%