1. Measurement September 2007

2. Today 9/13/07 Review of Measurement –Metric system –Uncertainty –Significant Figures The Lab

3. Units of Measurement English (Imperial) –used in U.S. metric –most common, worldwide –used in science (not engineering) SI – offshoot of metric –only seven base units

4. Système Internationale Fundamental Quantity Unit Abbrev. MassKilogramkg LengthMeterm TimeSecondsec

5. Prefixes

6. Metric units Mass (distinct from weight) –gram (g) is the base metric unit –1 kg = 2.2 pounds Length –meter (m) is the base unit –1 m = 1.094 yd = 3.281 ft = 39.37 in

7. Metric units Temperature –Celsius scale (°C) °C = 5/9 (°F – 32) °F = 9/5(°C) + 32 –Kelvin scale (K) K = °C + 273.15 Absolute temperature

8. Metric units Volume (derived unit in SI) –liter (l or L) is the base unit –1 l = 1 dm 3 = 1.06 qt –1 ml = 1 cm 3 = 1 cc –1 m 3

9. Metric units Density –mass/volume –g/ml or g/cc (liquids) –g/ cm 3 (solids) –Density of liquid water is 1.0 g/ml –Density often confused with weight

10. Uncertainty in Measurement Measurements are inexact Two terms dealing with uncertainty: –accuracy correctness –precision grouping

11. Significant Figures Expression of uncertainty — How do we know how uncertain a value is? — What is the difference between 1 m and 1.00 m? 25 ml and 25.00 ml? 34 °C and 34.0 °C

12. Rounding Method 1 — 1) — ≥ 5 rounds up (1.5 -> 2) Method 2 — 1) — > 5 rounds up (1.5 -> 2) — 5 rounds to nearest even number 1.5 -> 2 2.5 -> 2

13. Significant Figures 1)Nonzero digits are always significant 2)Zeros between nonzero digits are always significant 3)Zeros to the right of the decimal and to the right of a nonzero digit are always significant 4)Exact numbers have infinite significant digits (e.g., there are exactly 100 cm in 1 m)

14. Significant Figures What if we want to measure something that is 100 m ±1 m? Three ways ● 100. m ● 100 m ● 1.00 x 10 2 m (Scientific notation)

15. Significant Figures in Calculations Multiplication/Division –keep least number of significant figures 2.5 x 3.76 x 4.986 = 46.8684 -> 47 Addition/Subtraction –round to least precise value

16. Dimensional Analysis By carrying units all the way through the calculation, and cancelling where appropriate, we can more easily solve scientific problems Consider the relationship 1 cm = 2.54 in