Metric units and conversion

01Why this matters

A length written in metres and the same length in centimetres should describe the same object. Consistent units are essential before calculation.

02See it

03Understand it

Metric prefixes describe powers of ten applied to a unit. Converting changes the numerical representation without changing the quantity.

Kilo means 1,000, centi means one hundredth and milli means one thousandth. One kilometre is 1,000 metres; one metre is 100 centimetres. Converting to a smaller unit needs more of those units, so the number grows. For area and volume, the conversion factor is squared or cubed.

04Guided example

Convert 2.4 km to metres.

1. Use the relationship 1 km = 1,000 m.
2. Multiply 2.4 by 1,000 because metres are smaller units: 2.4 × 1,000 = 2,400.
3. Write the new unit: 2,400 m. The distance itself has not changed.

05Try it

06Practise it

07Use it in the real world

A 750 mL bottle contains 0.75 L. Three bottles contain 2.25 L, because 1 L = 1,000 mL.

08Quick check

09Summary

Metric prefixes describe powers of ten applied to a unit. Converting changes the numerical representation without changing the quantity. Write the new unit: 2,400 m. The distance itself has not changed.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea