SI base units
Chemistry measurements are built on the International System of Units (SI). Every other unit you'll use in chemistry, whether it's a volume in liters or a concentration in molarity, is defined in terms of these base units. Knowing them cold makes every conversion problem a matter of bookkeeping instead of guesswork.
| Quantity | SI base unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Amount of substance | mole | mol |
| Electric current | ampere | A |
| Luminous intensity | candela | cd |
Lab-bench units aren't always the base unit
In lab you weigh in grams (g), not kilograms, and measure volume in liters (L) or milliliters (mL), even though volume isn't an SI base quantity at all (it's derived: 1 L = 1000 cm³). That's normal. The base unit is the reference point the prefixes below scale from, not the unit you're required to use on every measurement.
Metric prefixes
A metric prefix attached to a base unit multiplies or divides it by a power of ten. Learn the ladder once and it applies to every base unit: meters, grams, liters, seconds, all of it.
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| giga | G | ×10⁹ | 1 Gg = 10⁹ g |
| mega | M | ×10⁶ | 1 Mg = 10⁶ g |
| kilo | k | ×10³ | 1 kg = 10³ g |
| hecto | h | ×10² | 1 hg = 10² g |
| deka | da | ×10¹ | 1 dag = 10¹ g |
| (base unit) | — | ×10⁰ | 1 g = 1 g |
| deci | d | ×10⁻¹ | 1 dg = 10⁻¹ g |
| centi | c | ×10⁻² | 1 cg = 10⁻² g |
| milli | m | ×10⁻³ | 1 mg = 10⁻³ g |
| micro | µ | ×10⁻⁶ | 1 µg = 10⁻⁶ g |
| nano | n | ×10⁻⁹ | 1 ng = 10⁻⁹ g |
| pico | p | ×10⁻¹² | 1 pg = 10⁻¹² g |
The ones you'll actually use
In a typical high school chemistry course, kilo, centi, milli, and micro cover the vast majority of problems (kg, cm, mL, µg, µL). Memorize those four cold before worrying about the rest of the ladder.
The factor-label method (dimensional analysis)
Dimensional analysis, also called the factor-label method, converts a quantity from one unit to another by multiplying it by one or more conversion factors. A conversion factor is a fraction built from an equality (like 1000 m = 1 km) that equals exactly 1, so multiplying by it changes the units without changing the actual quantity. The method in three steps: 1. Write the given quantity with its unit. 2. Multiply by a conversion factor, arranged so the unit you don't want is on the bottom (it cancels the matching unit on top from the previous step). 3. Keep chaining factors until only the unit you want is left standing, uncancelled.
Worked example. Convert 5.00 km to meters, using the equality 1 km = 1000 m: 5.00 km × (1000 m / 1 km) = 5.00 × 1000 m = 5.00 × 10³ m The km unit is on top in the given quantity and on the bottom in the conversion factor, so it cancels, leaving m.
The #1 mistake: the factor upside down
If you write the conversion factor with km on top instead of bottom, the km units DON'T cancel and you're left with km²/m, a meaningless unit. Before you multiply, check that the unit you're trying to eliminate appears once on top and once on bottom. If it doesn't cancel on paper, it's wrong, even if the arithmetic looks fine.
Multi-step conversions
Most real conversions need more than one factor chained together. Set up the whole chain before multiplying anything, so you can check that every intermediate unit cancels before you touch a calculator.
Worked example. Convert 2.50 days to seconds, using 1 day = 24 h, 1 h = 60 min, 1 min = 60 s: 2.50 d × (24 h / 1 d) × (60 min / 1 h) × (60 s / 1 min) Days cancel with days, hours cancel with hours, minutes cancel with minutes, leaving seconds: = 2.50 × 24 × 60 × 60 s = 216,000 s = 2.16 × 10⁵ s
| Equality | Type |
|---|---|
| 1 km = 1000 m | Exact (defined metric relationship) |
| 1 in = 2.54 cm | Exact (defined by international agreement, 1959) |
| 1 L = 1000 mL = 1000 cm³ | Exact (defined metric relationship) |
| 1 mol = 6.022 × 10²³ particles | Exact (defined value of Avogadro's number) |
| 1 lb = 453.6 g | Measured / rounded, not exact |
Chemistry-specific conversions: mole, density, temperature
Where these come from
Molar mass, the mole, and Avogadro's number are introduced in full in the The Mole, Molar Mass & Particle Count reference sheet. Here we use them only as ready-made conversion factors, so if the mole is new to you, read that sheet first.
Three conversion factors show up constantly once you're past pure unit conversion and into actual chemistry problems: molar mass (links grams and moles), Avogadro's number (links moles and particles), and density (links mass and volume for a specific substance).
Worked example — grams to moles. How many moles are in 25.0 g of NaCl? Molar mass of NaCl = 22.99 g/mol (Na) + 35.45 g/mol (Cl) = 58.44 g/mol. 25.0 g NaCl × (1 mol NaCl / 58.44 g NaCl) = 0.428 mol NaCl
Worked example — moles to particles. How many formula units are in 0.428 mol NaCl? 0.428 mol NaCl × (6.022 × 10²³ formula units / 1 mol) = 2.58 × 10²³ formula units
Worked example — density as a conversion factor. The density of water is 1.00 g/mL. How many grams is 250. mL of water? 250. mL × (1.00 g / 1 mL) = 250. g
Temperature isn't a simple factor-label conversion
Celsius, Kelvin, and Fahrenheit conversions involve an OFFSET, not just a multiplier, so you can't cancel them like a normal conversion factor: K = °C + 273.15 °C = (°F − 32) × 5/9 °F = °C × 9/5 + 32 A Celsius degree and a Kelvin are the same SIZE (0 °C = 273.15 K, 100 °C = 373.15 K), which is why chemistry problems can add or subtract Celsius and Kelvin temperature CHANGES interchangeably, but converting a specific temperature always needs the addition or the full formula, never a bare multiplication.
Significant figures in conversions
A conversion factor built from a defined equality (1 km = 1000 m, 1 mol = 6.022 × 10²³ particles, 12 in = 1 ft, 1 in = 2.54 cm) is an exact number with infinite significant figures. It never limits the precision of your answer. The sig figs in your final answer come only from the measured quantities in the problem.
| Operation | Rule | Example |
|---|---|---|
| Multiplication / division | Result has the same number of sig figs as the measurement with the FEWEST sig figs | 5.00 km × (1000 m/km) → 3 sig figs → 5.00 × 10³ m |
| Addition / subtraction | Result has the same number of decimal places as the measurement with the FEWEST decimal places | 12.52 mL + 3.7 mL = 16.2 mL (1 decimal place) |
How to spot an exact number
Ask "is this a definition, or something someone measured?" 1000 m in a km is a definition. 453.6 g in a pound is a rounded conversion between two measurement systems, not an exact definition, so treat it as a measured value with limited sig figs unless your teacher's key says otherwise.
Common pitfall: counting the conversion factor's digits
Students often see "1000 m" and think it has 1 or 4 sig figs and let that limit the answer. Defined conversion factors are exact and NEVER reduce your sig figs, no matter how many digits they're written with. Only the numbers that came from a measurement in the problem (a ruler reading, a balance reading, a given quantity) control the sig figs in your answer.
Try it yourself
unit-conversion-lab-measurements.csvDownload unit-conversion-lab-measurements.csv: https://restedteacher.com/practice-files/chemistry/unit-conversion-lab-measurements.csv
Eight lab measurements, each asking for a conversion from one unit to another; the note column carries any extra information a trial needs, such as a density.
Open it as a spreadsheet
Open unit-conversion-lab-measurements.csv in Google Sheets or Excel. Add a converted-value column and fill it down once you've worked out the factor for each row's fromunit -> tounit pair.
Using the values in the file, answer these. Round every converted value to 3 significant figures. 1. Convert trial 4's measurement from inches to centimeters, using 1 in = 2.54 cm (exact). 2. Trial 8 gives a mass and, in the note column, a density. Calculate the volume in mL. 3. Which trial's conversion requires adding an offset instead of multiplying by a conversion factor, and what is the converted value? Use K = °C + 273.15.