Metric units and appropriate precision | Year 7

01 / LEARN

Understand the idea.

A unit tells us what one step means

A measurement combines a number with a unit. Changing units changes the number, not the object: one metre and one hundred centimetres describe the same length. Convert to a smaller unit by counting how many smaller units fit in each larger unit.

Area and volume conversions act in two or three directions. A square metre is $100 cm$ by $100 cm$ , so it contains $10 000 {cm}^{2}$ . A cubic metre contains $100^{3} = 1 000 000$ cubic centimetres.

\begin{aligned} 1 m & = 100 cm \\ 1 m^{2} & = 10 000 {cm}^{2} \end{aligned}

Precision should suit the instrument

Precision describes how finely a measurement is reported. Match rounding to the requested unit or the measuring instrument. Nearest centimetre means a step of $0.01 m$ when reporting in metres. Keep calculation digits until the final rounding.

Capacity describes how much a container holds. Use $1 {cm}^{3} = 1 mL$ and $1000 mL = 1 L$ to connect capacity and volume. Always include units; a bare number does not tell the reader what has been measured.

Useful metric links
Quantity	Conversion
Length	1 km = 1,000 m; 1 cm = 10 mm
Area	1 m² = 10,000 cm²
Volume and capacity	1 cm³ = 1 mL; 1 L = 1,000 mL

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Convert a length

A ribbon is 2.45 m long. Express its length in centimetres.

Worked solution

1
Choose the metres-to-centimetres factor.
$1 m = 100 cm$
Centimetres are smaller units, so more of them describe the same ribbon.
2
Multiply by the conversion factor.
$2.45 \times 100 = 245$
Each metre contributes one hundred centimetres.
3
State the unchanged length in its new unit.
$2.45 m = 245 cm$
Only the unit and numerical description change.

Answer

$245 cm$

EXAMPLE 02

Choose honest precision

A length calculated from measurements is 3.476 m. Report it to the nearest centimetre.

Worked solution

1
Express the requested rounding step in metres.
$1 cm = 0.01 m$
Nearest centimetre requires two decimal places in metres.
2
Inspect the next decimal digit.
$3.476 m \approx 3.48 m$
The thousandths digit is six, so the hundredths digit rounds upwards.
3
Give the equivalent centimetre measurement.
$3.48 \times 100 = 348 cm$
The rounded measurement is a whole number of centimetres.

Answer

$3.48 m$ , or 348 cm.

03 / YOUR TURN

Try it yourself.

Check your understanding

Convert 0.8 m to millimetres.

Show answer & reasoning

800 mm

One metre contains $1000$ millimetres. Therefore $0.8 \times 1000 = 800$ , so the length is $800 mm$ .

Keep practising

6 worksheet questions · 10 marks

Open worksheet Worked solutions

Read the questions online

Convert 3.6 m to centimetres.
1 mark
Convert 2,750 mm to metres.
2 marks
A small floor has area 2 m². Express this in cm².
2 marks
A jug holds 1.25 L. Express this capacity in mL.
1 mark
Round 2.384 m to the nearest centimetre.
2 marks
A student reports a classroom door as 198.37291 cm high after measuring with a ruler marked in whole centimetres. Explain a more sensible report.
2 marks

Read the worked solutions

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

Convert 3.6 m to centimetres.
1 mark
$3.6 \times 100 = 360$ .
360 cm
Convert 2,750 mm to metres.
2 marks
$1 m = 1.000 mm$ .
$2.750 \div 1.000 = 2.75$ .
2.75 m
A small floor has area 2 m². Express this in cm².
2 marks
Each square metre has 10,000 cm².
$2 \times 10.000 = 20.000$ .
20,000 cm²
A jug holds 1.25 L. Express this capacity in mL.
1 mark
$1.25 \times 1.000 = 1.250$ .
1,250 mL
Round 2.384 m to the nearest centimetre.
2 marks
A centimetre is 0.01 m.
The third decimal is 4, so keep the hundredths digit.
2.38 m, or 238 cm
A student reports a classroom door as 198.37291 cm high after measuring with a ruler marked in whole centimetres. Explain a more sensible report.
2 marks
The instrument does not justify all the decimal places.
Round to a precision consistent with whole-centimetre readings.
About 198 cm

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 7 measurement and spatial representation: areas of triangles/parallelograms, prism volumes, circle circumference, nets and views. Precision is integrated into practical measurement; circle area is not introduced here.

Official curriculum source ↗

In this lesson

Understand the idea.

A unit tells us what one step means

Precision should suit the instrument

See the method in action.

Convert a length

Choose the metres-to-centimetres factor.

Multiply by the conversion factor.

State the unchanged length in its new unit.

Choose honest precision

Express the requested rounding step in metres.

Inspect the next decimal digit.

Give the equivalent centimetre measurement.

Try it yourself.

Check your understanding

Keep practising