Measurement

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 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