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E1.1 · Explore a geometric concept or measurement system

Learn to explore a geometric concept or measurement system through clear examples and targeted practice.

Ontario Grade 9 Mathematics

Geometry and Measurement

How units help us describe and compare distances

Imagine measuring the length of a classroom desk. Saying that it is 12 long does not give enough information. Twelve what: millimetres, centimetres, or metres? A measurement needs a number and a unit. In this lesson, you will explore the metric system for length. You will see how its units are related and practise choosing a suitable unit and converting between units.

What you will learn

  • Explain why a measurement needs both a number and a unit.
  • Name common metric units for measuring length.
  • Describe how metric units are related by groups of ten.
  • Convert a length between millimetres, centimetres, metres, and kilometres.

1. A measurement needs a unit

Length tells how far it is from one point to another. You already use length measurements in daily life, such as the height of a person or the distance to a nearby store.
A unit is an agreed amount used to measure something. For example, a centimetre is a unit of length. If you measure a book and get 24 centimetres, the number is 24 and the unit is centimetres. Leaving out the unit makes the measurement unclear.
A measuring tool compares an object with units marked on it. A ruler has marks for units such as millimetres and centimetres. To measure accurately, line up the object's start with the ruler's zero mark, then read the mark at its end.
  • Length describes the distance between two points.
  • A measurement has a number and a unit.
  • Use a unit that suits the size of what you are measuring.

2. Explore metric units

The metric system is a measurement system used in many places, including Canada. It has units for different kinds of measurement. This lesson focuses only on units of length.
A millimetre is useful for a very small length, such as the thickness of a thin card. A centimetre can suit the length of a pencil. A metre can suit the height of a door. A kilometre can describe a longer distance, such as the distance along a road.
The units are connected by groups of ten. Ten millimetres make one centimetre, and one hundred centimetres make one metre. One thousand metres make one kilometre. These relationships help you change a measurement from one unit to another.
The table gives common units from smaller to larger. The examples are suggestions, not exact measurements; objects of the same kind can have different lengths.
10 mm=1 cm; 100 cm=1 m; 1000 m=1 km10\text{ mm}=1\text{ cm};\ 100\text{ cm}=1\text{ m};\ 1000\text{ m}=1\text{ km}
  • Choose a small unit for a short length and a larger unit for a long distance.
  • Metric length units are linked by factors of ten.
  • The unit tells what the measurement number counts.

3. Convert between units

To convert means to express the same length using a different unit. The length does not change; only the number and the unit change. For instance, a length written in centimetres has a different number than the same length written in metres.
Use the unit relationships to decide what to do. When changing from a larger unit to a smaller unit, the number gets larger because more of the small units fit into the same length. When changing from a smaller unit to a larger unit, the number gets smaller.
You can use multiplication or division by the relevant conversion number. For example, because one metre contains one hundred centimetres, multiply a number of metres by one hundred to write the same length in centimetres. To change centimetres to metres, divide by one hundred.
Keep the unit with the result. A number alone is not a complete length measurement. You can check a conversion by asking whether the size of the number makes sense: the same length should have more millimetres than centimetres.
1 m=100 cm1\text{ m}=100\text{ cm}
  • Larger unit to smaller unit: multiply by the number of smaller units in one larger unit.
  • Smaller unit to larger unit: divide by the number of smaller units in one larger unit.
  • A conversion changes the way a length is written, not the length itself.

4. Put the ideas together

When you meet a measurement task, first identify what is being measured. Next, choose a unit that makes the measurement easy to understand. A desk length is easier to describe in centimetres or metres than in kilometres.
If you need to compare two lengths, first make sure they use the same unit. A length in centimetres and a length in metres cannot be compared by looking only at their numbers. Convert one measurement so both use the same unit, then compare the numbers.
The metric system is useful because its unit relationships are regular. Knowing those relationships lets you move between units without changing the actual length.
  • Choose a sensible unit for the object or distance.
  • Use the same unit when directly comparing measurements.
  • Use the metric unit relationships to convert.

Common metric units of length

UnitSymbolA useful scale
millimetremmVery small lengths
centimetrecmSmall objects
metremPeople, rooms, or furniture
kilometrekmLong distances

Worked example

Measure a ribbon in two units

A ribbon is 3 m long. How many centimetres long is it?
  1. Identify the conversion
    The ribbon is measured in metres, and the answer is needed in centimetres. One metre contains 100 centimetres, so the number of centimetres will be greater than the number of metres.
    1 m=100 cm1\text{ m}=100\text{ cm}
  2. Multiply by the number of centimetres per metre
    There are 100 centimetres in each metre. For 3 metres, multiply 3 by 100. This counts three groups of 100 centimetres.
    3×100=3003\times100=300
  3. Include the unit
    The result is a length in centimetres. The ribbon has the same length as before; it is now written using a smaller unit.
    3 m=300 cm3\text{ m}=300\text{ cm}
Answer: The ribbon is 300 cm long.
Check: The answer is greater than 3 because centimetres are smaller than metres. Since each metre contains 100 centimetres, 3 metres contain 300 centimetres.

Common mistakes and how to avoid them

Writing only a number, such as saying a desk is 12 long.
Correction: Include a unit so the length is clear, such as 12 cm.
Multiplying when converting from a smaller unit to a larger unit.
Correction: Divide when moving from centimetres to metres, because fewer metres describe the same length.
Comparing two measurements with different units by comparing their numbers.
Correction: Convert both measurements to the same unit before comparing their numbers.
Thinking a conversion changes the object's actual length.
Correction: A conversion changes only how the measurement is written. The length stays the same.

Lesson summary

  • Length measures the distance between two points.
  • A complete measurement includes a number and a unit.
  • Metric length units include millimetres, centimetres, metres, and kilometres.
  • The metric length units are connected by groups of ten.
  • Multiply to change from a larger metric length unit to a smaller one; divide to change from a smaller unit to a larger one.
  • Use the same unit when comparing lengths.

Check your understanding

Question 1

Which unit is usually the most sensible choice for describing the distance along a road between two towns?
  1. Millimetres
  2. Centimetres
  3. Metres
  4. Kilometres
Show answer and explanation
Kilometres
Kilometres are useful for long distances. Millimetres and centimetres are too small for this purpose.

Question 2

How many centimetres are in 5 metres?
  1. 5 cm
  2. 50 cm
  3. 500 cm
  4. 5000 cm
Show answer and explanation
500 cm
One metre contains 100 centimetres, so 5 metres contain 5 times 100, or 500, centimetres.

Question 3

A length is written first in millimetres and then in centimetres. What happens to the number?
  1. It gets larger because centimetres are smaller.
  2. It gets smaller because centimetres are larger.
  3. It stays the same because the length is unchanged.
  4. It becomes zero because the units are different.
Show answer and explanation
It gets smaller because centimetres are larger.
A centimetre is larger than a millimetre, so fewer centimetres describe the same length. The number gets smaller, even though the length does not change.

Key terms

Length
The distance from one point to another.
Unit
An agreed amount used to measure something.
Metric system
A measurement system whose units are connected by groups of ten.
Convert
To write the same measurement using a different unit.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 9 Mathematics (MTH1W), expectation E1.1. It is a study resource, not an official curriculum publication.

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