1. 2 - 1 Measurement Data Measurements and observations.Results Data obtained from an experiment.Units All measurements must have units.

2. 2 - 2 Measurements in Chemistry Metric Units Massg, mg, kg Lengthm, cm, mm, µsnitch Volumecm 3, L, mL

3. 2 - 3 Common Metric Prefixes. PrefixSymbolMeaningExample giga-G10 9 4 GB mega-M10 6 6 MB kilo-k10 3 2 km deci-d10 -1 2 dm centi-c10 -2 2 cm milli-m10 -3 2 mm micro-µ10 -6 2 µm

4. 2 - 4 Significant Figures  Significant figures are the digits in a measurement that are known for sure plus one estimated digit.  The right most digit is always estimated. 612 mL 207 K 0.047 m 3.60 L 10 pens none

5. 2 - 5 Determining Significant Figures  If a measurement is written with an explicit (visible) decimal point, then start at the left most digit.  Move to the right until you find the first non-zero digit.  Count that digit and every digit to the right end of the value or 0. Stop counting at the 0.

6. 2 - 6 Determining Significant Figures  If a measurement is written with an implicit (invisible) decimal point, then start at the right most digit.  Move to the left until you find the first non-zero digit.  Count that digit and every digit to the right end of the value or 0. Stop counting at the 0.

7. 2 - 7 Sig Figs. Measurement# of Sig Figs 75.456 g5 690 004 km6 87 000 000 km2 6 0.0007060 kg4 0.00033 mg2 0.534 L3 1.00033 g6

8. 2 - 8 Rounding Off Calculations If the digit immediately to the right of the last significant digit you want to keep is: 1)> 5, the last significant digit should be increased by 1, i.e. 42.68 g rounded to 3 sig figs: 42.7 g

9. 2 - 9 2) < 5, the last significant digit should remain the same, i.e. 17.32 m rounded to 3 sig figs: 17.3 m 3) 5, followed by nonzero digits, the last significant digit should be increased by 1, i.e. 2.7851 cm rounded to 3 sig figs: 2.79 cm

10. 2 - 10 4) 5, not followed by nonzero digits, and preceded by an odd digit, then the last significant digit should be increased by 1, i.e. 4.635 kg rounded to 3 sig figs: 4.64 kg

11. 2 - 11 5) 5, not followed by nonzero digits, and preceded by an even digit, then the last significant digit should remain the same, i.e. 78.65 mL rounded to 3 sig figs: 78.6 mL

12. 2 - 12 Adding With Significant Figures The sum or difference of measurements must contain as many decimal places as there are in the measurement containing the least number of decimal places.  38.102 cm + 18.9984 cm = 57.100 cm 3 dp’s 4 dp’s 3 dp’s

13. 2 - 13 Subtracting With Significant Figures  55.320 g - 6 g = 49 g 3 dp’s 0 dp’s

14. 2 - 14 Multiplying With Sig Figs The product or quotient must contain the same number of significant figures as the measurement with the least number of significant figures.  34.2051 mm × 3.22 mm = 110. mm 2 = 110 m 2 6 sf’s 3 sf’s

15. 2 - 15 Dividing With Sig Figs  57.90 g/7.41 mL = 7.81 g/mL 4 sf’s3 sf’s Units do not cancel, therefore g/mL!

16. 2 - 16 Dimension Analysis – Factor Label 1) 14.5 km = ? m 14.5 km x 10 3 m 1 km = 1.45 x 10 4 m 2) 3.54 g = ? mg 3.54 g x 10 3 mg 1 g = 3.54 x 10 3 mg

17. 2 - 17 Dimension Analysis – Factor Label 3) 125 cm = ? m 125 cm x 1m 10 2 cm = 1.25 m 4) 0.5420 kg = ? mg 0.5420 kg x 10 3 g 1 kg x 10 3 mg 1 g = 5.420 x 10 5 mg

18. 2 - 18 Density Problems A sample of oil has a density of 0.916 g/mL. (a)What is the mass of 225 mL of the oil? (b)What volume is occupied by 45.0 g of the oil?

19. 2 - 19 (a)D = 0.916 g/mL V = 225 mL D = m = D × V = 0.916 × 225 mL=206 g (b) m = 45.0 g V = = 45.0 g 0.916 = 49.1 mL V m D m

20. 2 - 20 Density Problem A block of copper 6.00 cm long, 3.50 cm wide, and 4.00 cm thick has a mass of 1802 g. What is the density of the copper? l = 6.00 cm w = 3.50 cm h = 4.00 cm m = 1802 g

21. 2 - 21. D = V = l × w × h V = 6.00 cm × 3.50 cm × 4.00 cm = 84.0 cm 3 D = 1802 g 84.0 cm 3 =21.4 g/ cm 3 V m

22. 2 - 22 Accuracy and Precision Accuracy measures how close your measured value agrees with the accepted value. Precision measures the reproducibility of your measurements.

23. 2 - 23 Good Accuracy and Good Precision. × × × × ×

24. 2 - 24 Poor Accuracy and Good Precision. × × × × ×

25. 2 - 25 Poor Accuracy and Poor Precision. × × × × ×

26. 2 - 26 Percent Error % error = × 100%  O is the observed value which is determined by experiment.  A is the accepted value or the true value.  Only the magnitude (size) matters, therefore you ignore plus and minus signs.

27. 2 - 27 Percent Error The accepted value for the boiling point of methyl alcohol is 65.0°C. In the lab, you measured the boiling point to be 64.0°C. What is your percent error? O = 64.0°CA = 65.0°C %error = × 100%

28. 2 - 28 Percent Error. %error = 64.0°C – 65.0°C 65.0°C × 100% %error = 1.54%