A number and a unit
“This cup holds 250.” 250 what? Milliliters? Grams? A measurement always needs both a number and a unit: 250 mL. Without the unit, the number means nothing.
Common units
| Quantity | SI unit | Common in chemistry |
|---|---|---|
| Length | meter, m | cm, mm, nm |
| Mass | kilogram, kg | g, mg |
| Volume | cubic meter, m³ | L, mL (1 mL = 1 cm³) |
| Temperature | kelvin, K | degrees Celsius, °C |
| Time | second, s | min |
| Amount of substance | mole, mol | Coming in Stage 2 |
Prefixes: size at a glance
A prefix in front of a unit multiplies it by a power of 10:
| Prefix | Symbol | Meaning | Example |
|---|---|---|---|
| kilo | k | 10³ = 1000 | 1 kg = 1000 g |
| centi | c | 10⁻² = 1/100 | 1 m = 100 cm |
| milli | m | 10⁻³ = 1/1000 | 1 L = 1000 mL |
| micro | μ | 10⁻⁶ | 1 g = 10⁶ μg |
| nano | n | 10⁻⁹ | 1 m = 10⁹ nm |
10⁻² is read “10 to the power −2.” A negative exponent means “1 divided by that power of 10”: 10⁻ⁿ = 1/10ⁿ. So 10⁻² = 1/100 = 0.01, and 10⁻⁶ = 1/1,000,000 = 0.000001. A positive exponent is just 1 followed by that many zeros: 10⁶ = 1,000,000. Writing a number as 5 × 10⁴, as in an example below, is called scientific notation; the Scientific Notation tool card in lesson 1.3.2 covers it fully.
Temperature: T (K) = t (°C) + 273 (more precisely, 273.15). Water freezes at 0 °C = 273 K and boils at 100 °C = 373 K.
🔧 Math tool card · Units & ConversionsSkip it if you already know this
Conversion factors: write “1 L = 1000 mL” as a fraction equal to 1, . Multiplying by 1 doesn’t change the amount, only the unit.
Which way up? Put the unit you want to get rid of in the denominator, so it cancels the unit you started with.
Example:
To convert 350 mL to L, which conversion factor do you multiply by?
To get rid of mL, put mL in the denominator: 350 mL × (1 L / 1000 mL) = 0.35 L.
Choose a quantity, enter a value, and switch units to see how the conversion factor is written:
Example 1: Two steps
How many centimeters are in 0.5 km?
- Convert to meters first.
- Then to centimeters.
- Or chain them together.
Example 2: Temperature
Normal body temperature is about 37 °C. What is that in kelvins?
- Use the formula. T (K) = t (°C) + 273.
- Substitute. T = 37 + 273 = 310 K.
- The mass of one vitamin C tablet
About 100 mg.
- The mass of an egg
About 50 g.
- The mass of a high school student
About 50 kg.
- The volume of a bottle of water
About 500 mL.
- The volume of a water-cooler bottle
About 19 L.
- The hydrochloric acid measured out for one experiment
About 10 mL.
Common mistakes
Mistake 1: Writing a number with no unit. “Add 5 of hydrochloric acid” means nothing. Write “add 5 mL of hydrochloric acid.”
Mistake 2: Flipping the conversion factor. In , the units don’t cancel and you end up with a strange unit. Checking that units cancel is a great way to catch mistakes.
Mistake 3: Ignoring capital letters. m means milli (10⁻³) and M means mega (10⁶), so mg and Mg differ by a factor of 10⁹. And Mg is also the symbol for magnesium!
Quick check
How many milliliters are in 1.5 L?
1.5 L × (1000 mL / 1 L) = 1500 mL.
What is −10 °C in kelvins?
T = −10 + 273 = 263 K.
Summary
- Every measurement is a number plus a unit.
- Common prefixes: k (10³), c (10⁻²), m (10⁻³), μ (10⁻⁶), n (10⁻⁹). 1 mL = 1 cm³. T (K) = t (°C) + 273.
- To convert, multiply by a conversion factor equal to 1, with the unit you want to remove in the denominator so it cancels.
On to AP (for later)
AP Chemistry relies heavily on this kind of dimensional analysis. Calculations with moles, concentrations, and gases can almost all be written as a chain of conversion factors with the units canceling one by one. Lesson 2.1.2 in Stage 2 practices multi-step conversions.