Units of Measurement and Conversion

Converting between metric units of length, mass, and capacity using powers of 10.

The Metric System

Metric units are based on powers of 10, making conversion easy.

Length

\text{km} \xrightarrow{\times 1000} \text{m} \xrightarrow{\times 100} \text{cm} \xrightarrow{\times 10} \text{mm}

To convert	Multiply/Divide
km → m	× 1000
m → cm	× 100
cm → mm	× 10
mm → cm	÷ 10
cm → m	÷ 100
m → km	÷ 1000

Mass

\text{t} \xrightarrow{\times 1000} \text{kg} \xrightarrow{\times 1000} \text{g} \xrightarrow{\times 1000} \text{mg}

Capacity (Volume of Liquids)

1\text{ L} = 1000\text{ mL}, \quad 1\text{ cl} = 10\text{ mL}

How to Convert

Bigger unit → smaller unit: multiply. Smaller unit → bigger unit: divide.

Convert 3.5 km to metres

$3.5 \times 1000 = 3500 \text{ m}$

Convert 250 cm to metres

$250 \div 100 = 2.5 \text{ m}$

Convert 4.2 kg to grams

$4.2 \times 1000 = 4200 \text{ g}$

Note

A useful trick: moving the decimal point left = dividing; moving it right = multiplying.

Real world: cooking with different recipe units

A British recipe calls for 8 oz of flour, but the kitchen scale shows only grams. Since 1 oz ≈ 28.35 g, $8 \times 28.35 \approx 227\text{ g}$ . Unit conversion lets cooks follow recipes from any country without guesswork.

Real world: road distances when travelling abroad

A US road sign shows a town is 25 miles away. To convert to kilometres: $25 \times 1.609 \approx 40\text{ km}$ . Travellers in countries that use different systems must convert distances to judge journey times correctly.

Real world: weather temperature conversion

A weather app shows $95°F$ for a summer day in the USA. Converting to Celsius: $C = (95 - 32) \times \frac{5}{9} = 63 \times \frac{5}{9} = 35°C$ . Understanding temperature conversions is essential for international travel and scientific communication.

Tip Write out the conversion factor as a fraction equal to 1 (e.g.

\frac{1000\text{ m}}{1\text{ km}}

) and multiply. Units cancel out just like numbers, leaving only the unit you want.

Practice Problems

Convert 6,500 m to kilometres.

Show answer

6,500 ÷ 1,000 = 6.5 km.

A bottle holds 750 mL. How many litres is that?

Show answer

750 ÷ 1,000 = 0.75 L.

A parcel weighs 2.35 kg. Express this in grams.

Show answer

2.35 × 1,000 = 2,350 g.