Fundamentals of Scientific Measurement and Vector Analysis

Understanding Science and the Scientific Method

Science is knowledge obtained through observation and reasoning, systematically structured. The scientific method consists of observation, which leads to a hypothesis that must be proven or disproven.

Observation and Measurement

Observation is the activity of a living being that detects and registers data using the senses as the primary tools. The term can also refer to any data collected during this activity.

Measurement is the comparison of a magnitude with another, arbitrarily taken as a reference standard to express how many times it is contained. A standard of measurement is a pattern of actions isolated to serve as a foundation for creating a unit of measurement. While many units have patterns, the metric system relies on patterns of action.

Systems and Error Analysis

A measurement system is a set of elements, rules, or objects related to each other to fulfill a specific purpose. The rounding method is the process by which insignificant decimals are removed from a decimal number.

Uncertainty and Errors: This includes precision, accuracy, significant figures, absolute and relative errors, histograms, systematic and accidental errors, and error propagation.

• Absolute error: The difference between the measured value and the exact value. It can be positive or negative depending on whether the measure exceeds or falls short of the actual value. It shares the same units as the measure.
• Error percentage: The relative error multiplied by one hundred (100).

Significant Figures and Vectors

Significant figures represent the use of a level of uncertainty under certain approximations. The use of these considers the last digit to be an uncertain approach.

A vector is any directed line segment in space. Each vector has specific characteristics: Source, Module, Direction, and Sense.

• Unit vector: A vector is unitary if its norm is one. A unit vector can be found in the direction of another non-zero vector by dividing it by its standard.
• Module of a vector: A number that matches the "length" of the vector in graphical representation.
• Reverse vector: Placed in the opposite direction on the Cartesian plane.
• Void vector: A vector with a module (or extension) of zero. It is represented as or .

Physical Science and Standards

Physical science is the study of the properties of space, time, matter, and energy, taking into account their interactions.

Criteria for a Yardstick

What features should a yardstick provide?

• Be unchanged: It must not change over time or depending on who performs the measurement.
• Be universal: It must be widely used or at least recognized.
• Be easily reproducible: It should not be too expensive to manufacture, allowing for consistent measurements.

A law of science states a constant relationship between two or more variables, each of which represents (at least partially and indirectly) a property of concrete systems.