Measurement September 2007 Today 91307 Review of Measurement

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 Mass Kilogram Length Meter Time Second Abbrev. kg m sec

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 = 1. 094 yd = 3. 281 ft = 39. 37 in

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

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 25. 00 ml? • 34 °C and 34. 0 °C

Rounding • Method 1 — — < 5 rounds down (1. 2 -> 1) ≥ 5 rounds up (1. 5 -> 2) • Method 2 — — — < 5 rounds down (1. 2 -> 1) > 5 rounds up (1. 5 -> 2) 5 rounds to nearest even number • 1. 5 -> 2 • 2. 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 102 m (Scientific notation)

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

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