# Units and Unit Conversions

> SI units, prefixes, mass, volume and temperature conversions, and scientific notation.

From HSC Chemistry on WhizzNotes, free study notes for NSW students: https://whizznotes.com/chemistry/unit-conversions/. Updated 3 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The recipe that went wrong
Ella found a cake recipe online that said "add 0.25 kg of flour". Her kitchen scale only showed grams. She guessed 25 g. The cake came out as a flat, sweet pancake.

Her brother laughed. "A kilogram is 1000 grams. So 0.25 kg is 250 g. You used ten times too little."

Chemists face this every day. One lab reports in millilitres, another in litres. One balance shows grams, a formula wants kilograms. Getting units right is the difference between a good result and a flat cake.

**In short:** Chemistry uses SI units such as the kilogram, metre, second, kelvin and mole, plus everyday units like grams, millilitres and degrees Celsius. To convert, multiply when going from a big unit to a small one and divide the other way, with 1 L = 1000 mL and K = °C + 273.

## SI units

Scientists around the world use the same base units, called **SI units**.

| Quantity | SI unit | Symbol | Common in chemistry |
|---|---|---|---|
| Mass | kilogram | kg | gram (g) |
| Length | metre | m | centimetre (cm), nanometre (nm) |
| Time | second | s | minute (min) |
| Temperature | kelvin | K | degree Celsius (°C) |
| Amount of substance | mole | mol | mol |
| Volume | cubic metre | m³ | litre (L), millilitre (mL) |

## Prefixes

A **prefix** in front of a unit makes it bigger or smaller by a power of ten.

| Prefix | Symbol | Means | Example |
|---|---|---|---|
| kilo | k | $\times 1000$ | 1 kg = 1000 g |
| hecto | h | $\times 100$ | 1 hL = 100 L |
| deka | da | $\times 10$ | 1 dam = 10 m |
| deci | d | $\div 10$ | 10 dL = 1 L |
| centi | c | $\div 100$ | 100 cm = 1 m |
| milli | m | $\div 1000$ | 1000 mL = 1 L |
| micro | μ | $\div 1\,000\,000$ | 1 000 000 μg = 1 g |
| nano | n | $\div 1\,000\,000\,000$ | Atoms are about 0.1 nm across |

## The conversion rule

### Key idea: Big unit to small unit: multiply. Small unit to big unit: divide.
Going to a **smaller** unit, you need **more** of them, so the number gets bigger. Going to a **bigger** unit, the number gets smaller.

*Diagram: Conversion staircase: kilograms to grams multiply by 1000, grams to milligrams multiply by 1000. Going back up divide by 1000.*
*Step down the stairs: multiply. Step up: divide.*

### Worked example: Mass
Convert 2.5 kg to grams: big to small, so multiply. $2.5 \times 1000 = 2500 \text{ g}$.

Convert 450 mg to grams: small to big, so divide. $450 \div 1000 = 0.45 \text{ g}$.

## Volume

Volume units trip up many students. Learn these links.

$$1 \text{ L} = 1000 \text{ mL} \qquad 1 \text{ mL} = 1 \text{ cm}^3 \qquad 1 \text{ L} = 1 \text{ dm}^3 = 1000 \text{ cm}^3$$

### Worked example: Volume
Convert 250 mL to litres: $250 \div 1000 = 0.250 \text{ L}$.

Convert 0.75 L to cm³: $0.75 \times 1000 = 750 \text{ cm}^3$.

## Temperature

Chemists use two scales. The **kelvin** scale starts at **absolute zero**, the coldest possible temperature, where particles have the least possible energy.

$$T(\text{K}) = T(^\circ\text{C}) + 273 \qquad T(^\circ\text{C}) = T(\text{K}) - 273$$

A change of 1 °C is the same size as a change of 1 K. There are no negative kelvin temperatures, and we write "300 K", not "300 °K".

### Worked example: Temperature
Water boils at 100 °C. In kelvin: $100 + 273 = 373 \text{ K}$.

Nitrogen boils at 77 K. In Celsius: $77 - 273 = -196\,^\circ\text{C}$.

## Converting with unit factors

For conversions with more than one step, multiply by **unit factors**: fractions that are equal to 1, such as $\frac{1000 \text{ mm}}{1 \text{ m}}$. Put the unit you **want** on top and the unit you **have** on the bottom, so the old unit cancels.

### Worked example: Metres to millimetres
Convert 0.809 m to mm.

$$0.809 \text{ m} \times \frac{1000 \text{ mm}}{1 \text{ m}} = 809 \text{ mm}$$

### Worked example: Hours to seconds
Convert 2.5 hours to seconds.

$$2.5 \text{ h} \times \frac{60 \text{ min}}{1 \text{ h}} \times \frac{60 \text{ s}}{1 \text{ min}} = 9000 \text{ s}$$

h cancels with h, min cancels with min, and seconds are left.

This method is called **dimensional analysis**. It works for any conversion, even ones you have never seen, as long as you know the links between the units.

## Scientific notation

Chemists deal with very big and very small numbers. **Scientific notation** writes them as a number between 1 and 10 times a power of ten.

$$602\,000\,000\,000\,000\,000\,000\,000 = 6.02 \times 10^{23}$$
$$0.000\,000\,000\,1 \text{ m} = 1 \times 10^{-10} \text{ m}$$

- Moving the decimal point **left** makes a **positive** power (big number).
- Moving it **right** makes a **negative** power (small number).

### Exam tip: Show the units in every line
Write units next to every number in your working. If the units at the end do not match what the question asked for, you know something went wrong.

### Watch out: mL and cm³ are the same size
Students often multiply or divide when going from mL to cm³. Do not. $1 \text{ mL} = 1 \text{ cm}^3$ exactly.

**Mind map**

```text
Units
  SI units
    kg, m, s, K, mol
  Prefixes
    kilo: × 1000
    milli: ÷ 1000
    micro, nano: very small
  Rule
    Big to small: multiply
    Small to big: divide
  Volume
    1 L = 1000 mL
    1 mL = 1 cm³
  Temperature
    K = °C + 273
  Scientific notation
    a × 10ⁿ
```

### Year 11: Converting squared and cubed units
When a unit is cubed, the conversion factor is cubed too.

$$1 \text{ m} = 100 \text{ cm} \quad\Rightarrow\quad 1 \text{ m}^3 = 100^3 \text{ cm}^3 = 1\,000\,000 \text{ cm}^3$$

So $1 \text{ m}^3 = 1000 \text{ L}$.

**Density** units: $1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3$. Water has a density of about $1 \text{ g/cm}^3$, or $1000 \text{ kg/m}^3$.

**Significant figures**: keep the same number of significant figures when converting. $3.50 \text{ g} = 0.00350 \text{ kg} = 3.50 \times 10^{-3} \text{ kg}$, all three significant figures.

### Year 12: Chaining conversions with unit factors
For harder conversions, multiply by fractions that equal 1. A concentration of 5.0 g/L in mg/mL:

$$5.0 \frac{\text{g}}{\text{L}} \times \frac{1000 \text{ mg}}{1 \text{ g}} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 5.0 \frac{\text{mg}}{\text{mL}}$$

Units cancel like numbers. If the unit you want is left at the end, the method is right. This is called **dimensional analysis**, and it works for any conversion, including mol/L, ppm and gas volumes.

## Quick summary

- SI units: kg, m, s, K, mol. Chemists often use g, mL, L and °C too.
- kilo = × 1000, centi = ÷ 100, milli = ÷ 1000.
- Big unit to small unit: **multiply**. Small to big: **divide**.
- 1 L = 1000 mL and 1 mL = 1 cm³.
- K = °C + 273.
- Scientific notation: a number from 1 to 10 times a power of ten.

## Quiz

Try these questions from the chapter quiz.

1. How many grams are in 3.2 kg?
   - A. 0.0032 g
   - B. 32 g
   - C. 3200 g
   - D. 320 g
   - Answer: C. 3200 g. kg to g is big to small, so multiply by 1000.

2. Convert 750 mg to grams.
   - A. 0.75 g
   - B. 7.5 g
   - C. 75 g
   - D. 750 000 g
   - Answer: A. 0.75 g. mg to g is small to big, so divide by 1000.

3. 1.5 L is the same as:
   - A. 15 mL
   - B. 150 mL
   - C. 1500 mL
   - D. 0.0015 mL
   - Answer: C. 1500 mL. 1 L = 1000 mL, so 1.5 × 1000 = 1500 mL.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/chemistry/unit-conversions/#quiz