1. MEASUREMENTS

2. What is the difference between these two measurement rulers? Should we record the same number for each scale reading? The second scale gives us more information, it is more precise.

3. When writing measurements, we record the digits that we are certain of plus one estimated or uncertain digit. We consider these number significant digits 8.9 cm 8.95 cm

4. 6.00 cm

5. 1120 cm

6. 0.0260 cm

7. Significant Digits or Significant Figures We must be aware of the limits of precision for each piece of lab equipment that we use. We must record our data to the proper number of significant figures. You are always allowed one estimated figure in measurements When measured quantities are given to you, it is assumed that the proper number of significant figures were recorded.

8. Rules for Counting Significant Figures All non-zero digits are significant. 1 473 in _____ 785 m _____ 387.56 cm ____ Zeros: – Leading Zeros are not significant. 0.421 L _____ 0.5 mL _____ 0.0011 cm _____ – Captive Zeros are significant. 70 304 m _____ 395.01 L _____ 1.008 m _____ – Trailing Zeros are significant if there is a decimal point. 12.380 cm _____ 1.30 in _____ 1691.100 L _____ – Trailing Zeros are not significant if there is no decimal point. 2 500 in _____ 800 m _____ 9 010 mL _____ 7 35 3 12 5 54 53 4 21 3

9. Determine the amount of significant figures in the following examples: 967 L _____ 0.111 0 mL _____ 0.005 670 m _____ 4.530 cm _____ 2.700 mm _____ 0.006 007 m _____ 9.67 L _____ 0.000 008 mL _____ 0.800 008 m _____ 3 4 4 4 4 4 3 1 6

10. Calculating with Significant Figures Multiply/Divide: The number with the fewest number of sig figs will determine the number of sig figs in the answer. – Example (13.92 g/cm 3 )(23.3 cm 3 ) = 324.103 g 4 sig figs3 sig figs 324 g

11. Calculating with Significant Figures Addition/Subtraction: The number with the fewest amount of decimal places determines the amount of decimal places in the answer. – Example 3.76 g + 14.83 g + 2.1 g = 20.69 g 2 decimal places 20.7 g 2 decimal places 1 decimal places

12. How many times could you imagine dividing the smallest increment? What length measurement would you record?6.83 cm cm 10 times; each increment being worth 0.01 cm Uncertainty in Measurements Therefore your uncertainty is 0.01 cm. We can express this by writing our measurement as 6.83 cm ± 0.01 cm