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E2.1 · Measure and convert metric length, area, mass, and capacity

Learn to measure and convert metric length, area, mass, and capacity through clear examples and targeted practice.

Ontario Grade 6 Mathematics

Spatial Sense

Choose a suitable unit, then convert carefully

A metric measurement has a number and a unit. The unit tells what kind of amount the number describes. For example, centimetres can describe the length of a book, while square centimetres can describe the area of its cover. Area is the amount of flat surface inside a shape. Mass tells how much matter an object has. Capacity tells how much a container can hold. In this lesson, you will use familiar metric units and their relationships to convert measurements.

What you will learn

  • Name common metric units for length, area, mass, and capacity.
  • Use relationships between metric units to convert measurements.
  • Explain why area conversions use a different scale from length conversions.

1. Match the unit to what you measure

You already use centimetres to measure small lengths and metres to measure longer ones. A length tells how far it is from one end to another. Millimetres are smaller than centimetres, and kilometres are useful for long distances.
Area measures a flat surface. Its units are square units, such as square centimetres (cm2\text{cm}^2) and square metres (m2\text{m}^2). The small 2 means that the unit is used in two directions: across and down.
Mass is commonly measured in grams and kilograms. A small item may be measured in grams; a heavier item may be measured in kilograms. Capacity is commonly measured in millilitres and litres. Millilitres suit smaller amounts of liquid, while litres suit larger amounts.
  • Length: mm, cm, m, km.
  • Area: square units such as cm² and m².
  • Mass: g and kg.
  • Capacity: mL and L.

2. Use unit relationships to convert

A conversion gives the same amount in a different unit. The amount does not change; only the unit and number change. First identify the two units and the relationship between them.
For length, 1010 millimetres make 11 centimetre, and 100100 centimetres make 11 metre. For mass, 1,0001{,}000 grams make 11 kilogram. For capacity, 1,0001{,}000 millilitres make 11 litre. These relationships help you decide what to do: when changing to a smaller unit, the number gets larger; when changing to a larger unit, the number gets smaller.
Area needs special care. A square that is 11 metre long on each side is 100100 centimetres long on each side. It contains 100100 rows of 100100 square centimetres, so 11 square metre equals 10,00010{,}000 square centimetres. Do not use the length relationship of 100 only once for this area conversion.
A useful check is to estimate before calculating. If you change metres to centimetres, expect a larger number. If you change grams to kilograms, expect a smaller number. Include the unit in your answer so the reader knows what the number measures.
1 m=100 cm,1 kg=1,000 g,1 L=1,000 mL,1 m2=10,000 cm21\text{ m}=100\text{ cm},\quad 1\text{ kg}=1{,}000\text{ g},\quad 1\text{ L}=1{,}000\text{ mL},\quad 1\text{ m}^2=10{,}000\text{ cm}^2
  • Smaller units need more units to describe the same amount.
  • For area, convert both directions of the square.
  • Keep the unit attached to the number.

3. A steady method for conversions

Use the same three questions each time. What quantity is being measured? Which unit relationships connect the starting unit and the requested unit? Should the number become larger or smaller?
Then calculate using the relationship. For example, if each metre contains 100 centimetres, the number of centimetres is 100 times the number of metres. For a conversion from grams to kilograms, group the grams into groups of 1,000. For area, use the area relationship rather than the length relationship.
Read your answer aloud with its unit. Ask whether it describes the same length, area, mass, or capacity as the starting measurement. This helps catch a wrong unit or an answer that changed in the wrong direction.
  • Identify the quantity and units.
  • Use the matching unit relationship.
  • Check the direction and include the new unit.

4. Practise choosing and checking units

A measurement should use a unit that makes sense for the amount. A room's length is more naturally given in metres than in millimetres. A drink in a small container is often given in millilitres. These choices do not change the amount; they make the measurement easier to read.
When a number has a decimal, convert it in the same way as a whole number. For instance, 2.42.4 metres means 2.42.4 groups of one metre. Since each metre contains 100 centimetres, the equivalent number of centimetres is 2.42.4 groups of 100.
For an area conversion, imagine the square itself. If the side length changes from metres to centimetres, both the horizontal and vertical measurements change. That is why the area relationship is not the same as the length relationship.
  • Choose units that suit the size of the measurement.
  • Decimals can be converted using the same unit relationship.
  • Check area conversions by thinking about the square's sides.

Useful metric relationships

QuantityRelationship
Length1 m = 100 cm; 1 cm = 10 mm
Area1 m² = 10,000 cm²
Mass1 kg = 1,000 g
Capacity1 L = 1,000 mL

Worked example

Convert a length

A ribbon is 3.4 m long. How many centimetres long is it?
  1. Use the length relationship
    One metre contains 100 centimetres. Since centimetres are smaller units, the number should become larger.
    1 m=100 cm1\text{ m}=100\text{ cm}
  2. Convert the amount
    There are 3.4 groups of one metre. Multiply 3.4 by 100 to find the same length in centimetres.
    3.4×100=3403.4\times100=340
Answer: The ribbon is 340 cm long.
Check: 340 cm is 3.4 groups of 100 cm, so it matches 3.4 m.

Worked example

Convert mass

A parcel has a mass of 2,750 g. Express its mass in kilograms.
  1. Find how many grams make a kilogram
    One kilogram contains 1,000 grams. Changing from grams to kilograms means using a larger unit, so the number should become smaller.
    1 kg=1,000 g1\text{ kg}=1{,}000\text{ g}
  2. Group the grams
    Divide 2,750 grams into groups of 1,000 grams. The result is the mass in kilograms.
    2,750÷1,000=2.752{,}750\div1{,}000=2.75
Answer: The parcel has a mass of 2.75 kg.
Check: 2.75 kg is 2,750 g because each kilogram contains 1,000 g.

Worked example

Convert area and capacity

A square card has an area of 2 m². A jug holds 1.6 L. Express the area in cm² and the capacity in mL.
  1. Convert the area
    Each square metre contains 10,000 square centimetres. The area is 2 groups of 10,000 square centimetres.
    2×10,000=20,0002\times10{,}000=20{,}000
  2. Convert the capacity
    One litre contains 1,000 millilitres. Since millilitres are smaller units, multiply the number of litres by 1,000.
    1.6×1,000=1,6001.6\times1{,}000=1{,}600
Answer: The card's area is 20,000 cm², and the jug's capacity is 1,600 mL.
Check: The area conversion uses 10,000 cm² per m², while the capacity conversion uses 1,000 mL per L.

Common mistakes and how to avoid them

Multiplying when changing to a larger unit, such as changing grams to kilograms.
Correction: The number should become smaller when the unit becomes larger. Use the relationship to decide whether to divide.
Using 100 as the area conversion from square metres to square centimetres.
Correction: Area covers two directions. One square metre contains 10,000 square centimetres.
Writing a converted number without a unit.
Correction: Include the unit, such as 340 cm, so the measurement is clear.

Lesson summary

  • Length, area, mass, and capacity use different metric units.
  • A conversion changes the number and unit, but not the amount.
  • Use the unit relationship to choose whether the number gets larger or smaller.
  • Area conversions account for both directions of a square.

Check your understanding

Question 1

How many centimetres are in 4.2 m?
  1. 42 cm
  2. 420 cm
  3. 4,200 cm
  4. correctIndex
Show answer and explanation
420 cm
Each metre contains 100 centimetres, so 4.2 multiplied by 100 is 420.

Question 2

How many grams are in 3 kg?
  1. 30 g
  2. 300 g
  3. 3,000 g
  4. correctIndex
Show answer and explanation
3,000 g
Each kilogram contains 1,000 grams, so 3 kilograms contain 3,000 grams.

Question 3

How many square centimetres are in 1 m²?
  1. 100 cm²
  2. 1,000 cm²
  3. 10,000 cm²
  4. correctIndex
Show answer and explanation
10,000 cm²
A square metre contains 100 rows of 100 square centimetres, which is 10,000 cm².

Key terms

Area
The amount of flat surface inside a shape.
Capacity
The amount a container can hold.
Convert
Write the same measurement using a different unit.
Mass
A measure of how much matter an object has.
Metric unit
A measurement unit such as a centimetre, metre, gram, or litre.

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