Units
High-Yield Summary
- The SI system defines 7 base units (meter, kilogram, second, Kelvin, ampere, mole, candela); every other unit is derived from combining these.
- Metric prefixes (giga- to nano-) rescale a unit by a power of ten without changing what's being measured.
- Dimensional analysis converts between units using conversion factors arranged so unwanted units cancel.
- A measurement is meaningless without its unit — always carry units through a calculation, not just the numbers.
The 7 SI Base Units
| Quantity | Unit (Symbol) |
|---|---|
| Length | Meter (m) |
| Mass | Kilogram (kg) |
| Time | Second (s) |
| Temperature | Kelvin (K) |
| Electric current | Ampere (A) |
| Amount of substance | Mole (mol) |
| Luminous intensity | Candela (cd) |
Common Metric Prefixes
| Prefix | Power of Ten |
|---|---|
| Giga- (G) | 10⁹ |
| Mega- (M) | 10⁶ |
| Kilo- (k) | 10³ |
| (base unit) | 10⁰ |
| Centi- (c) | 10⁻² |
| Milli- (m) | 10⁻³ |
| Micro- (μ) | 10⁻⁶ |
| Nano- (n) | 10⁻⁹ |
Dimensional Analysis — The Three-Step Method
- 1Write down what you want to know — identify the final unit(s) your answer should be in.
- 2Start with the given measured quantity — begin with the value and unit you were given.
- 3Apply conversion factors so unwanted units cancel, multiplying until only the desired unit remains.
Common MCAT Trap
- Derived units aren't a separate category to memorize — they're just combinations of the 7 base units (e.g., volume = m³, from length × width × height).
- Don't confuse Milli- (m, 10⁻³) with the base unit symbol for meter (m) — context determines which one a lowercase 'm' means.
Quick Recall
How many SI base units are there, and what makes a unit 'derived'?
What are the three steps of dimensional analysis?