Notes on Measurement and Scientific Investigation

Physical Sciences: Includes Physics, Chemistry, Geology, Meteorology, and Astronomy. These disciplines describe and measure the physical world to understand the environment.
Natural Sciences: A broader category consisting of both Physical Sciences and Biological Sciences.

Assumptions: Scientists assume the universe is orderly and understandable.
Scientific Method Components:
- Observations & Measurements: Gathering quantitative data.
- Hypothesis: A tentative explanation or educated guess to be tested (e.g., Atomic Theory basics).
- Experiments: Testing under controlled conditions; results must be reproducible.
- Theory: A broad, well-tested explanation for natural phenomena (e.g., Atomic Theory).
- Law: A concise mathematical or verbal statement of a fundamental relationship in nature (e.g., Law of Conservation of Mass).

Sensory Tools: Sight, hearing, smell, taste, and touch. Sight and hearing provide the most data.
Limitations: Senses can be deceived by optical illusions and have physical limits; instruments are used to extend our ability to learn about the environment.

Standard Unit: A fixed, reproducible value for accurate measurements.
Systems of Units:
- Metric System (mks): Base-10 (decimal) system used globally; includes the International System of Units (SI).
- British (English) System: Primarily used in the United States; includes units like miles, inches, and pounds.
Fundamental Quantities:
- Length: Metric standard is the Meter ( $m$ ), currently defined by the distance light travels in a vacuum per unit of time.
- Mass: Metric standard is the Kilogram ( $kg$ ). It is constant throughout the universe. The U.S. Prototype #20 Kilogram is approximately $0.999\,999\,961\,kg$ .
- Time: Standard unit is the Second ( $s$ ), defined by the radiation frequency of the $Cs\,133$ atom ( $9,192,631,770$ oscillations).
Mass vs. Weight: Mass is a fundamental constant, while Weight ( $lb$ ) varies based on gravitational attraction (e.g., an object weighing $300\,lb$ on Earth weighs $50\,lb$ on the Moon).

Seven Base Units:
- Meter ( $m$ ) for length.
- Kilogram ( $kg$ ) for mass.
- Second ( $s$ ) for time.
- Ampere ( $A$ ) for electrical current.
- Kelvin ( $K$ ) for temperature.
- Mole ( $mol$ ) for amount of substance.
- Candela ( $cd$ ) for luminous intensity.
Common Prefixes:
- Mega ( $M$ ): $10^{6}$
- Kilo ( $k$ ): $10^{3}$
- Centi ( $c$ ): $10^{-2}$
- Milli ( $m$ ): $10^{-3}$

Derived Units: Combinations of base units, such as Area ( $m^2$ ), Volume ( $m^3$ ), and Speed ( $m/s$ ).
Common Derived Physical Units:
- Newton ( $N$ ): $kg \times m/s^2$
- Joule ( $J$ ): $kg \times m^2/s^2$
- Watt ( $W$ ): $kg \times m^2/s^3$
Density ( $\rho$ ): Defined as mass per unit volume ( $\rho = \frac{m}{V}$ ). Measured in $g/cm^3$ or $kg/m^3$ .
- Liquid Density: Measured using a hydrometer. Higher floatation indicates greater density (e.g., Pure water is $1\,g/cm^3$ ; Seawater is $1.025\,g/cm^3$ ).
Volume & Mass Relationships: $1\,liter = 1000\,cm^3 = 1000\,ml$ . For water, $1\,ml = 1\,cm^3 = 1\,g$ .

Conversion Factors: Multipliers used to switch units (e.g., $1\,in. = 2.54\,cm$ ).
Examples:
- $1\,mi/h = 1.61\,km/h$
- $1\,km/h = 0.621\,mi/h$
- $1\,quart = 0.946\,liter$

Significant Figures (SF): Rules for precision in reporting measured numbers.
- Non-zero digits: Always significant.
- Captive zeros: Significant.
- Leading zeros: Not significant.
- Calculation Rule: Results cannot have more SF than the quantity with the least SF.
Rounding: If the first dropped digit is < 5, leave unchanged; if $\geq 5$ , round up.
Scientific Notation: Expressing numbers as powers-of-10.
- Shift decimal left: Increase exponent (e.g., $360,000 = 3.6 \times 10^5$ ).
- Shift decimal right: Decrease exponent (e.g., $0.0694 = 6.94 \times 10^{-2}$ ).
Example Calculation: Earth's orbit circumference ( $c = 2\pi r$ ) with a radius of $93 \times 10^6\,miles$ equals $5.8 \times 10^8\,miles$ after rounding.

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