Introduction to SI Units and Measurement

Fundamental Principles of Physics:
- Physics involves observing the natural world through three primary actions: measuring, comparing, and thinking about causes of observations.
- The Critical Role of Units: Every measurement must specify the units used. Quantities written without units are considered meaningless.
- Scientific Units vs. Everyday Units: Units common in daily life (e.g., kilometers per hour) are often avoided in physics. Physics uses a system designed to simplify the mathematical relationships between different physical quantities.

Definition: The standard system is the Systme International (SI), or International System of Units. It is the modern iteration of the metric system and is the standard for physics research.
The 7 Base SI Units: While there are seven total, five are most commonly encountered:
- Length: Measured in metres ( $m$ ).
- Mass: Measured in kilograms ( $kg$ ).
- Time: Measured in seconds ( $s$ ).
- Electrical Currents: Measured in amperes ( $A$ ).
- Temperature: Measured in Kelvin ( $K$ ).
- Amount of Substance: Measured in Mole (less common in general physics).
- Luminous Intensity: Measured in Candela (less common in general physics).
Standardization and Definitions:
- SI units are standardized to be consistent globally and are very precisely defined.
- Historical Reference: "Le Grand K," or the International Prototype of the Kilogram, is a platinum-iridium alloy that served as the reference for the kilogram since $1889$ .
- Modern Definition: Modern SI units are defined based on universal constants, allowing them to be determined via experimentation anywhere in the universe.

Becquerel ( $Bq$ ): The SI unit of radioactivity. It is defined as the activity of a quantity of radioactive material in which one nucleus decays per second.
Gray ( $Gy$ ): The SI unit of ionizing radiation dose. It is defined as one joule of radiation energy per kilogram of matter ( $1\,J/kg$ ).
Sieverts ( $Sv$ ): The SI unit of ionizing radiation dose that specifically measures the health effect of radiation on living tissue (the human body).

Definition: Derived units are obtained by the multiplication or division of base units without introducing numerical factors.
Examples of Derived Units:
- Velocity: Measured in metres per second ( $m/s$ ).
- Acceleration: Measured in metres per second per second ( $m/s^2$ ).
- Energy: Measured in kilogram metres squared per second squared ( $kg\,m^2/s^2$ ).

Purpose: Conversion is necessary when units provided differ from requirements, such as converting non-standard units (pounds, miles) to SI units.
Methodology: Ensure that the fraction containing the conversion factor has the units in the correct order to cancel out the unwanted units.
Case Study: The Alaska Pipeline:
- Context: The pipeline is $799\,\text{miles}$ long.
- Conversion Factor: $1\,km = 0.621\,\text{miles}$ .
- Problem A: Calculate length in $km$ .
- Problem B: If oil flows at $3.7\,\text{miles/hour}$ , calculate speed in $km/h$ and $m/s$ .
- Problem C: Calculate the total time taken for oil to travel the length of the pipeline.

Utility: Physics deals with scales ranging from galaxies to atoms. Scientific notation provides a manageable way to represent extreme numbers.
The Golden Rule: In scientific notation, the number in front of the base ( $10$ ) must always be between $1$ and $10$ .
- If the number is less than $1$ , decrease the power of ten.
- If the number is $10$ or greater, increase the power of ten.
Specific Examples (Conversion to Scientific Notation):
- $300 = 3 \times 10^2$
- $1500 = 1.5 \times 10^3$
- $0.03 = 3 \times 10^{-2}$
- $0.0015 = 1.5 \times 10^{-3}$
- $123456789 = 1.23456789 \times 10^8$
- $7 = 7 \times 10^0$

Purpose: Prefixes serve as shorthand for powers of ten when used with units.
Common Prefixes:
- Tera ( $T$ ): $10^{12}$
- Giga ( $G$ ): $10^9$
- Mega ( $M$ ): $10^6$
- Kilo ( $k$ ): $10^3$
- Centi ( $c$ ): $10^{-2}$
- Milli ( $m$ ): $10^{-3}$
- Micro ( $\mu$ ): $10^{-6}$ (sometimes called "microns" for length).
- Nano ( $n$ ): $10^{-9}$
Usage Patterns: Multiples of $3$ in the power of $10$ index are standard because humans typically communicate in thousands.
Exceptions and Familiarity: Usage can depend on convention. For example, the distance from Sydney to London ( $17000\,km$ ) is never referred to as $17\,\text{megametres}$ .
Medical/Nuclear Context Examples:
- milliSieverts ( $mSv$ )
- microCuries ( $\mu Ci$ )
- kilo-electronvolts ( $keV$ )

Definition: Significant figures are the digits in a real-world number that are reliably known through measurement.
Measurement vs. Constants: Sig figs apply to things measured in real life (speed, time, length) rather than mathematical constants (such as $\pi$ or $1/2$ ).
Purpose: They measure precision and prevent over-reporting the calculated precision based on calculator output.
The Role of Zero: Zeros are written even when they have no numerical value if they indicate the degree of precision. For example, $5.000$ indicates a higher level of precision than $5.00$ or $5$ .

Multiplication and Division: The final answer should have no more significant figures than the input number with the fewest significant figures.
- Example: $4.51 \times 62 = 279.62$ . Rounded to $2$ significant figures (based on $62$ ), the answer is $280$ .
Adding and Subtracting: The final answer should have no more decimal places than the input with the fewest decimal places.
- Example: $184.2 + 3.884 = 188.084$ . Rounded to $1$ decimal place (based on $184.2$ ), the answer is $188.1$ .