What Is the Metric System?

The metric system is a system of measurement based mainly on powers of 10.

It is used around the world for measuring quantities such as:

• length
• mass
• volume
• temperature
• area
• scientific measurements

One major advantage of the metric system is that conversions between related units can usually be performed by multiplying or dividing by powers of 10.

For example:

1 kilometre = 1,000 metres

1 metre = 100 centimetres

1 litre = 1,000 millilitres

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Base Units

For the conversions in this topic, three important units are:

metre (m) — length

gram (g) — mass

litre (L) — volume

Prefixes can be attached to units to indicate larger or smaller quantities.

For example:

kilometre

centimetre

milligram

millilitre

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Metric Prefixes

A prefix is added to the beginning of a unit to indicate a particular scale.

Important prefixes include:

For this topic, the most important are:

kilo- = 1,000

centi- = 1/100

milli- = 1/1,000

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Understanding Kilo-

The prefix kilo- means:

1,000

Therefore:

1 kilometre = 1,000 metres

1 kilogram = 1,000 grams

For example:

3 km = 3,000 m

because:

3 × 1,000 = 3,000

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Understanding Centi-

The prefix centi- means:

one hundredth

or:

1/100

Therefore:

1 metre = 100 centimetres

and:

1 cm = 0.01 m

For example:

2.5 m = 250 cm

because:

2.5 × 100 = 250

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Understanding Milli-

The prefix milli- means:

one thousandth

or:

1/1,000

Therefore:

1 metre = 1,000 millimetres

1 gram = 1,000 milligrams

1 litre = 1,000 millilitres

For example:

4 L = 4,000 mL

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The Metric Conversion Pattern

Metric units are related by powers of 10.

A useful sequence is:

kilo → hecto → deca → base unit → deci → centi → milli

Each step toward the right represents a unit that is 10 times smaller.

Each step toward the left represents a unit that is 10 times larger.

The base unit might be:

metre

gram

or:

litre

depending on what is being measured.

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Converting to a Smaller Unit

When converting from a larger unit to a smaller unit, the numerical value becomes larger.

For example:

2 m = 200 cm

One metre contains 100 centimetres, so:

2 × 100 = 200

Another example:

5 kg = 5,000 g

because:

5 × 1,000 = 5,000

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Converting to a Larger Unit

When converting from a smaller unit to a larger unit, the numerical value becomes smaller.

For example:

500 cm = 5 m

because:

500 ÷ 100 = 5

Similarly:

3,000 g = 3 kg

because:

3,000 ÷ 1,000 = 3

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A Useful Reasonableness Rule

Ask:

Am I converting to a smaller or larger unit?

If you convert to a smaller unit, you need more of those units, so the numerical value should become larger.

For example:

2 m = 200 cm

If you convert to a larger unit, you need fewer of those units, so the numerical value should become smaller.

For example:

2,000 m = 2 km

This provides a quick way to check whether an answer makes sense.

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Converting Length

Common metric units of length include:

kilometre (km)

metre (m)

centimetre (cm)

millimetre (mm)

Important relationships:

1 km = 1,000 m

1 m = 100 cm

1 m = 1,000 mm

1 cm = 10 mm

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Kilometres to Metres

To convert kilometres to metres:

multiply by 1,000

Example:

4.2 km = ? m

Calculate:

4.2 × 1,000 = 4,200

Therefore:

4.2 km = 4,200 m

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Metres to Kilometres

To convert metres to kilometres:

divide by 1,000

Example:

7,500 m = ? km

Calculate:

7,500 ÷ 1,000 = 7.5

Therefore:

7,500 m = 7.5 km

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Metres to Centimetres

To convert metres to centimetres:

multiply by 100

Example:

3.6 m = ? cm

Calculate:

3.6 × 100 = 360

Therefore:

3.6 m = 360 cm

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Centimetres to Metres

To convert centimetres to metres:

divide by 100

Example:

275 cm = ? m

Calculate:

275 ÷ 100 = 2.75

Therefore:

275 cm = 2.75 m

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Centimetres and Millimetres

Remember:

1 cm = 10 mm

Therefore:

cm → mm: multiply by 10

mm → cm: divide by 10

Example:

8.5 cm = 85 mm

Example:

126 mm = 12.6 cm

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Metres to Millimetres

Since:

1 m = 1,000 mm

convert metres to millimetres by multiplying by 1,000.

Example:

1.75 m = ? mm

1.75 × 1,000 = 1,750

Therefore:

1.75 m = 1,750 mm

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Choosing Appropriate Length Units

Different units are useful for different scales.

A kilometre might be appropriate for:

• distance between locations
• road journeys
• running routes

A metre might be appropriate for:

• room dimensions
• height of a person
• length of furniture

A centimetre might be appropriate for:

• books
• pencils
• small objects

A millimetre might be appropriate for:

• thickness
• small machine parts
• very small measurements

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Converting Mass

Common metric units of mass include:

kilogram (kg)

gram (g)

milligram (mg)

Important relationships:

1 kg = 1,000 g

1 g = 1,000 mg

Therefore:

1 kg = 1,000,000 mg

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Kilograms to Grams

Convert kilograms to grams by multiplying by:

1,000

Example:

2.75 kg = ? g

Calculate:

2.75 × 1,000 = 2,750

Therefore:

2.75 kg = 2,750 g

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Grams to Kilograms

Convert grams to kilograms by dividing by:

1,000

Example:

850 g = ? kg

Calculate:

850 ÷ 1,000 = 0.85

Therefore:

850 g = 0.85 kg

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Grams to Milligrams

Convert grams to milligrams by multiplying by:

1,000

Example:

4.5 g = ? mg

Calculate:

4.5 × 1,000 = 4,500

Therefore:

4.5 g = 4,500 mg

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Milligrams to Grams

Convert milligrams to grams by dividing by:

1,000

Example:

750 mg = ? g

Calculate:

750 ÷ 1,000 = 0.75

Therefore:

750 mg = 0.75 g

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Kilograms to Milligrams

Sometimes a conversion requires moving across more than one unit.

Example:

2 kg = ? mg

First:

2 kg = 2,000 g

Then:

2,000 g = 2,000,000 mg

Therefore:

2 kg = 2,000,000 mg

You could also multiply directly by:

1,000,000

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Choosing Appropriate Mass Units

A kilogram might be appropriate for:

• a person's mass
• luggage
• bags of food
• larger objects

A gram might be appropriate for:

• ingredients
• small packages
• laboratory samples

A milligram might be appropriate for:

• very small laboratory quantities
• tiny masses used in scientific measurements

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Converting Volume

A common metric unit of volume is the:

litre (L)

For smaller volumes, we often use:

millilitre (mL)

The important relationship is:

1 L = 1,000 mL

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Litres to Millilitres

Convert litres to millilitres by multiplying by:

1,000

Example:

2.4 L = ? mL

Calculate:

2.4 × 1,000 = 2,400

Therefore:

2.4 L = 2,400 mL

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Millilitres to Litres

Convert millilitres to litres by dividing by:

1,000

Example:

650 mL = ? L

Calculate:

650 ÷ 1,000 = 0.65

Therefore:

650 mL = 0.65 L

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Choosing Appropriate Volume Units

A litre is useful for larger liquid volumes.

Examples:

• bottle of water
• fuel
• milk
• aquarium capacity

A millilitre is useful for smaller volumes.

Examples:

• drinks
• laboratory liquids
• cooking ingredients
• small containers

The most useful unit depends on the scale of the measurement.

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Millilitres and Cubic Centimetres

There is an important relationship between volume units:

1 mL = 1 cm³

Therefore:

250 mL = 250 cm³

and:

500 cm³ = 500 mL

This relationship is especially useful in science.

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Litres and Cubic Centimetres

Since:

1 L = 1,000 mL

and:

1 mL = 1 cm³

then:

1 L = 1,000 cm³

For example:

2.5 L = 2,500 cm³

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Using Place Value

Because metric conversions are based on powers of 10, place value is very important.

Consider:

3.47 m

Converting to centimetres:

3.47 × 100 = 347 cm

Converting to millimetres:

3.47 × 1,000 = 3,470 mm

The measurement itself has not changed.

Only the unit used to describe it has changed.

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The Quantity Stays the Same

This is one of the most important ideas in unit conversion.

Consider:

1.5 m

150 cm

1,500 mm

These all represent exactly the same length.

Changing units does not change the physical quantity.

It changes the number used to represent that quantity.

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Using Conversion Factors

A more advanced and reliable method is to use conversion factors.

Suppose:

2.5 km = ? m

We know:

1 km = 1,000 m

Write:

2.5 km × 1,000 m / 1 km

The kilometre units cancel:

2.5 × 1,000 m

= 2,500 m

This method is particularly useful for more complicated scientific conversions.

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Example with Mass

Convert:

3.2 kg to g

Use:

3.2 kg × 1,000 g / 1 kg

The kg units cancel.

Result:

3,200 g

This method is often called dimensional analysis or the factor-label method.

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Real-World Example: Running Distance

A runner completes:

7.5 km

How many metres did the runner travel?

Use:

1 km = 1,000 m

Calculate:

7.5 × 1,000 = 7,500

Therefore:

7.5 km = 7,500 m

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Real-World Example: Cooking

A recipe requires:

1.5 L

of liquid.

You have a measuring container marked in millilitres.

Convert:

1.5 × 1,000 = 1,500

Therefore:

1.5 L = 1,500 mL

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Real-World Example: Food Packaging

A bag contains:

2.25 kg

of rice.

How many grams is this?

2.25 × 1,000 = 2,250

Therefore:

2.25 kg = 2,250 g

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Real-World Example: Construction

A board is:

2.4 m

long.

A builder wants the measurement in millimetres.

Calculate:

2.4 × 1,000 = 2,400

Therefore:

2.4 m = 2,400 mm

Millimetres are often useful when measurements need to be recorded with smaller units.

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Real-World Example: Science Laboratory

A student needs:

0.075 L

of water.

Convert to millilitres:

0.075 × 1,000 = 75

Therefore:

0.075 L = 75 mL

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Comparing Measurements

Suppose:

Object A = 1.8 m

Object B = 175 cm

Which is longer?

Convert to the same unit.

Object A:

1.8 m = 180 cm

Now compare:

180 cm > 175 cm

Therefore, Object A is:

5 cm longer

You should generally convert measurements to the same unit before comparing them.

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Adding Measurements with Different Units

Suppose a piece of rope is:

1.4 m

and another piece is:

85 cm

Find the total length.

Convert:

1.4 m = 140 cm

Then:

140 cm + 85 cm = 225 cm

Convert if desired:

225 cm = 2.25 m

Therefore:

Total length = 2.25 m

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Subtracting Measurements

A container holds:

2 L

It currently contains:

650 mL

How much additional liquid could it hold?

Convert:

2 L = 2,000 mL

Subtract:

2,000 − 650 = 1,350 mL

Therefore:

1,350 mL

or:

1.35 L

of additional volume is available.

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Multi-Step Problem: Shopping

A store sells nuts in:

250 g packages

You need:

2 kg

First convert:

2 kg = 2,000 g

Number of packages:

2,000 ÷ 250 = 8

Therefore:

8 packages

are required.

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Multi-Step Problem: Water

A container holds:

5 L

Each cup holds:

250 mL

Convert:

5 L = 5,000 mL

Number of cups:

5,000 ÷ 250 = 20

Therefore:

20 cups

could be filled.

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Multi-Step Problem: Walking Route

A walking route has three sections:

Section A = 1.2 km

Section B = 850 m

Section C = 650 m

Convert A:

1.2 km = 1,200 m

Total:

1,200 + 850 + 650

= 2,700 m

Convert to kilometres:

2,700 ÷ 1,000 = 2.7 km

Therefore:

Total distance = 2.7 km

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Multi-Step Problem: Recipe

A recipe needs:

750 mL

of milk for one batch.

You make:

4 batches

Total milk:

750 × 4 = 3,000 mL

Convert:

3,000 mL = 3 L

Therefore:

3 L of milk

is required.

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Working with Decimal Measurements

Metric conversions frequently involve decimals.

Example:

0.35 kg = ? g

Calculate:

0.35 × 1,000 = 350

Therefore:

0.35 kg = 350 g

Example:

45 mm = ? m

Calculate:

45 ÷ 1,000 = 0.045

Therefore:

45 mm = 0.045 m

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Working with Very Small Values

Suppose:

0.006 m = ? mm

Since:

1 m = 1,000 mm

calculate:

0.006 × 1,000 = 6

Therefore:

0.006 m = 6 mm

Notice that the number becomes larger because millimetres are smaller units than metres.

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Working with Large Values

Convert:

12,500 m to km

Calculate:

12,500 ÷ 1,000 = 12.5

Therefore:

12,500 m = 12.5 km

Again, the numerical value becomes smaller because kilometres are larger units.

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Metric Units and Scientific Notation

Metric prefixes are closely connected to powers of ten.

kilo = 10³

centi = 10⁻²

milli = 10⁻³

Therefore:

1 km = 10³ m

1 cm = 10⁻² m

1 mm = 10⁻³ m

This connection becomes particularly important in science.

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Be Careful with Area

Length conversions cannot always be used directly for area.

We know:

1 m = 100 cm

But:

1 m² ≠ 100 cm²

Instead:

1 m² = 100 cm × 100 cm

Therefore:

1 m² = 10,000 cm²

Why?

Because area has two dimensions.

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Be Careful with Volume

Similarly:

1 m = 100 cm

but:

1 m³ = 100 cm × 100 cm × 100 cm

Therefore:

1 m³ = 1,000,000 cm³

Volume has three dimensions, so the conversion factor is cubed.

This is different from converting litres and millilitres:

1 L = 1,000 mL

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Worked Example 1: Length

Convert:

6.4 km to m

6.4 × 1,000 = 6,400

Answer:

6,400 m

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Worked Example 2: Length

Convert:

425 cm to m

425 ÷ 100 = 4.25

Answer:

4.25 m

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Worked Example 3: Length

Convert:

0.82 m to mm

0.82 × 1,000 = 820

Answer:

820 mm

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Worked Example 4: Mass

Convert:

3.75 kg to g

3.75 × 1,000 = 3,750

Answer:

3,750 g

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Worked Example 5: Mass

Convert:

625 mg to g

625 ÷ 1,000 = 0.625

Answer:

0.625 g

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Worked Example 6: Volume

Convert:

4.8 L to mL

4.8 × 1,000 = 4,800

Answer:

4,800 mL

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Worked Example 7: Volume

Convert:

325 mL to L

325 ÷ 1,000 = 0.325

Answer:

0.325 L

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Worked Example 8: Comparing Lengths

Which is longer?

2.4 m

or:

235 cm

Convert:

2.4 m = 240 cm

Compare:

240 cm > 235 cm

Therefore, the first measurement is:

5 cm longer

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Worked Example 9: Mass in Packages

A recipe requires:

1.8 kg

of flour.

Flour is sold in:

300 g packages

Convert:

1.8 kg = 1,800 g

Calculate:

1,800 ÷ 300 = 6

Therefore:

6 packages

are required.

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Worked Example 10: Volume

A tank contains:

3.5 L

of water.

Another:

850 mL

is added.

Convert:

3.5 L = 3,500 mL

Add:

3,500 + 850 = 4,350 mL

Convert:

4,350 mL = 4.35 L

Answer:

4.35 L

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Estimating Conversions

Estimation helps check whether an answer is reasonable.

Suppose:

4.8 km

is converted to metres.

Since:

5 km ≈ 5,000 m

we expect:

4.8 km ≈ 4,800 m

If a calculator gives:

0.0048 m

we know something has gone wrong.

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Checking with Unit Size

A useful question is:

Which unit is smaller?

Suppose:

3 kg → g

Grams are smaller than kilograms.

Therefore, the number should become larger:

3 kg = 3,000 g

Suppose:

3,000 mm → m

Metres are larger than millimetres.

Therefore, the number should become smaller:

3,000 mm = 3 m

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A Reliable Conversion Strategy

Step 1: Identify the starting unit.

Example:

2.4 kg

Starting unit = kilograms.

Step 2: Identify the required unit.

Required unit = grams.

Step 3: Write the relationship.

1 kg = 1,000 g

Step 4: Decide whether the number should become larger or smaller.

Grams are smaller units, so the number should become larger.

Step 5: Multiply or divide.

2.4 × 1,000 = 2,400

Step 6: Write the correct unit.

2,400 g

Step 7: Check whether the answer is reasonable.

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Common Mistakes

Mistake 1: Multiplying when you should divide

Remember:

Larger unit → smaller unit:

number becomes larger

Smaller unit → larger unit:

number becomes smaller

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Mistake 2: Forgetting the unit

Writing:

2.5 × 1,000 = 2,500

is incomplete.

Write:

2.5 kg = 2,500 g

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Mistake 3: Assuming every conversion uses 1,000

For example:

1 m = 100 cm

but:

1 m = 1,000 mm

and:

1 cm = 10 mm

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Mistake 4: Confusing mass and volume

Grams measure mass.

Litres measure volume.

They are different physical quantities.

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Mistake 5: Comparing measurements before converting units

Convert quantities to the same unit first.

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Mistake 6: Moving the decimal point without understanding why

It is better to understand that:

×100

or:

÷1,000

changes the place value.

This prevents errors when conversions become more complicated.

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Mistake 7: Treating area and volume conversions like length conversions

Remember:

1 m = 100 cm

but:

1 m² = 10,000 cm²

and:

1 m³ = 1,000,000 cm³

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Metric Units in Everyday Life

Metric conversions appear frequently in everyday situations.

Examples include:

Travel

kilometres and metres

Construction

metres, centimetres, and millimetres

Cooking

kilograms, grams, litres, and millilitres

Shopping

kilograms and grams

Science

metres, grams, millilitres, milligrams, and many smaller or larger units

Sports

kilometres, metres, and millimetres

Understanding metric conversions allows information expressed in different units to be compared and used correctly.

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Did You Know?

The metric system is based on powers of 10, which makes it closely connected to decimal place value.

The prefix itself tells us the scale.

For example:

kilo- = 1,000

centi- = 1/100

milli- = 1/1,000

Once these relationships are understood, many conversions can be solved without memorizing separate rules for every measurement.

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Key Terms

• Metric system: Measurement system based mainly on powers of 10.
• Prefix: Part added before a unit that indicates its scale.
• kilo-: Prefix meaning 1,000.
• centi-: Prefix meaning one hundredth.
• milli-: Prefix meaning one thousandth.
• metre (m): Metric unit of length.
• kilometre (km): 1,000 metres.
• centimetre (cm): One hundredth of a metre.
• millimetre (mm): One thousandth of a metre.
• kilogram (kg): 1,000 grams.
• gram (g): Metric unit of mass commonly used for smaller objects.
• milligram (mg): One thousandth of a gram.
• litre (L): Metric unit commonly used for liquid volume.
• millilitre (mL): One thousandth of a litre.
• Conversion factor: Numerical relationship used to convert between units.
• Dimensional analysis: Conversion method that uses unit relationships so unwanted units cancel.
• Volume: Amount of three-dimensional space occupied.
• Mass: Measure of the amount of matter in an object.
• Length: Measurement of distance.

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Key Metric Relationships

Length

1 km = 1,000 m

1 m = 100 cm

1 m = 1,000 mm

1 cm = 10 mm

Mass

1 kg = 1,000 g

1 g = 1,000 mg

1 kg = 1,000,000 mg

Volume

1 L = 1,000 mL

1 mL = 1 cm³

1 L = 1,000 cm³

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Key Takeaways

• The metric system is based mainly on powers of 10.
• Prefixes indicate the size of a unit.
• kilo- means 1,000.
• centi- means one hundredth.
• milli- means one thousandth.
• Kilometres, metres, centimetres, and millimetres measure length.
• Kilograms, grams, and milligrams measure mass.
• Litres and millilitres measure volume.
• Converting to a smaller unit makes the numerical value larger.
• Converting to a larger unit makes the numerical value smaller.
• The physical quantity does not change when its unit changes.
• Measurements should normally be converted to the same unit before they are added, subtracted, or compared.
• Decimal place value is central to metric conversions.
• Conversion factors provide a reliable method for more complicated problems.
• 1 mL = 1 cm³ is an important connection between liquid volume and cubic units.
• Area and cubic-volume conversions require special care because their conversion factors are squared or cubed.
• Estimation and unit size can be used to check whether a conversion is reasonable.
• Metric conversions are used constantly in travel, cooking, shopping, construction, sports, and science.