Decimal metric conversions | Year 6

01 / LEARN

Understand the idea.

Use the unit relationship

A unit conversion describes the same length, mass or capacity in a different-sized unit. Think of replacing each metre with its $100$ centimetres: the object stays the same length, but the number used to describe it increases.

Choose the relationship before calculating: $1 m = 100 cm$ , while $1 km = 1000 m$ . Kilograms to grams and litres to millilitres also use $1000$ . The names of the two units determine the factor.

Useful metric relationships
Larger unit	Equivalent smaller units
1 m	100 cm
1 km	1,000 m
1 kg	1,000 g
1 L	1,000 mL

Check the direction

Predict the direction first. Smaller units need a larger count, so multiply when changing metres to centimetres. Larger units need a smaller count, so divide when changing grams to kilograms.

Keep the unit beside the answer and check its size. For instance, $650 mL = 0.65 L$ makes sense because the original amount is less than one litre; $650 L$ would describe a very different quantity.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Convert 1.75 metres to centimetres.

Worked solution

1
Identify the conversion factor.
$1 m = 100 cm$
Each metre contains one hundred centimetres.
2
Multiply the number of metres by one hundred.
$1.75 \times 100 = 175$
Centimetres are smaller, so their count must be larger.
3
Write the equivalent measurement.
$1.75 m = 175 cm$
The unit changes while the length stays the same.

Answer

175 cm.

EXAMPLE 02

Worked example 2

Convert 2,450 grams to kilograms.

Worked solution

1
Identify how many grams make a kilogram.
$1000 g = 1 kg$
The conversion groups grams into thousands.
2
Divide the gram count by one thousand.
$2450 \div 1000 = 2.45$
Kilograms are larger units, so fewer of them are needed.
3
Check the converted mass.
$2.45 kg = 2450 g$
Two whole kilograms account for 2000 grams and the remaining 0.45 kilogram accounts for 450 grams.

Answer

2.45 kg.

03 / YOUR TURN

Try it yourself.

Check your understanding

Convert 0.6 litres to millilitres.

Show answer & reasoning

600 mL.

A litre contains $1000$ millilitres, so $0.6 \times 1000 = 600$ . The answer is $600 mL$ , which is less than one full litre.

Keep practising

6 worksheet questions · 7 marks

Open worksheet Worked solutions

Read the questions online

Convert 3.25 m to centimetres.
1 mark
Convert 740 cm to metres.
1 mark
Convert 0.85 kg to grams.
1 mark
Convert 1,250 mL to litres.
1 mark
A walk is 2.3 km. How many metres is that?
1 mark
A learner writes $4.2 m = 42 cm$ . Explain the error and correct it.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Convert 3.25 m to centimetres.
1 mark
$3.25 \times 100 = 325$ .
325 cm.
Convert 740 cm to metres.
1 mark
$740 \div 100 = 7.4$ .
7.4 m.
Convert 0.85 kg to grams.
1 mark
$0.85 \times 1, 000 = 850$ .
850 g.
Convert 1,250 mL to litres.
1 mark
$1, 250 \div 1, 000 = 1.25$ .
1.25 L.
A walk is 2.3 km. How many metres is that?
1 mark
$2.3 \times 1, 000 = 2, 300$ .
2,300 m.
A learner writes $4.2 m = 42 cm$ . Explain the error and correct it.
2 marks
Each metre contains 100 centimetres, not 10.
$4.2 m = 420 cm$ .

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Decimal metric conversions; deriving rectangle area; missing dimensions; practical measurement.

Official curriculum source ↗

In this lesson

Understand the idea.

Use the unit relationship

Check the direction

See the method in action.

Worked example 1

Identify the conversion factor.

Multiply the number of metres by one hundred.

Write the equivalent measurement.

Worked example 2

Identify how many grams make a kilogram.

Divide the gram count by one thousand.

Check the converted mass.

Try it yourself.

Check your understanding

Keep practising