Notes on SI Units and Measurements: Base Units, Prefixes, Mass, Weight, and Volume
Basic idea of a measurement
A measurement has two parts: a number and a unit.
Even though this is a lecture, you’ll be given measurements and will perform calculations with them.
We will look at units first, then examine mass and weight, and then volume.
The SI system (International System of Units)
SI stands for the International System (French: Système international d’unités).
It is based on the metric system and is more fine-tuned than the metric system alone.
For the most part, we’ll use SI units in these lessons.
Base SI units (and what you should know about them in this course)
The slide lists the base units and their symbols; length and time are assumed to be familiar, so they are given special emphasis (as indicated by an asterisk).
Base units in the list include:
Length: the meter, symbol m
Time: the second, symbol s
Mass: the kilogram, symbol kg
Electrical current: the ampere, symbol A (not covered until much later; not in General Chemistry I)
Temperature: the kelvin, symbol K
Amount of substance: the mole, symbol mol (note: students are cautioned about abbreviation)
Candela: the candela, symbol cd (not used in general chemistry)
Volume is not listed as a base unit in the table; it will be treated as a derived quantity later (Volume = length × width × height).
Temperature scales to be examined later: Fahrenheit and Celsius, in addition to Kelvin.
The table represents the “basis” of SI units, but many other SI units and derived units exist beyond this list.
Important practical note: you should not abbreviate mole as M (M stands for meter); the conventional abbreviation is mol.
Candela is not used in general chemistry; it is listed here as part of the SI base units but not relevant for this course.
SI prefixes (key concept for chemists)
You will need to memorize the list of metric prefixes, including the prefix word, its symbol, and its meaning (powers of ten).
The most common prefixes (often encountered in problems) are marked with an asterisk in teaching materials: milli, kilo, and micro are the examples highlighted for frequent use.
While many prefixes exist, the instruction emphasizes getting comfortable with the common ones first.
The instructor emphasizes knowing the meaning of the prefix in terms of powers of ten, for example:
milli: meaning 10^{-3}
kilo: meaning 10^{3}
micro: meaning 10^{-6}
The teaching approach uses practical, intuitive relationships to avoid confusion when converting between units:
For milli (10^{-3}): one millimeter (mm) equals 10^{-3} meters (m). Equivalently, 1000 millimeters equal 1 meter, a common benchmark statement, but not the preferred framing for problem solving.
For kilo (10^{3}): one kilometer (km) or one kilogram (kg) equals 1,000 of the base unit. The rule stated: one with the prefix equals the meaning without the prefix.
For micro (10^{-6}): one micrometer (μm) equals 10^{-6} meters; the pattern remains: one with the prefix equals the base (without the prefix).
A practical pattern to use in calculations: always place a leading 1 in front of the prefixed quantity and place the prefix meaning after it; this ensures a consistent relationship for calculations.
This approach helps when converting between different unit scales (e.g., base units to scaled units) and reduces confusion in long or multi-step problems.
Note on usage: nano and pico are less common in introductory chemistry but may appear in General Chemistry II; you’ll encounter them more in deeper coursework.
Mass vs. weight (conceptual distinction)
Mass is the amount of matter in an object; it does not change with location.
Weight is the force of gravity acting on that mass; weight changes with gravity.
A kilogram is the SI unit of mass; it is defined such that 1 kilogram equals 1000 grams (1 kg = 1000 g).
In many contexts, people use mass and weight interchangeably, but scientifically they are different quantities.
Mass is measured with a balance (which balances masses on opposite sides).
Weight is measured with a spring scale (a spring stretching under gravity indicates weight).
The relationship between mass and weight is governed by gravity; the lecturer notes an Earth-to-Moon comparison: weight on the Moon would be about a tenth of what it is on Earth (emphasized in the lecture; not a precise physical statement, but the point is that weight changes with gravity while mass remains constant).
Volume: derived unit and practical units
Volume is a derived unit: V = length × width × height, i.e., a product of three length measurements.
In SI base units, length is the meter, so the SI unit for volume is cubic meters: V = l imes w imes h \text{with units: } V ext{ in } ext{m}^3. (Mathematically, V = l imes w imes h.)
The cubic meter is quite large for chemical quantities; in practice we use smaller units:
A cubic centimeter (cm^3) is a convenient unit for small volumes: 1 cm = 10^{-2} m; therefore, 1 cm^3 = (10^{-2} m)^3 = 10^{-6} m^3.
A sugar cube is roughly 1 cm^3 in volume.
Common volume units used in chemistry
The liter (L) is commonly used in chemistry, but it is not an SI base unit.
Relationships:
1 liter = 1000 milliliters (mL): 1\ ext{L} = 1000\ ext{mL}.
1 milliliter = 10^{-3} liters: 1\ \text{mL} = 10^{-3}\ \text{L}.
1 mL is exactly equal to 1 cm^3: 1\ \text{mL} = 1\ \text{cm}^3.
A commonly memorized connection: between the world of length (cm) and the world of volume (L), memorize that 1 mL = 1 cm^3 to smoothly convert between mL and cm^3 (often used when switching between volume in liquids and dimensional measurements).
Practical notes and study tips
The SI base unit list is foundational, but there are many derived units and additional SI rules not exhaustively listed here.
For mass and volume, remember practical conversions that come up most, such as 1 kg = 1000 g and 1 L = 1000 mL.
When writing problems, prefer using the explicit relationships for prefixes (e.g., 1 mm = 10^{-3} m) rather than relying solely on the mental anchor of 1000 of one unit per base unit; this helps reduce errors later in more complex problems.
Be mindful of abbreviations:
Mole should be abbreviated as mol, not M (which stands for meter).
Do not rely solely on memorizing long lists of prefixes; focus on understanding the meaning (power of ten) and translating between the prefixed and unprefixed forms using the stated patterns.
Although Candela and certain base units are listed in the SI table, they are not used in this general chemistry course, and some topics (current, Fahrenheit, Celsius) will be addressed later in the curriculum.
Quick reference equations and relations (in LaTeX)
Volume from dimensions: V = l \cdot w \cdot h
SI base to common volume units:
1\ \text{L} = 1000\ \text{mL}
1\ \text{mL} = 10^{-3}\ \text{L}
1\ \text{cm} = 10^{-2}\ \text{m}
1\ \text{cm}^3 = 10^{-6}\ \text{m}^3
1\ \text{mL} = 1\ \text{cm}^3
Mass relation:
1\ \text{kg} = 1000\ \text{g}
Prefix meaning examples:
milli: 10^{-3}
kilo: 10^{3}
micro: 10^{-6}
For prefixes, the consistent pattern to remember: one with the prefix equals the base unit without the prefix; e.g., 1\ \text{mm} = 10^{-3}\ \text{m}.