1. Uncertainty & significant figures Feb 7, 2013

2. 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.

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

4. 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?

5. Uncertainties of some instruments

6. 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 …..

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

8. 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.)

9. 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 __________.

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

11. 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%