The Metric System: SI Base Units and Prefixes
Learn the seven SI base units and how metric prefixes let a single base unit cover scales from subatomic to astronomical.
The metric system is used by every country in the world for science, medicine, and international trade — including the United States in those contexts. It was designed with one goal: make unit conversion as simple as arithmetic. When a chemist measures 0.005 grams, a physicist measures 5,000,000 grams, and an engineer measures 5 kilograms, they are all describing the exact same mass using the same base unit and different prefixes. Once you learn the seven base units and the prefix table, you can work in any field of science or engineering without learning a new system — because it is all one system.
- Name the seven SI base units and what physical quantity each measures
- Apply metric prefixes from pico (10⁻¹²) to tera (10¹²) to any base unit
- Convert between prefix scales by moving the decimal point
Every other unit in the metric system — newtons, joules, watts, pascals — is built by combining these seven.
Metric Prefix Table (most common)
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| tera- | T | \(10^{12}\) | 1 TB = 10¹² bytes |
| giga- | G | \(10^{9}\) | 1 GHz = 10⁹ cycles/s |
| mega- | M | \(10^{6}\) | 1 MW = 10⁶ watts |
| kilo- | k | \(10^{3}\) | 1 km = 1,000 m |
| (base) | — | \(10^{0} = 1\) | 1 m, 1 g, 1 s |
| centi- | c | \(10^{-2}\) | 1 cm = 0.01 m |
| milli- | m | \(10^{-3}\) | 1 mL = 0.001 L |
| micro- | μ | \(10^{-6}\) | 1 μm = 10⁻⁶ m (a bacterium) |
| nano- | n | \(10^{-9}\) | 1 nm = 10⁻⁹ m (wavelength of light) |
| pico- | p | \(10^{-12}\) | 1 pF = 10⁻¹² farads (tiny capacitor) |
A lab report lists a measurement of 3.5 km. What does that mean?
kilo- = \(10^3\), so 1 km = 1,000 m.
\[ 3.5 \text{ km} = 3.5 \times 1{,}000 \text{ m} = 3{,}500 \text{ m} \]km is the base unit (meter) scaled by the prefix kilo- (1,000).
A computer has a 512 GB hard drive. Express this capacity in bytes using scientific notation.
\[ 512 \text{ GB} = 512 \times 10^9 \text{ bytes} = 5.12 \times 10^{11} \text{ bytes} \]The prefix giga- (\(10^9\)) combined with the base unit (byte) gives the conversion; scientific notation makes the result manageable.
A patient is prescribed 250 micrograms (μg) of a cardiac medication. The pharmacy stocks it in milligram (mg) tablets. How many mg is that?
\[ 250 \, \mu\text{g} \times \frac{1 \text{ mg}}{1{,}000 \, \mu\text{g}} = 0.25 \text{ mg} \]μg (micro-) is \(10^{-6}\) g; mg (milli-) is \(10^{-3}\) g. Moving from μg to mg divides by 1,000. Confusing these two prefixes — a factor of 1,000 — is one of the most common and dangerous medication errors.
- How many meters are in 4.2 kilometers?
- A bacterium is 2 micrometers long. Write this in meters using scientific notation.
- What SI unit measures electric current, and what is its symbol?
▶ Show Answers
- \(4.2 \times 1{,}000 = \mathbf{4{,}200 \text{ m}}\)
- \(2 \, \mu\text{m} = 2 \times 10^{-6} \text{ m}\)
- The ampere, symbol A.
- Confusing the prefix m (milli-) with M (mega-): Lowercase m = milli (\(10^{-3}\)); uppercase M = mega (\(10^6\)). The difference is nine orders of magnitude. Always check capitalization.
- Thinking kg is a "derived" unit: Despite containing the prefix kilo-, the kilogram is an SI base unit — defined directly, not derived from the gram. The gram is actually the derived unit.
- Applying prefixes to non-metric units: Prefixes only work with SI units. "Kilofoot" is not a standard unit — and for good reason.
- The metric system has 7 base units; all other units are derived from these.
- Prefixes are powers of 10 added to any base unit — learn them once, apply them everywhere.
- Each prefix step = multiply or divide by 10 — no memorizing arbitrary conversion factors.
- Scientific notation and metric prefixes work together to express any scale from subatomic to astronomical.
Electrical engineers work in millivolts, microfarads, and gigahertz — all in the same schematic. Biologists measure in micrometers and nanometers for cells and molecules. Software engineers deal with kilobytes through petabytes of storage. Chemists use millimoles and micromoles for reaction stoichiometry. In every technical field, the metric prefix system is the shared language. Knowing it cold means you can read any international datasheet, paper, or specification without translation.
Calculator Connection
The Metric Prefix Converter lets you enter a value and instantly see it expressed in every prefix from pico to tera — great for developing intuition about scale. The SI Unit Explorer shows all base and derived units with their dimensions.
Try it with the Calculator
Apply what you've learned with these tools.
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