Units of Measurement and Conversion

Explore the units used to measure length, mass, time, and volume, and practise converting between them using the correct conversion factors.

Why Do We Need Units?

A measurement without a unit is meaningless. Saying "the table is 120 long" tells us nothing — 120 millimetres is very different from 120 centimetres! Units give measurements their meaning and allow us to compare and calculate correctly.

Units of Length

Length tells us how long, wide, or tall something is.

Unit	Symbol	Relation
millimetre	mm	smallest
centimetre	cm	1 cm = 10 mm
decimetre	dm	1 dm = 10 cm = 100 mm
metre	m	1 m = 10 dm = 100 cm = 1 000 mm
kilometre	km	1 km = 1 000 m

Converting Length — Moving Down the Scale

\times 10 \quad (\text{km} \to \text{m} \to \text{dm} \to \text{cm} \to \text{mm})

Each step down the scale multiplies by 10. To convert from a larger to a smaller unit, multiply.

Converting Length — Moving Up the Scale

\div 10 \quad (\text{mm} \to \text{cm} \to \text{dm} \to \text{m} \to \text{km})

Each step up the scale divides by 10. To convert from a smaller to a larger unit, divide.

Convert 3.5 m into centimetres

$3.5 \text{ m} = 3.5 \times 100 = 350 \text{ cm}$

(m → cm is 2 steps down, so multiply by $10 \times 10 = 100$ )

Convert 4 800 mm into metres

$4\,800 \text{ mm} = 4\,800 \div 1\,000 = 4.8 \text{ m}$

(mm → m is 3 steps up, so divide by $10 \times 10 \times 10 = 1\,000$ )

Units of Mass

Mass tells us how heavy something is.

Unit	Symbol	Relation
milligram	mg	smallest
gram	g	1 g = 1 000 mg
decagram	dag	1 dag = 10 g
kilogram	kg	1 kg = 100 dag = 1 000 g
tonne	t	1 t = 1 000 kg

Key Mass Conversions

1 \text{ kg} = 1\,000 \text{ g} \qquad 1 \text{ t} = 1\,000 \text{ kg}

Kilograms and grams are the most common units. Remember: kilo means 1 000.

Convert 2.4 kg into grams

$2.4 \text{ kg} = 2.4 \times 1\,000 = 2\,400 \text{ g}$

Real world: cooking recipes

A recipe calls for 250 g of flour and 0.1 kg of butter.

$0.1 \text{ kg} = 0.1 \times 1\,000 = 100 \text{ g of butter}$

Converting to the same unit (grams) makes it easy to weigh both ingredients on the same scale.

Units of Time

Time tells us how long an event lasts or when it happens.

Unit	Relation
second (s)	smallest
minute (min)	1 min = 60 s
hour (h)	1 h = 60 min = 3 600 s
day	1 day = 24 h
week	1 week = 7 days
month	1 month ≈ 30 or 31 days (28/29 in February)
year	1 year = 12 months = 365 days (366 in a leap year)

Key Time Conversions

1 \text{ h} = 60 \text{ min} \qquad 1 \text{ min} = 60 \text{ s} \qquad 1 \text{ day} = 24 \text{ h}

Unlike length and mass, time does NOT use a base-10 system between seconds, minutes, and hours.

Convert 2 hours 35 minutes into minutes

$2 \text{ h } 35 \text{ min} = 2 \times 60 + 35 = 120 + 35 = 155 \text{ min}$

Real world: sports records

The world record for the 100 m sprint is about 9.58 seconds. A marathon takes the fastest runners about 2 hours 1 minute = $2 \times 60 + 1 = 121$ minutes. Comparing race times requires everyone to use the same unit.

Units of Volume

Volume tells us how much liquid a container holds (its capacity).

Unit	Symbol	Relation
millilitre	ml	smallest
decilitre	dl	1 dl = 100 ml
litre	l	1 l = 10 dl = 1 000 ml

Key Volume Conversions

1 \text{ l} = 1\,000 \text{ ml} \qquad 1 \text{ dl} = 100 \text{ ml}

Litres and millilitres are the most common capacity units in everyday life.

Convert 0.75 l into millilitres

$0.75 \text{ l} = 0.75 \times 1\,000 = 750 \text{ ml}$

Real world: travel distances

A car trip is 1.2 km long. A race track is 800 m long.

$1.2 \text{ km} = 1.2 \times 1\,000 = 1\,200 \text{ m}$

Now both distances are in metres, so we can compare them directly: the car trip (1 200 m) is longer than the race track (800 m).

Summary of Conversion Rules

Tip

Rule of thumb: To convert to a smaller unit, multiply (there are more of them). To convert to a larger unit, divide (there are fewer of them). Always write the unit alongside your answer!

1
Identify the starting unit and the target unit
Write down what you have and what you need.
2
Find the conversion factor
Use the tables above to see how many of the small unit make one of the large unit.
3
Multiply or divide
Going to a smaller unit → multiply. Going to a larger unit → divide.
4
Write the answer with its unit
Never leave a measurement without its unit!

Common Mistakes

Multiplying when you should divide (or vice versa) — always check: a smaller unit means more of them, so multiply.
Using the wrong conversion factor — for example, using ×10 when converting kg to g (should be ×1 000).
Confusing mass and weight — mass is measured in kg; weight is a force measured in newtons (not needed at this level).
Leaving out the unit in the answer — a number without a unit is not a complete measurement.

Practice Problems

Convert 5.2 km into metres.

Show answer

5.2 km × 1 000 = 5 200 m

A bottle contains 1.5 l of water. How many millilitres is that?

Show answer

1.5 l × 1 000 = 1 500 ml

A race takes 3 minutes and 45 seconds. How many seconds is that in total?

Show answer

3 × 60 + 45 = 180 + 45 = 225 seconds

Convert 3 500 g into kilograms.

Show answer

3 500 g ÷ 1 000 = 3.5 kg