Metric Units

Worked example

1. 1

   $\text{Two cities are }900\dots$ — First ask what is measured: the distance between two cities is a length.

2. 2

   $\to \text{kilometres}$ — It is a very long length. 900 metres is only a short walk, so kilometres.

3. 3

   $\text{A phone weighs }180\dots$ — Weighs means a mass, and a phone is light.

4. 4

   $\to \text{grams}$ — Grams, the small unit of mass. 180 kg would be as heavy as a fridge.

5. 5

   $\text{A bath holds }150\dots$ — Holds means how much water fits inside: a capacity.

6. 6

   $\to \text{litres}$ — A bath holds a lot. 150 ml is less than a cup, so litres.

7. 7

   $\text{A floor has area }40\dots$ — Area means how much surface the floor covers.

8. 8

   $\to \text{square metres}$ — Area needs a square unit. A floor is a few metres each way, so square metres.

Worked example

1. 1

   $\text{height of a bus}$ — You do not measure it. Pick something from the table whose size you know.

2. 2

   $\approx 2\text{ doors}$ — Picture doors stacked on top of each other. A bus is about two doors high.

3. 3

   $\approx 2\times 2=4\text{ metres}$ — Each door is about 2 metres, so multiply. Write the number with its unit.

Worked example

1. 1

   $1\text{ km}=1000\text{ m}$ — Kilo means 1000, so one kilometre is 1000 metres.

2. 2

   $7000\text{ ml}=7000÷1000$ — A litre is the bigger unit, so you need fewer of them: divide by 1000.

3. 3

   $=7\text{ litres}$ — 7000 ÷ 1000 = 7.

4. 4

   $43\text{ mm}=43÷10$ — A cm is bigger than a mm, and 10 mm make 1 cm, so divide by 10.

5. 5

   $=4.3\text{ cm}$ — 43 ÷ 10 = 4.3.

6. 6

   $2.4\text{ kg}=2.4\times 1000$ — A gram is the smaller unit, so you need more of them: multiply by 1000.

7. 7

   $=2400\text{ g}$ — 2.4 × 1000 = 2400. Check: 2400 g is more grams than 2.4, as it should be.

Worked example

1. 1

   $3\text{ m}=3\times 100=300\text{ cm}$ — The units are different. Change metres to cm, the smaller unit, so there are no decimals: 1 m = 100 cm.

2. 2

   $\frac{45}{300}$ — Now both are in cm. The part goes on top and the whole goes on the bottom.

3. 3

   $=\frac{9}{60}$ — Simplify: divide the top and the bottom by 5.

4. 4

   $=\frac{3}{20}$ — Divide both by 3. Nothing else divides 3 and 20, so this is the simplest form.

Worked example

1. 1

   $15\text{ kg}=15\times 1000=15000\text{ g}$ — The answer must be in grams, so change the kg to grams first: 1 kg = 1000 g.

2. 2

   $40\times 350=14000\text{ g}$ — The mass of all the tins: 40 tins of 350 g each.

3. 3

   $15000-14000=1000\text{ g}$ — Take the tins away from the total. What is left is the crate.