>Observations can be qualitative or quantitative

Qualitative observations are non-numerical, they ask “what”

Quantitative observations are numerical, they ask “how much”

Quantitative observations are also called measurements

Measurements:

Always involve a comparison

Require units

Involve numbers that are inexact (numbers in mathematics are exact)

Include uncertainty due to the inherent physical limitations of the observer and the instruments used (to make the measurement)

Uncertainty is also called error

Chemists use SI units for measurements

All SI units are based on a set of seven measured base units:

Derived units involve a combination of base units, including:

Base units are frequently to large or small for a measurement

Decimal multipliers are used to adjust the size of base units, including

You may encounter non-SI metric system units, including:

English and Metric units are related using conversion factors

To measure volumes in the laboratory, one might use one of these:

Mass is determined by weighing the object using a balance

Temperature is measured in degrees Celsius or Fahrenheit using a thermometer

The difference between a measurement and the “true” value we are attempting to measure is called the error

Errors are due to limitations inherent in the measurement procedure

In science, all digits in a measurement up to and including the first estimated digit are recorded

These digits are called significant digits or significant figures

The number of significant digits in a measurement may be increased by using a more precise instrument

Errors arise from a number of sources including:

Reading scales incorrectly

Using the measuring device incorrectly

Due to thermal expansion or contraction (temperature changes)

Errors can often be detected by making repeated measurements

The central value can be estimated by reporting the average or mean

Accuracy and precision are terms used to describe a collection of repeated measurements

An accurate measurement is close to the true or correct value

A precise measurement is close to the average of a series of repeated measurements

When calibrated instruments are used properly, the greater the number of significant figures, the greater is the degree of precision for a given measurement

Nonzero digits in a measured number are always significant

Zeros must be considered more carefully:

Zeros between significant digits are significant

Zeros to the right of the decimal point are always counted as significant

Zeros to the left of the first nonzero digit are never counted as significant

Zeros at the end of a number without a decimal point are assumed not to be significant

Confusion can be avoided by representing measurement in scientific or exponential notation

Scientific notation is reviewed on the web site at http://www.wiley.com/college/brady

When measurements are expressed in scientific notation to the correct number of significant digits, the number of digits written is the same regardless of the units used to express the measurement

Measurements limit the precision of the results calculated from them

Rules for combining measurements depend on the type of operation performed:

Multiplication and division

The number of significant figures in the answer should not be greater than the number of significant figures in the least precise measurement.

Addition and Subtraction

The answer should have the same number of decimal places as the quantity with the fewest number of decimal places

The factor-label method, or dimensional analysis, can be used to help perform the correct arithmetic to solve a problem

This involves treating a numerical problem as one involving a conversion from one kind of units to another

This is done using one or more conversion factors to change the units of the given quantity to the units of the answer

A conversion factor is a fraction formed from a valid relationship or equality between units

Conversion factors are used to switch from one system of measure to another

Example: Convert 72.0 in. to cm using the equality 1 in. = 2.54 cm (exactly).

Density (d) is an intensive property defined as the ratio of an objects mass (m) to volume (v), d = m/v

Each pure substance has its own characteristic density

At room temperature:

Most substances expand when heated

This means density depends on temperature

For water:

Density relates a samples mass and volume

Blood has a density of 1.05 g/cm3

We can say that 1.05 g blood is equivalent to 1.00 cm3

Conversion factors can be constructed from this equivalence, which could be used in the factor-label method

The numerical value for the density of a substance depends on the units used for mass and volume

The specific gravity is defined as the ratio of the density of the substance to the density of water :

The specific gravity of a substance:

Is less than one for substances less dense than water

Is greater than one for substances more dense than water

Is independent of units

In order to rely on measured properties of substances, reliable measurements must be made

The accuracy and precision of measured results allow us to estimate their reliability

To trust conclusions drawn from measurements, the measurements must be accurate and of sufficient precision

This is a key consideration when designing experiments

*KIMIA*

Posted on February 25, 20090