Measurements and SI Units

Qualitative Statements: In science, we describe observations based on the qualities of an object or phenomenon without using numerical values. For example, observing that "the metal bar expands when heated" is a qualitative statement.
Quantitative Statements: These involve taking measurements to provide precise data. For example, stating that "the metal bar expands $2.6\,mm$ " is a quantitative statement.
Requirement for Units: Whenever a quantitative statement is made, the number provided should always include a specific unit. All measurements must have units to ensure clarity and accuracy.

To prevent confusion in global scientific communication, researchers use the S.I. Units.
SI stands for the International System of Units (Le Système International d'Unités).
It is defined as a universal base unit and standard system of measurement used across all scientific disciplines.

Fundamental quantities are the basic physical quantities that are not defined in terms of other quantities. The following table identifies the standard SI units for these quantities:
Mass
- Symbol: $m$
- SI Unit Name: Kilogram
- SI Unit Symbol: $kg$
Length
- Symbol: $L$
- SI Unit Name: Metres
- SI Unit Symbol: $m$
Time
- Symbol: $t$
- SI Unit Name: Seconds
- SI Unit Symbol: $s$
Current
- Symbol: $I$
- SI Unit Name: Amperes
- SI Unit Symbol: $A$
Temperature (Standard SI)
- Symbol: $T$
- SI Unit Name: Kelvin
- SI Unit Symbol: $K$
Temperature (Common Metric)
- Symbol: $\Theta$
- Unit Name: degrees Celsius
- Unit Symbol: $^\circ C$
Luminous Intensity
- Symbol: $l_v$
- SI Unit Name: candela
- SI Unit Symbol: $cd$

Physicists often deal with measurements that are extremely large or extremely small. Prefixes are used to modify the base unit by a power of $10$ .
Multiple Units: These units are larger than the basic unit (base unit multiplied by a power of $10$ ).
- Giga ( $G$ ): $10^9$
- Mega ( $M$ ): $10^6$
- Kilo ( $k$ ): $10^3$
Submultiple Units: These units are smaller than the basic unit (base unit divided by a power of $10$ ).
- Milli ( $m$ ): $10^{-3}$
- Micro ( $\mu$ ): $10^{-6}$
- Nano ( $n$ ): $10^{-9}$
- Pico ( $p$ ): $10^{-12}$

Science students must be proficient in converting measurements between higher and lower units of scale.
Converting a Smaller Unit to a Larger Unit:
- Rule: Divide the number by the appropriate multiple of ten.
- Example: Convert $6000\,g$ to $kg$ .
- Process: Since there are $1000\,g$ in $1\,kg$ , divide by $1000$ .
- Result: $6000 / 1000 = 6\,kg$ .
- Hint: Your final number should be smaller than the original numerical value.
Converting a Larger Unit to a Smaller Unit:
- Rule: Multiply the number by the appropriate multiple of ten.
- Example: Convert $7\,m$ to $mm$ .
- Process: Since $1\,m$ contains $1000\,mm$ , multiply by $1000$ .
- Result: $7 \times 1000 = 7000\,mm$ .
- Hint: Your final number should be larger than the original numerical value.

1. Table Completion: Copy and complete the following table:
- Length | [Metre] | $m$
- Mass | [Kilogram] | $kg$
- [Time] | [Seconds] | $s$
- [Current] | Ampere | [ $A$ ]
- Temperature | [Kelvin] | [ $K$ ]
- Area | [Square Metres] | $m^2$
- [Force/Weight] | Newton | [ $N$ ]
2. Unit Relationship Quantities:
- a) How many $mg$ are there in $1\,g$ ?
- b) How many $g$ are there in $1\,kg$ ?
- c) How many $mg$ are there in $1\,kg$ ?
- d) How many $mm$ are there in $4\,km$ ?
- e) How many $cm$ are there in $5\,km$ ?
3. Value Conversion Exercises:
- a) Convert $300\,cm$ to $m$ .
- b) Convert $500\,g$ to $kg$ .
- c) Convert $500\,m$ to $km$ .
- d) Convert $250\,ms$ to $s$ .
- e) Convert $0.5\,s$ to $ms$ .
- f) Convert $0.75\,km$ to $m$ .
- g) Convert $2.5\,kg$ to $g$ .
- h) Convert $0.8\,m$ to $mm$ .

Note: Document authored/compiled by T. Harding, A. Lovell & D. Whitehall.