Quick Reference
Convert before substitute
It is usually cleaner to convert all inputs into compatible units before inserting them into an equation.
Prefix = power
kilo means 10³; milli means 10⁻³; micro means 10⁻⁶.
Dimensional analysis
Units can behave like algebra. They can reveal impossible combinations before you finish the arithmetic.
Sig figs are not “rounding vibes”
The number of reported digits carries information about measurement precision.
1. The SI Backbone
The SI system organizes measurement around defined base units and derived units. NIST describes unit conversion as a relationship between equal quantities, typically expressed through conversion factors. In school-level problem solving, the most useful habit is to keep one coherent unit system through the calculation.
| Quantity | SI unit | Symbol | Common MDCAT context |
|---|---|---|---|
| Length | metre | m | motion, waves, geometry |
| Mass | kilogram | kg | mechanics, density, energy |
| Time | second | s | motion, frequency, power |
| Temperature | kelvin | K | gas laws, thermodynamics |
| Amount of substance | mole | mol | stoichiometry, molarity |
| Electric current | ampere | A | circuits, charge, electromagnetism |
2. Prefixes Worth Automating
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| kilo | k | 10³ | 1 km = 10³ m |
| mega | M | 10⁶ | 1 MJ = 10⁶ J |
| centi | c | 10⁻² | 1 cm = 10⁻² m |
| milli | m | 10⁻³ | 1 mA = 10⁻³ A |
| micro | μ | 10⁻⁶ | 1 μm = 10⁻⁶ m |
| nano | n | 10⁻⁹ | 1 nm = 10⁻⁹ m |
| pico | p | 10⁻¹² | 1 ps = 10⁻¹² s |
NIST also lists the newer very-large and very-small SI prefixes. You do not need to over-memorize rare prefixes for MDCAT if your syllabus does not require them; concentrate on the factors that actually appear in your calculations.
3. Scientific Notation
Scientific notation writes a number as a × 10ⁿ, where 1 ≤ |a| < 10. Moving the decimal to the right produces a negative exponent; moving it to the left produces a positive exponent.
4. Dimensional Analysis
Dimensional analysis treats units as algebraic objects. Suppose a formula proposes velocity = distance / time. The dimensions become metres per second, which matches the SI unit of speed. If your calculation produces kilograms per second for a quantity that is supposed to be a velocity, something upstream is wrong.
It cannot prove that an equation is physically correct by itself, but it can quickly disprove an equation or reveal a conversion mistake.
5. Significant Figures
OpenStax describes significant figures as a way of communicating the precision associated with a measurement. The key reporting rules used in introductory work are:
- Multiplication/division: report no more significant figures than the least precise measured factor.
- Addition/subtraction: report no more decimal places than the least precise measured quantity.
- Do not manufacture precision by writing extra digits after a measurement.
Keep the distinction between accuracy (closeness to the accepted value) and precision (repeatability / agreement among measurements). A measurement can be precise but inaccurate.
6. The Three Giant Conversion Traps
Area & volume
Squaring or cubing a length conversion changes the conversion factor accordingly. 1 cm² is not 0.01 m²; it is 10⁻⁴ m².
mL vs L
1 mL = 10⁻³ L. Forgetting this factor changes a molarity calculation by 1000.
°C vs K
Gas-law temperature must be on the absolute scale: K = °C + 273.15.
Prefix collisions
m means milli in SI prefixes; M means mega. Case matters.
Frequently Asked Questions
PM&DC — Uniform Curriculum MDCAT-2025 (official PDF) · NIST — Metric (SI) Prefixes · NIST — Guide to the SI, Chapter 4 · OpenStax — College Physics 2e: Physical Quantities, Units, Accuracy & Significant Figures · OpenStax — College Physics: Accuracy, Precision, and Significant Figures
Scope: scientific explanations are written for student use and simplified where appropriate. Exact exam wording, syllabus scope and current administrative rules should be checked against PM&DC documents.