Significant Figures

Uncertainty We do not know infinite digits of a measurement Exact numbers are known for sure Inexact – have some question (estimates)

Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner. Precise but not accurate Neither accurate nor precise Precise AND accurate

Reporting Numbers When reading an instrument, all exact decimal places should be read – these are numbers actually represented by lines on the instrument In addition to the exact numbers, one inexact decimal place should also be estimated – this is a digit in between the smallest lines All digits including the uncertain one are called significant figures We are fairly confident of these digits

Which Digits Are Significant? Any non-zero number is significant Any number to the left of a decimal is significant Zeros to the right of a decimal and behind other numbers are significant Zeros to the right of a decimal but in front of other numbers are not significant

How many Significant Figures in each below? 28.6 9) 3440. 910 10) 0.04604 0.0076000 11) 804.05 0.0144030 12) 1002 400 13) 400. 700.0 14) 0.000625000 0.4004 15) 6000 1.30 16) 0.00067

Round each to 3 Significant Figures 31.068 6) 149.51 2.613 7) 6.561 81.436 8) 13.1252 0.001567 9) 143.81 1.1353 10) 0.000355

Percent Error Mathematical measure of accuracy Tells how far a measurement varies from the actual value Actual Value – Measured Value X 100 % Error = Actual Value