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.
• Mass Kilogram kg
• Length Meter m
• Time Second sec
Prefixes
Prefix Value Abbreviation
Tera- 1012 T
Giga- 109 G
Mega- 106 M*
kilo- 103 k
deci- 10-1 d
milli- 10-3 m*
micro- 10-6
nano- 10-9 n
pico- 10-12 p
femto- 10-15 f
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 dm3 = 1.06 qt– 1 ml = 1 cm3 = 1 cc– 1 m3
Metric units
• Density– mass/volume– g/ml or g/cc (liquids)– g/ cm3 (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
1.2 2.35 +4.789 8.3
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