# Metric Units and Conversions

> Convert length, mass, capacity, area and time, including fractions of units like three quarters of a tonne.

From Selective School Maths on WhizzNotes, free study notes for NSW students: https://whizznotes.com/selective-school-maths/metric-units/. Updated 3 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The baker's mix-up
Mrs Patel runs a bakery. A new recipe from France says "250 g of butter and 0.5 L of milk". Her old scales only show kilograms, and her jug only shows millilitres.

She knows 1 kg is 1000 g, so 250 g is $\frac{250}{1000} = 0.25$ kg, a quarter of a kilogram. And 1 L is 1000 mL, so 0.5 L is 500 mL.

The metric system is built on 10, 100 and 1000. Once you know the few key facts, every conversion is just multiplying or dividing.

**In short:** Metric units go up in 10s, 100s and 1000s: 1 km = 1000 m, 1 kg = 1000 g and 1 L = 1000 mL. To change to a smaller unit, multiply, and to change to a bigger unit, divide. Time is different: it goes in 60s.

## Before you start

- Multiplying and dividing by 10, 100 and 1000 (see the Number Skills unit).
- Fractions of an amount: divide by the bottom, multiply by the top.
- The prefixes: **milli** means one thousandth, **centi** means one hundredth, **kilo** means one thousand.

## The key facts

| Measure | Facts |
|---|---|
| Length | 10 mm $=$ 1 cm, 100 cm $=$ 1 m, 1000 mm $=$ 1 m, 1000 m $=$ 1 km |
| Mass | 1000 mg $=$ 1 g, 1000 g $=$ 1 kg, 1000 kg $=$ 1 tonne |
| Capacity | 1000 mL $=$ 1 L, 1000 L $=$ 1 kL |
| Area | 10 000 m² $=$ 1 hectare (ha), 100 ha $=$ 1 km² |
| Volume | 1 cm³ holds 1 mL |
| Time | 60 s $=$ 1 min, 60 min $=$ 1 h, 24 h $=$ 1 day, 7 days $=$ 1 week, 52 weeks $=$ 1 year, 12 months $=$ 1 year |

## Big to small: multiply

### Key idea: Going to a smaller unit, the number gets bigger
Smaller units means more of them, so **multiply**.

$0.05$ km $= 0.05 \times 1000 = 50$ m

$1.25$ L $= 1250$ mL

## Small to big: divide

### Key idea: Going to a bigger unit, the number gets smaller
Bigger units means fewer of them, so **divide**.

$1250$ mL $= 1250 \div 1000 = 1.25$ L

$2\,000\,000$ mm $= 2000$ m $= 2$ km

### Exam tip: Two steps are fine
mm to km is a long way. Go mm to m (divide by 1000), then m to km (divide by 1000 again).

## Fractions of a unit

Find the fraction of the bigger unit's number.

### Worked example: Fractions into small units
$\frac{1}{8}$ kg $= 1000 \div 8 = 125$ g

$\frac{7}{8}$ kg $= 125 \times 7 = 875$ g

$\frac{3}{4}$ tonne $= 750$ kg

$\frac{3}{8}$ L $= 1000 \div 8 \times 3 = 375$ mL

$\frac{3}{5}$ m $= 1000 \div 5 \times 3 = 600$ mm

## Time is not decimal

### Watch out: 1.5 hours is not 1 h 50 min
Time uses 60s, not 100s. $1.5$ hours is $1\frac{1}{2}$ hours $= 1$ hour 30 minutes $= 90$ minutes.

### Worked example: Time conversions
$1\frac{3}{4}$ hours $= 60 + 45 = 105$ minutes

$\frac{1}{4}$ day $= 6$ hours $= 360$ minutes

$\frac{1}{2}$ week $= 3.5$ days $= 84$ hours

$4\frac{3}{4}$ years $= 48 + 9 = 57$ months

## Area and volume units

A **hectare** is a square 100 m by 100 m, so it is $10\,000$ m². Farms and parks are measured in hectares.

$\frac{1}{4}$ ha $= 2500$ m².

A box 5 cm by 7 cm by 10 cm has a volume of $5 \times 7 \times 10 = 350$ cm³, so it holds 350 mL of water.

### Challenge: Selective level: mixed problems
A tank measures 30 cm by 40 cm by 50 cm. Its volume is $60\,000$ cm³, which is $60\,000$ mL or 60 L.

How many 250 mL glasses can be filled from a 3 L bottle? $3000 \div 250 = 12$ glasses.

Which is longest: 0.3 km, 2800 cm or 31 000 mm? In metres: 300 m, 28 m and 31 m. So 0.3 km is longest.

**Mind map**

```text
Metric units
  Length
    10 mm = 1 cm
    100 cm = 1 m
    1000 m = 1 km
  Mass
    1000 g = 1 kg
    1000 kg = 1 t
  Capacity
    1000 mL = 1 L
    1 cm³ = 1 mL
  Area
    10 000 m² = 1 ha
  Rules
    To smaller units: multiply
    To bigger units: divide
    Time uses 60
```

## Quick summary

- Metric units go up in 10s, 100s and 1000s.
- To change to a smaller unit, multiply. To change to a bigger unit, divide.
- 1 kg $= 1000$ g, 1 L $= 1000$ mL, 1 km $= 1000$ m, 1 tonne $= 1000$ kg, 1 m $= 100$ cm.
- 1 hectare $= 10\,000$ m², and 1 cm³ holds 1 mL.
- Time uses 60s: $1.5$ hours is 90 minutes, not 150.

## Quiz

Try these questions from the chapter quiz.

1. $1250$ mL $=$
   - A. 12.5 L
   - B. 1.25 L
   - C. 0.125 L
   - D. 125 L
   - Answer: B. 1.25 L. Divide by 1000: $1.25$ L.

2. $0.05$ km $=$
   - A. 5 m
   - B. 50 m
   - C. 500 m
   - D. 0.5 m
   - Answer: B. 50 m. Multiply by 1000: 50 m.

3. $\frac{1}{8}$ kg $=$
   - A. 8 g
   - B. 80 g
   - C. 125 g
   - D. 250 g
   - Answer: C. 125 g. $1000 \div 8 = 125$ g.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/selective-school-maths/metric-units/#quiz