Units and Conversions
Metric units ride a ladder of tens — converting is a single × or ÷. The traps are elsewhere: time runs in sixties, and shops hide value behind packet sizes. One sense check protects you everywhere: smaller units mean bigger numbers.
National curriculum KS3: use standard units of mass, length, time, money and other measures; change freely between related standard units1 · The metric ladder
Metric units are powers of ten apart, so converting is just multiplying or dividing by 10, 100 or 1000. Going to a smaller unit means more of them (×); going to a bigger unit means fewer (÷). Pick a conversion and watch the path light up.
Sense check every answer. 3.5 m in cm must be a bigger number (350) because centimetres are smaller pieces. If your answer got smaller when the unit got smaller, you divided when you should have multiplied.
2 · Time is not metric
The big trap: time works in 60s and 24s, not 10s. 2.5 hours is 2 h 30 min — never 2 h 50 min. The decimal part is a fraction of an hour: 0.5 × 60 = 30 minutes.
3 · Money and unit pricing: best buys
To compare offers fairly, work out the price of one unit of each (per gram, per ml, per item). Cheapest per unit wins, whatever the packet size.
Worked examples
Convert 3.5 m to cm, and 4 200 g to kg.
4200 g ÷ 1000 = 4.2 kg
A film lasts 1.75 hours. When does it end if it starts at 7:40 pm?
Which is the better buy: 250 g for £1.80 or 400 g for £2.60?
B: 260p ÷ 4 = 65p per 100 g → B is better
Quick check
What you've learned
On the metric ladder, moving to a smaller unit multiplies (more pieces) and moving to a bigger unit divides. Time is not metric: the decimal part of an hour is multiplied by 60 to get minutes. For best buys, compare the price of one unit (per 100 g, per roll) — the bigger packet usually wins, but not always, so always check.