# Ralph & Bev Shock ### Chapter 2

#### Measurements

The accepted system of units and measurements in the scientific community is the (SI) or International system of Units.

 Quantity Name Symbol Length meter m Mass Kilograms kg Time second s Electric current ampere A Thermodynamic temperature kelvin K Amount of substance mole mol Luminous intensity candela cd Pressure (derived) Pascal Pa (N/m2)

When making measurements one must be concerned about the properties of the measurements:

1st: Accuracy - how close your measurement is to the right measurement or “answer”

2nd: Precision - how repeatable a measurements is, often related to the most significant figure or graduation on an instrument.

For example, a graduated cylinder with 1mL graduations on it is a more precise instrument than one with only 10 mL graduations but the accuracy of the measurement depends both on the instrument and the skill of the person using the instrument.

The last significant figure is an estimation one power (decimal place) smaller than the finest graduation on the instrument.
For example, a graduated cylinder that has 1mL graduations the last significant figure would be estimated to the nearest 10th of a mL.

When making measurements the final calculated “answer” is only as good as the least significant answer, that is if two students made two separate measurements and added them the result is only good to as many places as the measurement made in the most crude manner.

This led to a set of rules for carrying out mathmatical operations using scientific measurements often referred to as significant figures.

These rules are stated as follows:

1. Digits other than zero are always significant.

example 56.1 has 3 significant digits

2. Zeros between nonzero digits are always significant.

example 3.108 has 4 significants digits

3. Any ending zeros after a decimal point are significant

example 4.3200 has 5 significant digits

4. Zeros used solely for spacing the the decimal point, that is zero to the left of a nonzero ditgit and not bounded by a nonzero digit are not significant.

example 0.000403 has only 3 significant figures and should be written as 4.03x10-4

Whole numbers with trailing zeros are ambiguous and should always be expressed in scientific.

example for the number 4000 we don’t know how many significant figures it has because we don’t now what place represents the last estimated significant figure and what was the most significant graduation on the instrument.

Example: if the last graduation on the instrument is read to the one hundreds place and the last significant figure was estimated to the tens place. the number would have 3 significant figures and should be written as 4.00x103

#### Calculating Significant Figures in Calculations:

Multiplication and Division:
The answer must contain no more significant figures than the measurement with the least number of significant figures.

Example: 7.55 m x 0.34 m x 1.01 m x 0.00099 = 2.6 x 10-3
both 0.34 and 0.00099 only have 2 significant figures.

The answer of an addition or subtraction can have no more digits to the right of the decimal point than are contained in the measurement with the least number of digits to the right of the decimal point.
For whole number addition and subraction the answer can have no more significant figures than the least significant place in the whole numbers.

Example:

55.341
22.12
1.034
100.2
178.695 will be rounded to 178.7 because the number with the least significant place is 100.2 with the .2 being the least significant place.

Lets look at another example with whole numbers:
1.20 x 103 has three significant figures and looks like 1230 when it’s not in scientific notation.
7.4 x 102 has two significant figures and looks like 740 when it’s not in scientific notation.
1.3 x 101 has two significant figures and looks like 13 when it’s not in scientific notation.

1200
740
13
1983
Will be rounded to 2000 because 1200 has the least significant place (the tens place) and should be expressed as 2.0 x 103 with two significant figures.

#### Measuring Temperature:

Temperature is a measure of the average kinetic energy of a system. For example a glass of water has millions of molecules moving at differing velocities. The movement of a molecule represents its kinetic energy (energy of motion). When a themometer is placed in the water the molecules of water strike the thermometer transfering some of their energy to the themometer. This increases the kinetic energy of the mercury or other substance in the themometer causing it to expand beacause the atoms need more room to accommodate their greater movement. This causes the mercury to rise in the thermometer. But because the water molecules have different energies the thermometer is really only measuring the average kinetic energy of the water. So temperature is really just a measure of how hot or cold something is.

Several Temperature scales have been devised over history, many of them arbitrary based on the whim of the particular scientist. The Fahrenheit system that we use in the U.S. was derived by Gabriel Daniel Fahrenheit a physicist , amatuer zoologist and hunter. He used the body temperature of a deer as the point of 100ÂºF and the coldest temperature he could measure as 0ÂºF. Anders Celsius devised the Celsius scale and set 100 ÂºC at the point of boiling point of water at 1 atmosphere of pressure and 0Âº Celsius was set at the freezing point of water at 1 atmosphere.

Lord Kelvin, a Scottish physicist and mathematician saw the need for an absolute temperature scale i.e. a scale that starts at absolute zero where there is no kinetic energy (heat) in matter. Since the Celsius scale was already widely accepted Kelvin just shifted the Celsius scale by 273 degrees. This means the magnitude of a Celsius degree is the same as a unit in Kelvin but at 0 Kelvin the temperature is -273 ºC. To convert from Celsius to Kelvin just add 273. To convert from Kelvin to Celsius just subtract 273.

Example 100ºC = 100+273= 373 Kelvin.

74 Kelvin= 74-273 = -199ºC