The metric system is built on powers of ten.
The same staircase works for grams and litres — only the base unit changes. Going towards a smaller unit means more of them, so you multiply.
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Measurement and Unit Conversion
Write the conversion as a fraction and let the unwanted units cancel.
Convert
A tricycle travels at 36 km/h. What is that in metres per second?
36 km/h means 36,000 m in 3,600 s, and 36,000 ÷ 3,600 = 10 m/s. Two conversions are needed, not one — kilometres to metres and hours to seconds. A divides by 10, doing neither properly. D multiplies by 3.6 instead of dividing, which converts the wrong way round: m/s to km/h.
The unit-factor method proves itself.
Write the conversion as a fraction equal to 1, arranged so the old unit cancels.
convert 5.2 km to metres
1 km = 1,000 m
5.2 km × 1,000 m1 km
km on the bottom, so it cancels
= 5,200 m
only metres left
Upside down is the whole problem
If you had written 1 km1,000 m, the units would not cancel — you would be left with km²m, which is nonsense. That is the method's great advantage: a wrong set-up looks obviously wrong before you multiply anything.
Chain the factors when two things change at once.
36 km/h → m/s
the opening problem
36 km/h × 1,000 m1 km
= 36,000 m/h
× 1 h3,600 s
hours cancel
= 10 m/s
36,000 ÷ 3,600
The shortcut "divide by 3.6" comes straight from 1,000 ÷ 3,600. Worth knowing, but only after you have seen where it came from.
Time, and the English units still in daily use.
| Relationship | Use |
|---|---|
| 1 h = 60 min = 3,600 s | speed, duration |
| 1 day = 24 h = 1,440 min | schedules |
| 1 inch ≈ 2.54 cm | screen sizes, plywood |
| 1 foot = 12 inches ≈ 30.48 cm | height, rooms |
| 1 kg ≈ 2.2 pounds | market, luggage |
a 55-inch television
how many cm?
55 × 2.54
cm are smaller, so more of them
≈ 139.7 cm
about 1.4 m
Area and volume units: the factor is squared or cubed.
1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm². For volume, 1 m³ = 1,000 L and 1 L = 1,000 cm³.
A classroom floor measures 8 m by 650 cm. What is its area in square metres?
650 cm = 6.5 m
convert the lengths first, so both are in metres
8 × 6.5 = 52 m²
then multiply
Multiplying mixed units
8 × 650 = 5,200 gives metres times centimetres, which is not square metres or square centimetres. And converting an area with the length factor — 52 m² = 5,200 cm² — is out by a factor of 100: it is 52 × 10,000 = 520,000 cm².
A water tank is a box 1.2 m long, 0.5 m wide and 0.8 m deep. How many litres does it hold?
1.2 × 0.5 × 0.8 = 0.48 m³
volume in cubic metres
0.48 × 1,000 = 480 L
1 m³ = 1,000 L
Check another way: 120 cm × 50 cm × 80 cm = 480,000 cm³, and 480,000 ÷ 1,000 = 480 L ✓
Variations: several steps at once, a decimal of an hour, and speed the other way.
The same unit factors; these are the conversions that look different.
Convert 45 mm to metres.
45 mm × 1 m1,000 mm
milli to the base unit is three steps
= 0.045 m
a bigger unit, so a smaller number
The zero after the point is needed: 0.45 m would be 450 mm.
A bus trip takes 2.4 hours. Write it in hours and minutes.
0.4 h × 60 = 24 min
only the decimal part is converted
2.4 h = 2 h 24 min
not 2 h 40 min
Time is not decimal: 0.4 of an hour is 24 minutes, because an hour has 60 minutes, not 100.
A sprinter runs at 15 m/s. What is that in km/h?
15 m/s × 3,600 s1 h × 1 km1,000 m
seconds and metres both cancel
= 54 km/h
shortcut: × 3.6
km/h to m/s divides by 3.6; m/s to km/h multiplies. The km/h number is always the bigger one.
Convert before the main calculation, not after.
A tap fills 250 mL every 2 seconds
how long to fill 18 litres?
18 L = 18,000 mL
match the units first
18,000 ÷ 250 = 72
72 lots of 250 mL
72 × 2 = 144 s = 2 min 24 s
and convert the answer too
Sanity check
250 mL is a quarter of a litre
so a litre is 4 lots of 2 s = 8 s
18 litres
18 × 8 = 144 s
matches the working ✓
On the exam
Conversion is usually hidden inside another question: a speed in km/h to m/s, a rate in mL against a tank in litres, or a room measured in two different units. The fastest route is to convert everything to one unit before calculating; the 10-second check is direction — a smaller unit must give a bigger number.
Now you try
Practice problem
Convert
A rope is 4.5 m long. How many 15 cm pieces can be cut from it?
Match the units first: 4.5 m = 450 cm. Then 450 ÷ 15 = 30 pieces. A divides 4.5 by 15 without converting, which mixes metres and centimetres. D multiplies instead of dividing. Check: 30 × 15 = 450 cm = 4.5 m ✓
Hint: never divide a length in metres by a length in centimetres. Convert one to match the other before doing anything else.