Measurement September 2007

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

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

Système Internationale Fundamental Quantity Unit Abbrev. MassKilogramkg LengthMeterm TimeSecondsec

Prefixes

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 = yd = ft = in

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

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

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

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

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 ml? 34 °C and 34.0 °C

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

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)

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)

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

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