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