1. Quantitative Chemical Analysis Seventh Edition Quantitative Chemical Analysis Seventh Edition Chapter 3 Experimental Error Copyright © 2007 by W. H. Freeman and Company Daniel C. Harris

3. a cubic decimeter of water at its point of maximum density, 3.984 °C, has a mass that is 25.05 parts per million less than the kilogram.parts per million Cleaning the prototypes removes between 5 and 60 µg of contamination short-term instability of about 30 µg over a period of about a month in its after-cleaned mass

6. Random error Systematic error

8. 0.234 58.3

9. In experimental data, the first uncertain figure is the last significant figure. 0.234 58.3

11. significant figure: The number of significant digits in a quantity is the minimum number of digits needed to express the quantity in scientific notation..

12. Adding and subtracting with sig figs: Keep least sig figs beyond the decimal point 121.795

13. Adding and subtracting with sig figs: Keep least sig figs beyond the decimal point WATCH OUT: SAME POWERS OF 10!

14. Multiplying and dividing with sig figs: Keep least sig figs.

16. logarithms with sig figs: sig figs. in mantissa = sig figs in number

17. logarithms with sig figs: sig figs. in mantissa = sig figs in number log(3.39 x 10 2 ) = log(3.39) + log (10 2 ) = 0.530 + 2 = 2.530 log(3.39 x 10 -5 ) = log(3.39) + log (10 -5 ) = 0.530 – 5 = -4.470

18. NB 1 sig fig!

19. Propagation of Uncertainty from Random Error

21. This is like adding systematic errors

22. Propagation of Uncertainty from Random Error

27. The real rule: The first uncertain figure is the last significant figure. TIP: In our calculations, we retain extra insignificant digits and round off only at the end.

28. For systematic uncertainty, we add the uncertainties of each term in a sum or difference.

30. 0.71 1.18 Vernier scale